idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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34,901 | Ridge regression: regularizing towards a value | I have an answer for "Why regularize towards a value? Does this change the interpretation of $\beta$?"
Transfer learning is a type of Machine Learning where knowledge from the source domain when performing a task is transfered to the target domain when performing the same task i.e. the task remains the same but dataset... | Ridge regression: regularizing towards a value | I have an answer for "Why regularize towards a value? Does this change the interpretation of $\beta$?"
Transfer learning is a type of Machine Learning where knowledge from the source domain when perfo | Ridge regression: regularizing towards a value
I have an answer for "Why regularize towards a value? Does this change the interpretation of $\beta$?"
Transfer learning is a type of Machine Learning where knowledge from the source domain when performing a task is transfered to the target domain when performing the same ... | Ridge regression: regularizing towards a value
I have an answer for "Why regularize towards a value? Does this change the interpretation of $\beta$?"
Transfer learning is a type of Machine Learning where knowledge from the source domain when perfo |
34,902 | Ridge regression: regularizing towards a value | It is possible to understand it from a Bayesian point of view.
Ridge regularization for linear regression is a Bayesian method in disguise. See : https://en.wikipedia.org/wiki/Lasso_(statistics)#Bayesian_interpretation (it is easier to understand explained on the wikipedia"s Lasso page, but it's the same idea with Rid... | Ridge regression: regularizing towards a value | It is possible to understand it from a Bayesian point of view.
Ridge regularization for linear regression is a Bayesian method in disguise. See : https://en.wikipedia.org/wiki/Lasso_(statistics)#Baye | Ridge regression: regularizing towards a value
It is possible to understand it from a Bayesian point of view.
Ridge regularization for linear regression is a Bayesian method in disguise. See : https://en.wikipedia.org/wiki/Lasso_(statistics)#Bayesian_interpretation (it is easier to understand explained on the wikipedi... | Ridge regression: regularizing towards a value
It is possible to understand it from a Bayesian point of view.
Ridge regularization for linear regression is a Bayesian method in disguise. See : https://en.wikipedia.org/wiki/Lasso_(statistics)#Baye |
34,903 | Can cosine kernel be understood as a case of Beta distribution? | The cosine kernel is not a beta distribution.
Note that the following things are all true of the standard cosine density:
$f(0)=1$
$f(0.5)=0.5$
The right half of this density is rotationally symmetric about $x=\frac12$: (i.e. considering the other two properties it implies $1-f(x)=f(1-x)$ )
But no beta density on (-1... | Can cosine kernel be understood as a case of Beta distribution? | The cosine kernel is not a beta distribution.
Note that the following things are all true of the standard cosine density:
$f(0)=1$
$f(0.5)=0.5$
The right half of this density is rotationally symmetri | Can cosine kernel be understood as a case of Beta distribution?
The cosine kernel is not a beta distribution.
Note that the following things are all true of the standard cosine density:
$f(0)=1$
$f(0.5)=0.5$
The right half of this density is rotationally symmetric about $x=\frac12$: (i.e. considering the other two pro... | Can cosine kernel be understood as a case of Beta distribution?
The cosine kernel is not a beta distribution.
Note that the following things are all true of the standard cosine density:
$f(0)=1$
$f(0.5)=0.5$
The right half of this density is rotationally symmetri |
34,904 | Why are mean and median not equal for asymmetric distributions? | There's a related question here:
Does mean = median imply that a unimodal distribution is symmetric?
which you should also read, but your title question of why asymmetry can make mean and median unequal should be addressed in some detail (which is why I don't think of this question as a duplicate of that one), and I am... | Why are mean and median not equal for asymmetric distributions? | There's a related question here:
Does mean = median imply that a unimodal distribution is symmetric?
which you should also read, but your title question of why asymmetry can make mean and median unequ | Why are mean and median not equal for asymmetric distributions?
There's a related question here:
Does mean = median imply that a unimodal distribution is symmetric?
which you should also read, but your title question of why asymmetry can make mean and median unequal should be addressed in some detail (which is why I do... | Why are mean and median not equal for asymmetric distributions?
There's a related question here:
Does mean = median imply that a unimodal distribution is symmetric?
which you should also read, but your title question of why asymmetry can make mean and median unequ |
34,905 | What's the difference between a randomized block design and two factor design? | In both cases, you have two categorical variables and numerical response variable but in a randomised block design the second variable is a nuisance variable, while in the two factor factorial design the second variable is also of interest and you would like to understand the interaction. I think this is the main diffe... | What's the difference between a randomized block design and two factor design? | In both cases, you have two categorical variables and numerical response variable but in a randomised block design the second variable is a nuisance variable, while in the two factor factorial design | What's the difference between a randomized block design and two factor design?
In both cases, you have two categorical variables and numerical response variable but in a randomised block design the second variable is a nuisance variable, while in the two factor factorial design the second variable is also of interest a... | What's the difference between a randomized block design and two factor design?
In both cases, you have two categorical variables and numerical response variable but in a randomised block design the second variable is a nuisance variable, while in the two factor factorial design |
34,906 | What's the difference between a randomized block design and two factor design? | I agree with MachineEpsilon's answer but will clarify two issues. First, there is a design difference between the models even if the two-way ANOVA is estimated in the same way. With the randomized-block design, randomization to conditions on the factor occurs within levels of the blocking variable. That is, the sample ... | What's the difference between a randomized block design and two factor design? | I agree with MachineEpsilon's answer but will clarify two issues. First, there is a design difference between the models even if the two-way ANOVA is estimated in the same way. With the randomized-blo | What's the difference between a randomized block design and two factor design?
I agree with MachineEpsilon's answer but will clarify two issues. First, there is a design difference between the models even if the two-way ANOVA is estimated in the same way. With the randomized-block design, randomization to conditions on... | What's the difference between a randomized block design and two factor design?
I agree with MachineEpsilon's answer but will clarify two issues. First, there is a design difference between the models even if the two-way ANOVA is estimated in the same way. With the randomized-blo |
34,907 | Econometrics text claims that convergence in distribution implies convergence in moments | A sufficient additional condition is that of uniform integrability, i.e., that
$$\lim_{M\to\infty} \sup_n \int_{|X_n|>M}|X_n|dP= \lim_{M\to\infty} \sup_n E [|X_n|1_{|X_n|>M}]=0.$$
Then, one gets that $X$ is integrable and $\lim_{n\to\infty}E[X_n]=\mathbb{E}[X]$.
Heuristically, this condition rules out that there are s... | Econometrics text claims that convergence in distribution implies convergence in moments | A sufficient additional condition is that of uniform integrability, i.e., that
$$\lim_{M\to\infty} \sup_n \int_{|X_n|>M}|X_n|dP= \lim_{M\to\infty} \sup_n E [|X_n|1_{|X_n|>M}]=0.$$
Then, one gets that | Econometrics text claims that convergence in distribution implies convergence in moments
A sufficient additional condition is that of uniform integrability, i.e., that
$$\lim_{M\to\infty} \sup_n \int_{|X_n|>M}|X_n|dP= \lim_{M\to\infty} \sup_n E [|X_n|1_{|X_n|>M}]=0.$$
Then, one gets that $X$ is integrable and $\lim_{n... | Econometrics text claims that convergence in distribution implies convergence in moments
A sufficient additional condition is that of uniform integrability, i.e., that
$$\lim_{M\to\infty} \sup_n \int_{|X_n|>M}|X_n|dP= \lim_{M\to\infty} \sup_n E [|X_n|1_{|X_n|>M}]=0.$$
Then, one gets that |
34,908 | Econometrics text claims that convergence in distribution implies convergence in moments | Indeed, it is a known erratum of this book (see its website in the errata .pdf), that the specific lemma does not state the moment-boundedness condition $$\exists \; \delta : E(|z_n|^{s+\delta}) < M < \infty\;\; \forall n$$ | Econometrics text claims that convergence in distribution implies convergence in moments | Indeed, it is a known erratum of this book (see its website in the errata .pdf), that the specific lemma does not state the moment-boundedness condition $$\exists \; \delta : E(|z_n|^{s+\delta}) < M | Econometrics text claims that convergence in distribution implies convergence in moments
Indeed, it is a known erratum of this book (see its website in the errata .pdf), that the specific lemma does not state the moment-boundedness condition $$\exists \; \delta : E(|z_n|^{s+\delta}) < M < \infty\;\; \forall n$$ | Econometrics text claims that convergence in distribution implies convergence in moments
Indeed, it is a known erratum of this book (see its website in the errata .pdf), that the specific lemma does not state the moment-boundedness condition $$\exists \; \delta : E(|z_n|^{s+\delta}) < M |
34,909 | Econometrics text claims that convergence in distribution implies convergence in moments | I think that there is a bit of confusion in the question.
There are two possible interpretation of the question.
(1) the probability space is $\mathbb P$= Lebesgue measure on $\Omega=[0,1]$, and the random variable is $Z_n(\omega)=n$ when $0\le \omega\le 1/n$ and 0 otherwise. In this case the law of $Z_n$ is ${\mathbb ... | Econometrics text claims that convergence in distribution implies convergence in moments | I think that there is a bit of confusion in the question.
There are two possible interpretation of the question.
(1) the probability space is $\mathbb P$= Lebesgue measure on $\Omega=[0,1]$, and the r | Econometrics text claims that convergence in distribution implies convergence in moments
I think that there is a bit of confusion in the question.
There are two possible interpretation of the question.
(1) the probability space is $\mathbb P$= Lebesgue measure on $\Omega=[0,1]$, and the random variable is $Z_n(\omega)=... | Econometrics text claims that convergence in distribution implies convergence in moments
I think that there is a bit of confusion in the question.
There are two possible interpretation of the question.
(1) the probability space is $\mathbb P$= Lebesgue measure on $\Omega=[0,1]$, and the r |
34,910 | Difference-in-difference vs fixed effect models | The difference in differences (DiD) model is actually a type of fixed effects because the differencing gets rid of the individual fixed effects.$^1$ Regarding the pros and cons, it really depends what you want to do. DiD is mainly for causal inference with observational data whereas the fixed effects model primary task... | Difference-in-difference vs fixed effect models | The difference in differences (DiD) model is actually a type of fixed effects because the differencing gets rid of the individual fixed effects.$^1$ Regarding the pros and cons, it really depends what | Difference-in-difference vs fixed effect models
The difference in differences (DiD) model is actually a type of fixed effects because the differencing gets rid of the individual fixed effects.$^1$ Regarding the pros and cons, it really depends what you want to do. DiD is mainly for causal inference with observational d... | Difference-in-difference vs fixed effect models
The difference in differences (DiD) model is actually a type of fixed effects because the differencing gets rid of the individual fixed effects.$^1$ Regarding the pros and cons, it really depends what |
34,911 | Does Basu's Theorem require minimal sufficiency? | To realise that sufficiency is not enough, consider that, when $T(X)$ is a sufficient statistic, $(T(X),S(X))$ is also a sufficient statistic. Including the case when $S(X)$ is an ancillary statistic. Meaning that $(T(X),S(X))$ and $S(X)$ cannot be independent. | Does Basu's Theorem require minimal sufficiency? | To realise that sufficiency is not enough, consider that, when $T(X)$ is a sufficient statistic, $(T(X),S(X))$ is also a sufficient statistic. Including the case when $S(X)$ is an ancillary statistic. | Does Basu's Theorem require minimal sufficiency?
To realise that sufficiency is not enough, consider that, when $T(X)$ is a sufficient statistic, $(T(X),S(X))$ is also a sufficient statistic. Including the case when $S(X)$ is an ancillary statistic. Meaning that $(T(X),S(X))$ and $S(X)$ cannot be independent. | Does Basu's Theorem require minimal sufficiency?
To realise that sufficiency is not enough, consider that, when $T(X)$ is a sufficient statistic, $(T(X),S(X))$ is also a sufficient statistic. Including the case when $S(X)$ is an ancillary statistic. |
34,912 | Testing Slope significance for multiple factor levels in a linear model | It depends on what you mean by statistically different. Statistically different from each other?
Looking at your plot, you've got four that look pretty clearly the same and then two that are much different. So, if you run:
library(lme4)
summary(lmer(diam~day*race + (1+day|race), data=long))
You get, in part:
Fixed eff... | Testing Slope significance for multiple factor levels in a linear model | It depends on what you mean by statistically different. Statistically different from each other?
Looking at your plot, you've got four that look pretty clearly the same and then two that are much diff | Testing Slope significance for multiple factor levels in a linear model
It depends on what you mean by statistically different. Statistically different from each other?
Looking at your plot, you've got four that look pretty clearly the same and then two that are much different. So, if you run:
library(lme4)
summary(lme... | Testing Slope significance for multiple factor levels in a linear model
It depends on what you mean by statistically different. Statistically different from each other?
Looking at your plot, you've got four that look pretty clearly the same and then two that are much diff |
34,913 | Testing Slope significance for multiple factor levels in a linear model | Here's what I would do given the comments under your question:
## GENERATE SOME EXAMPLE DATA
set.seed(127)
d <- data.frame(
plate = rep(c(1:10), 42, each = 2),
strain = rep(c(letters[1:6]), 7, each = 20),
day = rep(c(1:7), each = 120),
diameter = rnorm(840, 6, 3)
)
require(ggplot2)
ggplot(d, aes(x = day, y ... | Testing Slope significance for multiple factor levels in a linear model | Here's what I would do given the comments under your question:
## GENERATE SOME EXAMPLE DATA
set.seed(127)
d <- data.frame(
plate = rep(c(1:10), 42, each = 2),
strain = rep(c(letters[1:6]), 7, eac | Testing Slope significance for multiple factor levels in a linear model
Here's what I would do given the comments under your question:
## GENERATE SOME EXAMPLE DATA
set.seed(127)
d <- data.frame(
plate = rep(c(1:10), 42, each = 2),
strain = rep(c(letters[1:6]), 7, each = 20),
day = rep(c(1:7), each = 120),
diam... | Testing Slope significance for multiple factor levels in a linear model
Here's what I would do given the comments under your question:
## GENERATE SOME EXAMPLE DATA
set.seed(127)
d <- data.frame(
plate = rep(c(1:10), 42, each = 2),
strain = rep(c(letters[1:6]), 7, eac |
34,914 | Testing Slope significance for multiple factor levels in a linear model | With multiple experimental replicates for each strain, you could use ANOVA to test if the slopes (growth rate) are statistically different. ANOVA will tell you if there are significant differences between the sample groups, not which strains are different. In order to do that you may want to use a multiple range test f... | Testing Slope significance for multiple factor levels in a linear model | With multiple experimental replicates for each strain, you could use ANOVA to test if the slopes (growth rate) are statistically different. ANOVA will tell you if there are significant differences bet | Testing Slope significance for multiple factor levels in a linear model
With multiple experimental replicates for each strain, you could use ANOVA to test if the slopes (growth rate) are statistically different. ANOVA will tell you if there are significant differences between the sample groups, not which strains are di... | Testing Slope significance for multiple factor levels in a linear model
With multiple experimental replicates for each strain, you could use ANOVA to test if the slopes (growth rate) are statistically different. ANOVA will tell you if there are significant differences bet |
34,915 | Testing Slope significance for multiple factor levels in a linear model | when you want to test whether the slope is different as a function of another variable, you include an interaction in the model. when the interacting variable is continuous, the slope changes linearly, but you can generalize this is a few ways. when the interacting variable is categorical, it allows different slopes in... | Testing Slope significance for multiple factor levels in a linear model | when you want to test whether the slope is different as a function of another variable, you include an interaction in the model. when the interacting variable is continuous, the slope changes linearly | Testing Slope significance for multiple factor levels in a linear model
when you want to test whether the slope is different as a function of another variable, you include an interaction in the model. when the interacting variable is continuous, the slope changes linearly, but you can generalize this is a few ways. whe... | Testing Slope significance for multiple factor levels in a linear model
when you want to test whether the slope is different as a function of another variable, you include an interaction in the model. when the interacting variable is continuous, the slope changes linearly |
34,916 | When the data set size is not a multiple of the mini-batch size, should the last mini-batch be smaller, or contain samples from other batches? | Same number, otherwise you're putting more weight on the samples in the final minibatch (unless you scale down the learning weight to match the smaller size).
Adding random samples from the training set should be fine too (as long as your sampling pool includes the runt minibatch), since each sample has an equal chan... | When the data set size is not a multiple of the mini-batch size, should the last mini-batch be small | Same number, otherwise you're putting more weight on the samples in the final minibatch (unless you scale down the learning weight to match the smaller size).
Adding random samples from the training | When the data set size is not a multiple of the mini-batch size, should the last mini-batch be smaller, or contain samples from other batches?
Same number, otherwise you're putting more weight on the samples in the final minibatch (unless you scale down the learning weight to match the smaller size).
Adding random sa... | When the data set size is not a multiple of the mini-batch size, should the last mini-batch be small
Same number, otherwise you're putting more weight on the samples in the final minibatch (unless you scale down the learning weight to match the smaller size).
Adding random samples from the training |
34,917 | Dirichlet conjugate update derivation | There is nothing wrong with this derivation
\begin{align}
p({\alpha}|{\theta},{\nu},\eta) &\propto p({\alpha},{\theta}|{\nu},\eta)\\
&= f({\theta}|{\alpha})p({\alpha}|{\nu},\eta)\\
&\propto \left[\frac{1}{B({\alpha})}\exp\left(\sum_{i=1}^{K}\alpha_{i}\ln(\theta_i)-\ln(\theta_i)\right)\right]\times\nonumber\\
&\phan... | Dirichlet conjugate update derivation | There is nothing wrong with this derivation
\begin{align}
p({\alpha}|{\theta},{\nu},\eta) &\propto p({\alpha},{\theta}|{\nu},\eta)\\
&= f({\theta}|{\alpha})p({\alpha}|{\nu},\eta)\\
&\propto \left[\ | Dirichlet conjugate update derivation
There is nothing wrong with this derivation
\begin{align}
p({\alpha}|{\theta},{\nu},\eta) &\propto p({\alpha},{\theta}|{\nu},\eta)\\
&= f({\theta}|{\alpha})p({\alpha}|{\nu},\eta)\\
&\propto \left[\frac{1}{B({\alpha})}\exp\left(\sum_{i=1}^{K}\alpha_{i}\ln(\theta_i)-\ln(\theta_i)\... | Dirichlet conjugate update derivation
There is nothing wrong with this derivation
\begin{align}
p({\alpha}|{\theta},{\nu},\eta) &\propto p({\alpha},{\theta}|{\nu},\eta)\\
&= f({\theta}|{\alpha})p({\alpha}|{\nu},\eta)\\
&\propto \left[\ |
34,918 | Dirichlet conjugate update derivation | First of all, exponential family updates are confusing in anything but the natural parametrization where the update rule is just addition. Stick to that parametrization.
I would derive the conjugate prior in this way. The basic idea is the natural parameter values of your conjugate prior distribution $F'$ are $\eta'$... | Dirichlet conjugate update derivation | First of all, exponential family updates are confusing in anything but the natural parametrization where the update rule is just addition. Stick to that parametrization.
I would derive the conjugate | Dirichlet conjugate update derivation
First of all, exponential family updates are confusing in anything but the natural parametrization where the update rule is just addition. Stick to that parametrization.
I would derive the conjugate prior in this way. The basic idea is the natural parameter values of your conjuga... | Dirichlet conjugate update derivation
First of all, exponential family updates are confusing in anything but the natural parametrization where the update rule is just addition. Stick to that parametrization.
I would derive the conjugate |
34,919 | Dirichlet conjugate update derivation | I'm not sure if it makes any intuitive sense, but $\eta$ can be interpreted in a physical context as how far the Dirichlet distribution is from equilibrium, in a micro-canonical sense. See http://arxiv.org/pdf/cond-mat/0603120v1.pdf. This probably isn't the balls-and-urns sort of interpretation that most would find sat... | Dirichlet conjugate update derivation | I'm not sure if it makes any intuitive sense, but $\eta$ can be interpreted in a physical context as how far the Dirichlet distribution is from equilibrium, in a micro-canonical sense. See http://arxi | Dirichlet conjugate update derivation
I'm not sure if it makes any intuitive sense, but $\eta$ can be interpreted in a physical context as how far the Dirichlet distribution is from equilibrium, in a micro-canonical sense. See http://arxiv.org/pdf/cond-mat/0603120v1.pdf. This probably isn't the balls-and-urns sort of i... | Dirichlet conjugate update derivation
I'm not sure if it makes any intuitive sense, but $\eta$ can be interpreted in a physical context as how far the Dirichlet distribution is from equilibrium, in a micro-canonical sense. See http://arxi |
34,920 | Plotting to check Homoskedasticity assumption for repeated-measures ANOVA in R | I'm assuming that a model which was fitted using the Error() function within aov() won't work when using in plot() because you will get more than one error stratum from which you can choose. Now according to this information here, one should use the proj() function which will give you the residuals for each error strat... | Plotting to check Homoskedasticity assumption for repeated-measures ANOVA in R | I'm assuming that a model which was fitted using the Error() function within aov() won't work when using in plot() because you will get more than one error stratum from which you can choose. Now accor | Plotting to check Homoskedasticity assumption for repeated-measures ANOVA in R
I'm assuming that a model which was fitted using the Error() function within aov() won't work when using in plot() because you will get more than one error stratum from which you can choose. Now according to this information here, one should... | Plotting to check Homoskedasticity assumption for repeated-measures ANOVA in R
I'm assuming that a model which was fitted using the Error() function within aov() won't work when using in plot() because you will get more than one error stratum from which you can choose. Now accor |
34,921 | Plotting to check Homoskedasticity assumption for repeated-measures ANOVA in R | Full disclaimer: I love using R for many different analyses, but I do not like doing ANOVAs in R.
Question 1: In the analytic context of ANOVAs, I'm more familiar with evaluating this assumption via tests of homogeneity of variances, vs. plotting homo/heteroscedasticity and visually evaluating it. Though there are mult... | Plotting to check Homoskedasticity assumption for repeated-measures ANOVA in R | Full disclaimer: I love using R for many different analyses, but I do not like doing ANOVAs in R.
Question 1: In the analytic context of ANOVAs, I'm more familiar with evaluating this assumption via t | Plotting to check Homoskedasticity assumption for repeated-measures ANOVA in R
Full disclaimer: I love using R for many different analyses, but I do not like doing ANOVAs in R.
Question 1: In the analytic context of ANOVAs, I'm more familiar with evaluating this assumption via tests of homogeneity of variances, vs. plo... | Plotting to check Homoskedasticity assumption for repeated-measures ANOVA in R
Full disclaimer: I love using R for many different analyses, but I do not like doing ANOVAs in R.
Question 1: In the analytic context of ANOVAs, I'm more familiar with evaluating this assumption via t |
34,922 | What is the name given to the set of numbers between quartiles | I don't think there is a universally accepted answer.
Some people are happy also to call the groups quartiles; and are thus explicitly or implicitly optimistic that any ambiguity will not bite, or at least can be clarified quickly in context, e.g. by inspection of some suitable table, graph and/or algebraic definition.... | What is the name given to the set of numbers between quartiles | I don't think there is a universally accepted answer.
Some people are happy also to call the groups quartiles; and are thus explicitly or implicitly optimistic that any ambiguity will not bite, or at | What is the name given to the set of numbers between quartiles
I don't think there is a universally accepted answer.
Some people are happy also to call the groups quartiles; and are thus explicitly or implicitly optimistic that any ambiguity will not bite, or at least can be clarified quickly in context, e.g. by inspec... | What is the name given to the set of numbers between quartiles
I don't think there is a universally accepted answer.
Some people are happy also to call the groups quartiles; and are thus explicitly or implicitly optimistic that any ambiguity will not bite, or at |
34,923 | Why doesn't PDF of Dirichlet Distribution seem to integrate to 1? | With two variables, you are defining a line segment in $\mathbb{R}^2$, as you pointed out. However, due to the simplex constraint, one of these two variables is redundant in terms of specifying the density, since there is a one-to-one relationship between $x_1$ and $x_2$. Therefore, the density is specified over $K-1$ ... | Why doesn't PDF of Dirichlet Distribution seem to integrate to 1? | With two variables, you are defining a line segment in $\mathbb{R}^2$, as you pointed out. However, due to the simplex constraint, one of these two variables is redundant in terms of specifying the de | Why doesn't PDF of Dirichlet Distribution seem to integrate to 1?
With two variables, you are defining a line segment in $\mathbb{R}^2$, as you pointed out. However, due to the simplex constraint, one of these two variables is redundant in terms of specifying the density, since there is a one-to-one relationship betwee... | Why doesn't PDF of Dirichlet Distribution seem to integrate to 1?
With two variables, you are defining a line segment in $\mathbb{R}^2$, as you pointed out. However, due to the simplex constraint, one of these two variables is redundant in terms of specifying the de |
34,924 | Optimal forecast window for timeseries | Using "window" to mean "how far to forecast into the future" is nonstandard usage. "Window" more frequently refers to a subsample of the past series, as in taking rolling means over a three-period window. You can see from the answers that this usage is confusing to experts. I recommend that you use the more common term... | Optimal forecast window for timeseries | Using "window" to mean "how far to forecast into the future" is nonstandard usage. "Window" more frequently refers to a subsample of the past series, as in taking rolling means over a three-period win | Optimal forecast window for timeseries
Using "window" to mean "how far to forecast into the future" is nonstandard usage. "Window" more frequently refers to a subsample of the past series, as in taking rolling means over a three-period window. You can see from the answers that this usage is confusing to experts. I reco... | Optimal forecast window for timeseries
Using "window" to mean "how far to forecast into the future" is nonstandard usage. "Window" more frequently refers to a subsample of the past series, as in taking rolling means over a three-period win |
34,925 | Optimal forecast window for timeseries | I don't think there is optimal forecast horizon. You can talk about maximum horizon, of course, which depends on the domain and the underlying process. Then again, there's no general rule of thumb.
For instance, in some applications in finance such as market value-at-risk of a portfolio, it's prescribed by regulators t... | Optimal forecast window for timeseries | I don't think there is optimal forecast horizon. You can talk about maximum horizon, of course, which depends on the domain and the underlying process. Then again, there's no general rule of thumb.
Fo | Optimal forecast window for timeseries
I don't think there is optimal forecast horizon. You can talk about maximum horizon, of course, which depends on the domain and the underlying process. Then again, there's no general rule of thumb.
For instance, in some applications in finance such as market value-at-risk of a por... | Optimal forecast window for timeseries
I don't think there is optimal forecast horizon. You can talk about maximum horizon, of course, which depends on the domain and the underlying process. Then again, there's no general rule of thumb.
Fo |
34,926 | Optimal forecast window for timeseries | As @IrishStat has nicely put, a daily data of one year would be sufficient if it accomodates the trends, activity and seasonality.
However, some trends(and/or) seasonality might not be captured even by the daily frequency. They might require data captured every minute for explaining the effects.
So, a rule of thumb wou... | Optimal forecast window for timeseries | As @IrishStat has nicely put, a daily data of one year would be sufficient if it accomodates the trends, activity and seasonality.
However, some trends(and/or) seasonality might not be captured even b | Optimal forecast window for timeseries
As @IrishStat has nicely put, a daily data of one year would be sufficient if it accomodates the trends, activity and seasonality.
However, some trends(and/or) seasonality might not be captured even by the daily frequency. They might require data captured every minute for explaini... | Optimal forecast window for timeseries
As @IrishStat has nicely put, a daily data of one year would be sufficient if it accomodates the trends, activity and seasonality.
However, some trends(and/or) seasonality might not be captured even b |
34,927 | Optimal forecast window for timeseries | One year of daily data would be insufficient to estimate/identify annual repetitive activity. It would be sufficient to characterize day-of-the-week structure but even then holiday effects would distort them. As @stephan-kolassa pointed out the preferred term is forecast horizon not "window" but I for one did understa... | Optimal forecast window for timeseries | One year of daily data would be insufficient to estimate/identify annual repetitive activity. It would be sufficient to characterize day-of-the-week structure but even then holiday effects would disto | Optimal forecast window for timeseries
One year of daily data would be insufficient to estimate/identify annual repetitive activity. It would be sufficient to characterize day-of-the-week structure but even then holiday effects would distort them. As @stephan-kolassa pointed out the preferred term is forecast horizon ... | Optimal forecast window for timeseries
One year of daily data would be insufficient to estimate/identify annual repetitive activity. It would be sufficient to characterize day-of-the-week structure but even then holiday effects would disto |
34,928 | Marginalization of GP regression hyperparameters with Laplace approximation | You might be interested in the gpml_extensions repository here:
https://github.com/rmgarnett/gpml_extensions/
There is code for computing the Hessian of the log likelihood wrt $\theta$ for both exact inference and the Laplace approximation for approximate GP inference. There is also convenience code for using these to... | Marginalization of GP regression hyperparameters with Laplace approximation | You might be interested in the gpml_extensions repository here:
https://github.com/rmgarnett/gpml_extensions/
There is code for computing the Hessian of the log likelihood wrt $\theta$ for both exact | Marginalization of GP regression hyperparameters with Laplace approximation
You might be interested in the gpml_extensions repository here:
https://github.com/rmgarnett/gpml_extensions/
There is code for computing the Hessian of the log likelihood wrt $\theta$ for both exact inference and the Laplace approximation for ... | Marginalization of GP regression hyperparameters with Laplace approximation
You might be interested in the gpml_extensions repository here:
https://github.com/rmgarnett/gpml_extensions/
There is code for computing the Hessian of the log likelihood wrt $\theta$ for both exact |
34,929 | Marginalization of GP regression hyperparameters with Laplace approximation | The best reference I could find online so far, and a very fitting one, is Ville Pietiläinen's MSc thesis:
Approximations for Integration Over the Hyperparameters in Gaussian Processes (2010).
Pietiläinen compares a point estimate approach (so-called MAP-II, since the latent variables are marginalized analytically give... | Marginalization of GP regression hyperparameters with Laplace approximation | The best reference I could find online so far, and a very fitting one, is Ville Pietiläinen's MSc thesis:
Approximations for Integration Over the Hyperparameters in Gaussian Processes (2010).
Pietilä | Marginalization of GP regression hyperparameters with Laplace approximation
The best reference I could find online so far, and a very fitting one, is Ville Pietiläinen's MSc thesis:
Approximations for Integration Over the Hyperparameters in Gaussian Processes (2010).
Pietiläinen compares a point estimate approach (so-... | Marginalization of GP regression hyperparameters with Laplace approximation
The best reference I could find online so far, and a very fitting one, is Ville Pietiläinen's MSc thesis:
Approximations for Integration Over the Hyperparameters in Gaussian Processes (2010).
Pietilä |
34,930 | Why is this time-series stationary? | I didn't replicate your analysis, but it's surely possible to reject the Null of the ADF test with a process like this (also note that these tests are notorious for having low statistical power). I would recommend fitting an AR(1) model to the data as a sanity check- this is basically what you are doing with the ADF te... | Why is this time-series stationary? | I didn't replicate your analysis, but it's surely possible to reject the Null of the ADF test with a process like this (also note that these tests are notorious for having low statistical power). I wo | Why is this time-series stationary?
I didn't replicate your analysis, but it's surely possible to reject the Null of the ADF test with a process like this (also note that these tests are notorious for having low statistical power). I would recommend fitting an AR(1) model to the data as a sanity check- this is basicall... | Why is this time-series stationary?
I didn't replicate your analysis, but it's surely possible to reject the Null of the ADF test with a process like this (also note that these tests are notorious for having low statistical power). I wo |
34,931 | Why is this time-series stationary? | Take a look at the graph of the differences of your series here. It looks like volatility clustering with a stationary mean to me. I'd try something like GARCH or stochastic volatility.
The other thing to note is that it appears that your jumps up are faster than drops down. This would suggest a threshold model, maybe... | Why is this time-series stationary? | Take a look at the graph of the differences of your series here. It looks like volatility clustering with a stationary mean to me. I'd try something like GARCH or stochastic volatility.
The other thi | Why is this time-series stationary?
Take a look at the graph of the differences of your series here. It looks like volatility clustering with a stationary mean to me. I'd try something like GARCH or stochastic volatility.
The other thing to note is that it appears that your jumps up are faster than drops down. This wo... | Why is this time-series stationary?
Take a look at the graph of the differences of your series here. It looks like volatility clustering with a stationary mean to me. I'd try something like GARCH or stochastic volatility.
The other thi |
34,932 | How to simulate a random slope model | @AdamO has done a good job identifying the specific error in your code. Let me address the question more generally. Here is how I simulate a linear mixed effects model:
Mixed effects models assume each unit has random effects drawn from a multivariate normal distribution. (When a model is estimated, it is the vari... | How to simulate a random slope model | @AdamO has done a good job identifying the specific error in your code. Let me address the question more generally. Here is how I simulate a linear mixed effects model:
Mixed effects models assume | How to simulate a random slope model
@AdamO has done a good job identifying the specific error in your code. Let me address the question more generally. Here is how I simulate a linear mixed effects model:
Mixed effects models assume each unit has random effects drawn from a multivariate normal distribution. (When... | How to simulate a random slope model
@AdamO has done a good job identifying the specific error in your code. Let me address the question more generally. Here is how I simulate a linear mixed effects model:
Mixed effects models assume |
34,933 | How to simulate a random slope model | There is an obvious mistake in your simulation. However, in general, it's impossible to generate data so that a random slopes model is guaranteed to converge.
The fix you need to apply is to timepoint. Timepoint is a factor. You should not be using a factor level variable in a random slopes model, it is completely alia... | How to simulate a random slope model | There is an obvious mistake in your simulation. However, in general, it's impossible to generate data so that a random slopes model is guaranteed to converge.
The fix you need to apply is to timepoint | How to simulate a random slope model
There is an obvious mistake in your simulation. However, in general, it's impossible to generate data so that a random slopes model is guaranteed to converge.
The fix you need to apply is to timepoint. Timepoint is a factor. You should not be using a factor level variable in a rando... | How to simulate a random slope model
There is an obvious mistake in your simulation. However, in general, it's impossible to generate data so that a random slopes model is guaranteed to converge.
The fix you need to apply is to timepoint |
34,934 | CausalImpact on single time series | There are two ways of running an analysis with the CausalImpact R package. The documentation covers both. You can either let the package construct a suitable model automatically or you can specify a custom model.
In the former case, the kind of model constructed by the package depends on your input data:
If your data,... | CausalImpact on single time series | There are two ways of running an analysis with the CausalImpact R package. The documentation covers both. You can either let the package construct a suitable model automatically or you can specify a c | CausalImpact on single time series
There are two ways of running an analysis with the CausalImpact R package. The documentation covers both. You can either let the package construct a suitable model automatically or you can specify a custom model.
In the former case, the kind of model constructed by the package depends... | CausalImpact on single time series
There are two ways of running an analysis with the CausalImpact R package. The documentation covers both. You can either let the package construct a suitable model automatically or you can specify a c |
34,935 | Significance of individual coefficients vs Significance of both | Consider the Wald statistic, which resembles the familiar F-statistic $F$ (we use the default version that is not robust to heteroskedasticity):
\begin{align*}
W&=n(Rb-u)'\left[R\left[n\cdot s^2\cdot(X'X)^{-1}\right]R'\right]^{-1}(Rb-u)\notag\\
&=(Rb-u)'\left[R(X'X)^{-1}R'\right]^{-1}(Rb-u)/s^2\\
&=J\cdot F\notag,
\end... | Significance of individual coefficients vs Significance of both | Consider the Wald statistic, which resembles the familiar F-statistic $F$ (we use the default version that is not robust to heteroskedasticity):
\begin{align*}
W&=n(Rb-u)'\left[R\left[n\cdot s^2\cdot( | Significance of individual coefficients vs Significance of both
Consider the Wald statistic, which resembles the familiar F-statistic $F$ (we use the default version that is not robust to heteroskedasticity):
\begin{align*}
W&=n(Rb-u)'\left[R\left[n\cdot s^2\cdot(X'X)^{-1}\right]R'\right]^{-1}(Rb-u)\notag\\
&=(Rb-u)'\l... | Significance of individual coefficients vs Significance of both
Consider the Wald statistic, which resembles the familiar F-statistic $F$ (we use the default version that is not robust to heteroskedasticity):
\begin{align*}
W&=n(Rb-u)'\left[R\left[n\cdot s^2\cdot( |
34,936 | What's the correct way to visualize discrete variables? | There's not 'one correct way'; there are some good ways.
The obvious one to my mind would be a Cleveland dot-chart; it's for displaying numeric data on a factor.
Some people would use a bar chart for this purpose instead. If you have a useful classification (such as by region), you'd split by that classification.
With... | What's the correct way to visualize discrete variables? | There's not 'one correct way'; there are some good ways.
The obvious one to my mind would be a Cleveland dot-chart; it's for displaying numeric data on a factor.
Some people would use a bar chart for | What's the correct way to visualize discrete variables?
There's not 'one correct way'; there are some good ways.
The obvious one to my mind would be a Cleveland dot-chart; it's for displaying numeric data on a factor.
Some people would use a bar chart for this purpose instead. If you have a useful classification (such... | What's the correct way to visualize discrete variables?
There's not 'one correct way'; there are some good ways.
The obvious one to my mind would be a Cleveland dot-chart; it's for displaying numeric data on a factor.
Some people would use a bar chart for |
34,937 | How to compute the R-squared for a transformed response variable? | It is not appropriate to compare linear regression models in terms of their summary/fit statistics (RMSE and $R^2$), when some models' dependent variables were transformed so that units changed, as summary statistics are not comparable. Consider the following nice explanation by Maddala (1988, p. 177):
When comparing ... | How to compute the R-squared for a transformed response variable? | It is not appropriate to compare linear regression models in terms of their summary/fit statistics (RMSE and $R^2$), when some models' dependent variables were transformed so that units changed, as su | How to compute the R-squared for a transformed response variable?
It is not appropriate to compare linear regression models in terms of their summary/fit statistics (RMSE and $R^2$), when some models' dependent variables were transformed so that units changed, as summary statistics are not comparable. Consider the foll... | How to compute the R-squared for a transformed response variable?
It is not appropriate to compare linear regression models in terms of their summary/fit statistics (RMSE and $R^2$), when some models' dependent variables were transformed so that units changed, as su |
34,938 | Skewed Distributions for Logistic Regression | The date as a predictor may be failing because it is highly collinear with the constant. If you enter it as a year, it's variability is about 10/2000 = 0.005 (in fact less because most of your data are in the more recent years), and when squared it becomes 4e-6. When inverting a matrix with eigenvalues 1 and 4e-6, the ... | Skewed Distributions for Logistic Regression | The date as a predictor may be failing because it is highly collinear with the constant. If you enter it as a year, it's variability is about 10/2000 = 0.005 (in fact less because most of your data ar | Skewed Distributions for Logistic Regression
The date as a predictor may be failing because it is highly collinear with the constant. If you enter it as a year, it's variability is about 10/2000 = 0.005 (in fact less because most of your data are in the more recent years), and when squared it becomes 4e-6. When inverti... | Skewed Distributions for Logistic Regression
The date as a predictor may be failing because it is highly collinear with the constant. If you enter it as a year, it's variability is about 10/2000 = 0.005 (in fact less because most of your data ar |
34,939 | Skewed Distributions for Logistic Regression | Restricted cubic splines would be expected to work well here. You are worried slightly too much about marginal distributions of predictors.
Length of stay is in the wrong part of the causal pathway to use it as a predictor of death. And watch out for other operation required.
I don't see much value in univariable ana... | Skewed Distributions for Logistic Regression | Restricted cubic splines would be expected to work well here. You are worried slightly too much about marginal distributions of predictors.
Length of stay is in the wrong part of the causal pathway t | Skewed Distributions for Logistic Regression
Restricted cubic splines would be expected to work well here. You are worried slightly too much about marginal distributions of predictors.
Length of stay is in the wrong part of the causal pathway to use it as a predictor of death. And watch out for other operation requir... | Skewed Distributions for Logistic Regression
Restricted cubic splines would be expected to work well here. You are worried slightly too much about marginal distributions of predictors.
Length of stay is in the wrong part of the causal pathway t |
34,940 | Cronbach's alpha in R | Cronbach's $\alpha$ is a measure of internal consistency of a questionnaire or test. It says how correlated the items are that are included in the scale. This is the reason why you need preferably much more than two items: you cannot correlate one item with itself and if you had only two items you could use a "traditio... | Cronbach's alpha in R | Cronbach's $\alpha$ is a measure of internal consistency of a questionnaire or test. It says how correlated the items are that are included in the scale. This is the reason why you need preferably muc | Cronbach's alpha in R
Cronbach's $\alpha$ is a measure of internal consistency of a questionnaire or test. It says how correlated the items are that are included in the scale. This is the reason why you need preferably much more than two items: you cannot correlate one item with itself and if you had only two items you... | Cronbach's alpha in R
Cronbach's $\alpha$ is a measure of internal consistency of a questionnaire or test. It says how correlated the items are that are included in the scale. This is the reason why you need preferably muc |
34,941 | p-value correction for multiple t-tests? | You absolutely do want to apply a correction. The key idea is identifying significance by chance. As you increase the number of comparisons you increase the number of those that will be significant by chance.
For example, let's take the generic example of doing 100 comparisons using a significance threshold of 0.05. ... | p-value correction for multiple t-tests? | You absolutely do want to apply a correction. The key idea is identifying significance by chance. As you increase the number of comparisons you increase the number of those that will be significant | p-value correction for multiple t-tests?
You absolutely do want to apply a correction. The key idea is identifying significance by chance. As you increase the number of comparisons you increase the number of those that will be significant by chance.
For example, let's take the generic example of doing 100 comparisons... | p-value correction for multiple t-tests?
You absolutely do want to apply a correction. The key idea is identifying significance by chance. As you increase the number of comparisons you increase the number of those that will be significant |
34,942 | p-value correction for multiple t-tests? | You say that no comparisons are being conducted because genes are not being compared to each other. However, each t-test is still a comparison. In fact, that's what a t-test is--a comparison of two means. In your case, each comparison is between the healthy group and the unhealthy group, rather than between gene A and ... | p-value correction for multiple t-tests? | You say that no comparisons are being conducted because genes are not being compared to each other. However, each t-test is still a comparison. In fact, that's what a t-test is--a comparison of two me | p-value correction for multiple t-tests?
You say that no comparisons are being conducted because genes are not being compared to each other. However, each t-test is still a comparison. In fact, that's what a t-test is--a comparison of two means. In your case, each comparison is between the healthy group and the unhealt... | p-value correction for multiple t-tests?
You say that no comparisons are being conducted because genes are not being compared to each other. However, each t-test is still a comparison. In fact, that's what a t-test is--a comparison of two me |
34,943 | Clarification: The covariance of intercept and slope in simple linear regression? | To answer your question as asked, if you adopt the frequentist view of statistics then $\beta_0$ and $\beta_1$ are not random variables and thus have no covariance. They are fixed (and unobserved) values that describe the true relationship between your $Y$ and $X$ variables. The covariance between them is undefined in ... | Clarification: The covariance of intercept and slope in simple linear regression? | To answer your question as asked, if you adopt the frequentist view of statistics then $\beta_0$ and $\beta_1$ are not random variables and thus have no covariance. They are fixed (and unobserved) val | Clarification: The covariance of intercept and slope in simple linear regression?
To answer your question as asked, if you adopt the frequentist view of statistics then $\beta_0$ and $\beta_1$ are not random variables and thus have no covariance. They are fixed (and unobserved) values that describe the true relationshi... | Clarification: The covariance of intercept and slope in simple linear regression?
To answer your question as asked, if you adopt the frequentist view of statistics then $\beta_0$ and $\beta_1$ are not random variables and thus have no covariance. They are fixed (and unobserved) val |
34,944 | How do I force the L-BFGS-B to not stop early? Projected gradient is zero | I don't know much about the SciPy wrapper, but the underlying L-BFGS-B code gives several options. The help file for the R interface lists several of them.
Assuming your gradient is just small but isn't actually zero, you have several options that will either increase the size of the gradient or decrease the size that... | How do I force the L-BFGS-B to not stop early? Projected gradient is zero | I don't know much about the SciPy wrapper, but the underlying L-BFGS-B code gives several options. The help file for the R interface lists several of them.
Assuming your gradient is just small but is | How do I force the L-BFGS-B to not stop early? Projected gradient is zero
I don't know much about the SciPy wrapper, but the underlying L-BFGS-B code gives several options. The help file for the R interface lists several of them.
Assuming your gradient is just small but isn't actually zero, you have several options th... | How do I force the L-BFGS-B to not stop early? Projected gradient is zero
I don't know much about the SciPy wrapper, but the underlying L-BFGS-B code gives several options. The help file for the R interface lists several of them.
Assuming your gradient is just small but is |
34,945 | How do I force the L-BFGS-B to not stop early? Projected gradient is zero | Scipy's BFGS solver uses a step size of epsilon = 1e-8 to calculate the gradient (meaning that it adds 1e-8 to each of the parameters in turn, to see how much the objective function changes), which is quite small for some applications. You can scale this up as much as you want based on the scale of the problem - for m... | How do I force the L-BFGS-B to not stop early? Projected gradient is zero | Scipy's BFGS solver uses a step size of epsilon = 1e-8 to calculate the gradient (meaning that it adds 1e-8 to each of the parameters in turn, to see how much the objective function changes), which is | How do I force the L-BFGS-B to not stop early? Projected gradient is zero
Scipy's BFGS solver uses a step size of epsilon = 1e-8 to calculate the gradient (meaning that it adds 1e-8 to each of the parameters in turn, to see how much the objective function changes), which is quite small for some applications. You can s... | How do I force the L-BFGS-B to not stop early? Projected gradient is zero
Scipy's BFGS solver uses a step size of epsilon = 1e-8 to calculate the gradient (meaning that it adds 1e-8 to each of the parameters in turn, to see how much the objective function changes), which is |
34,946 | Can multinomial distribution be simulated by a sequence of binomial draws? | This is correct, if
$$
(X_1,\ldots,X_K)\sim\mathcal{M}(N;p_1,\ldots,p_K)
$$
then
\begin{align*}
X_1 &\sim\mathcal{B}(N,p_1)\\
X_2|X_1 &\sim\mathcal{B}\{N-X_1,p_2/(1-p_1)\}\\
&\vdots\\
X_{K-1}|X_1,\ldots,X_{K-2} &\sim \mathcal{B}\big\{N-X_1-\cdots-X_{K-2},\frac{p_{K-1}}{\big(1 - \sum_{j<K-1}p_j\big)} \big\}
\end{align*}... | Can multinomial distribution be simulated by a sequence of binomial draws? | This is correct, if
$$
(X_1,\ldots,X_K)\sim\mathcal{M}(N;p_1,\ldots,p_K)
$$
then
\begin{align*}
X_1 &\sim\mathcal{B}(N,p_1)\\
X_2|X_1 &\sim\mathcal{B}\{N-X_1,p_2/(1-p_1)\}\\
&\vdots\\
X_{K-1}|X_1,\ldo | Can multinomial distribution be simulated by a sequence of binomial draws?
This is correct, if
$$
(X_1,\ldots,X_K)\sim\mathcal{M}(N;p_1,\ldots,p_K)
$$
then
\begin{align*}
X_1 &\sim\mathcal{B}(N,p_1)\\
X_2|X_1 &\sim\mathcal{B}\{N-X_1,p_2/(1-p_1)\}\\
&\vdots\\
X_{K-1}|X_1,\ldots,X_{K-2} &\sim \mathcal{B}\big\{N-X_1-\cdot... | Can multinomial distribution be simulated by a sequence of binomial draws?
This is correct, if
$$
(X_1,\ldots,X_K)\sim\mathcal{M}(N;p_1,\ldots,p_K)
$$
then
\begin{align*}
X_1 &\sim\mathcal{B}(N,p_1)\\
X_2|X_1 &\sim\mathcal{B}\{N-X_1,p_2/(1-p_1)\}\\
&\vdots\\
X_{K-1}|X_1,\ldo |
34,947 | Can multinomial distribution be simulated by a sequence of binomial draws? | A simple Python program to sample multinomial distribution according to this idea:
def sample_multinom(pVec, k):
n = len(pVec)
if n==1:
return int(np.random.uniform(0, 1, 1) > 1 - pVec[0])
k1 = sample_binom_using_random(k, pVec[0])
if n==2:
return (k1, k-k1)
else:
return (k1... | Can multinomial distribution be simulated by a sequence of binomial draws? | A simple Python program to sample multinomial distribution according to this idea:
def sample_multinom(pVec, k):
n = len(pVec)
if n==1:
return int(np.random.uniform(0, 1, 1) > 1 - pVec | Can multinomial distribution be simulated by a sequence of binomial draws?
A simple Python program to sample multinomial distribution according to this idea:
def sample_multinom(pVec, k):
n = len(pVec)
if n==1:
return int(np.random.uniform(0, 1, 1) > 1 - pVec[0])
k1 = sample_binom_using_random(k, pV... | Can multinomial distribution be simulated by a sequence of binomial draws?
A simple Python program to sample multinomial distribution according to this idea:
def sample_multinom(pVec, k):
n = len(pVec)
if n==1:
return int(np.random.uniform(0, 1, 1) > 1 - pVec |
34,948 | Ranking two models based on ROC-AUC and PR-AUC | Usually you would obtain the same conclusion based on both measures. It is possible to get conflicting conclusions if the performance curves (both PR and ROC) of the models cross, e.g. one model is better at low recall while the other is better at high recall. Relying on summaries like AUC is good, but don't neglect th... | Ranking two models based on ROC-AUC and PR-AUC | Usually you would obtain the same conclusion based on both measures. It is possible to get conflicting conclusions if the performance curves (both PR and ROC) of the models cross, e.g. one model is be | Ranking two models based on ROC-AUC and PR-AUC
Usually you would obtain the same conclusion based on both measures. It is possible to get conflicting conclusions if the performance curves (both PR and ROC) of the models cross, e.g. one model is better at low recall while the other is better at high recall. Relying on s... | Ranking two models based on ROC-AUC and PR-AUC
Usually you would obtain the same conclusion based on both measures. It is possible to get conflicting conclusions if the performance curves (both PR and ROC) of the models cross, e.g. one model is be |
34,949 | Ranking two models based on ROC-AUC and PR-AUC | ROC-AUC and PR-AUC are all AUC, confined by two axes with all thresholds.
ROC-AUC:
one axis is True Positive Rate (TPR), i.e., true positives / all positives
the other axis is False Positive Rate (FPR), i.e., false positives / all negatives
PR-AUC:
one axis is Recall (which is another name for TPR)
the other axi... | Ranking two models based on ROC-AUC and PR-AUC | ROC-AUC and PR-AUC are all AUC, confined by two axes with all thresholds.
ROC-AUC:
one axis is True Positive Rate (TPR), i.e., true positives / all positives
the other axis is False Positive Rate ( | Ranking two models based on ROC-AUC and PR-AUC
ROC-AUC and PR-AUC are all AUC, confined by two axes with all thresholds.
ROC-AUC:
one axis is True Positive Rate (TPR), i.e., true positives / all positives
the other axis is False Positive Rate (FPR), i.e., false positives / all negatives
PR-AUC:
one axis is Recal... | Ranking two models based on ROC-AUC and PR-AUC
ROC-AUC and PR-AUC are all AUC, confined by two axes with all thresholds.
ROC-AUC:
one axis is True Positive Rate (TPR), i.e., true positives / all positives
the other axis is False Positive Rate ( |
34,950 | Average and standard deviation of timestamps (time wraps around at midnight) | Let's use the simplification you suggest: only use the data from positive readings and disregard the value of the reading, so we are left with a single set of circular data. You can use the circular dispersion, as whuber suggested, possibly multiplied by some constant to determine how much of the data should be seen as... | Average and standard deviation of timestamps (time wraps around at midnight) | Let's use the simplification you suggest: only use the data from positive readings and disregard the value of the reading, so we are left with a single set of circular data. You can use the circular d | Average and standard deviation of timestamps (time wraps around at midnight)
Let's use the simplification you suggest: only use the data from positive readings and disregard the value of the reading, so we are left with a single set of circular data. You can use the circular dispersion, as whuber suggested, possibly mu... | Average and standard deviation of timestamps (time wraps around at midnight)
Let's use the simplification you suggest: only use the data from positive readings and disregard the value of the reading, so we are left with a single set of circular data. You can use the circular d |
34,951 | Average and standard deviation of timestamps (time wraps around at midnight) | This might be kind of dumb, but I just plotted the points as if they lie in a disc: the angle is taken to be time, and I assumed unit radius. The angle of the centroid of this point cloud is the mean angle of your data, i.e. the mean time of day which respects the "wrap around at midnight" property. This value also has... | Average and standard deviation of timestamps (time wraps around at midnight) | This might be kind of dumb, but I just plotted the points as if they lie in a disc: the angle is taken to be time, and I assumed unit radius. The angle of the centroid of this point cloud is the mean | Average and standard deviation of timestamps (time wraps around at midnight)
This might be kind of dumb, but I just plotted the points as if they lie in a disc: the angle is taken to be time, and I assumed unit radius. The angle of the centroid of this point cloud is the mean angle of your data, i.e. the mean time of d... | Average and standard deviation of timestamps (time wraps around at midnight)
This might be kind of dumb, but I just plotted the points as if they lie in a disc: the angle is taken to be time, and I assumed unit radius. The angle of the centroid of this point cloud is the mean |
34,952 | What do NORB and CIFAR stand for? | NORB = NYU Object Recognition Benchmark.
Source: http://www.cs.nyu.edu/~yann/research/norb/.
CIFAR = Canadian Institute for Advanced Research.
Source: http://www.cs.toronto.edu/~kriz/learning-features-2009-TR.pdf (page 32). | What do NORB and CIFAR stand for? | NORB = NYU Object Recognition Benchmark.
Source: http://www.cs.nyu.edu/~yann/research/norb/.
CIFAR = Canadian Institute for Advanced Research.
Source: http://www.cs.toronto.edu/~kriz/learning-features | What do NORB and CIFAR stand for?
NORB = NYU Object Recognition Benchmark.
Source: http://www.cs.nyu.edu/~yann/research/norb/.
CIFAR = Canadian Institute for Advanced Research.
Source: http://www.cs.toronto.edu/~kriz/learning-features-2009-TR.pdf (page 32). | What do NORB and CIFAR stand for?
NORB = NYU Object Recognition Benchmark.
Source: http://www.cs.nyu.edu/~yann/research/norb/.
CIFAR = Canadian Institute for Advanced Research.
Source: http://www.cs.toronto.edu/~kriz/learning-features |
34,953 | First differences vs. fixed effects model for panel data | If you have $N$ individuals and you include $N-1$ individual dummies (one less in order to avoid the dummy variable trap) in an OLS regression like
$$y_{it} = X'_{it}\beta + \sum_{i=1}^{N-1}\delta_i (\text{individual}_i) + \epsilon_{it}$$
then this is called a least squares dummy variable (LSDV) regression. In this cas... | First differences vs. fixed effects model for panel data | If you have $N$ individuals and you include $N-1$ individual dummies (one less in order to avoid the dummy variable trap) in an OLS regression like
$$y_{it} = X'_{it}\beta + \sum_{i=1}^{N-1}\delta_i ( | First differences vs. fixed effects model for panel data
If you have $N$ individuals and you include $N-1$ individual dummies (one less in order to avoid the dummy variable trap) in an OLS regression like
$$y_{it} = X'_{it}\beta + \sum_{i=1}^{N-1}\delta_i (\text{individual}_i) + \epsilon_{it}$$
then this is called a le... | First differences vs. fixed effects model for panel data
If you have $N$ individuals and you include $N-1$ individual dummies (one less in order to avoid the dummy variable trap) in an OLS regression like
$$y_{it} = X'_{it}\beta + \sum_{i=1}^{N-1}\delta_i ( |
34,954 | Specification of panel data | For the Stata commands in this answer let me collect your variables in a local:
local xlist sse01 wartosc_sr_trw_per_capita zatr_przem_bud podm_gosp_na_10tys_ludn proc_ludn_wiek_prod ludnosc_na_km2
So now you can always call all the variables with `xlist'
1) There are two commands that you can use after your fixed ef... | Specification of panel data | For the Stata commands in this answer let me collect your variables in a local:
local xlist sse01 wartosc_sr_trw_per_capita zatr_przem_bud podm_gosp_na_10tys_ludn proc_ludn_wiek_prod ludnosc_na_km2
| Specification of panel data
For the Stata commands in this answer let me collect your variables in a local:
local xlist sse01 wartosc_sr_trw_per_capita zatr_przem_bud podm_gosp_na_10tys_ludn proc_ludn_wiek_prod ludnosc_na_km2
So now you can always call all the variables with `xlist'
1) There are two commands that you... | Specification of panel data
For the Stata commands in this answer let me collect your variables in a local:
local xlist sse01 wartosc_sr_trw_per_capita zatr_przem_bud podm_gosp_na_10tys_ludn proc_ludn_wiek_prod ludnosc_na_km2
|
34,955 | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Reinforcement Learning? | The two definitions are not the same, but it essentially boils down to a modelling choice: for some problems, the reward function might be easier to define on the (state,action) pairs, while for others, the tuple (state,action,state) might be more appropriate. There's even a third option that only defines the reward o... | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Rei | The two definitions are not the same, but it essentially boils down to a modelling choice: for some problems, the reward function might be easier to define on the (state,action) pairs, while for other | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Reinforcement Learning?
The two definitions are not the same, but it essentially boils down to a modelling choice: for some problems, the reward function might be easier to define on the (state,action) pairs, while for othe... | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Rei
The two definitions are not the same, but it essentially boils down to a modelling choice: for some problems, the reward function might be easier to define on the (state,action) pairs, while for other |
34,956 | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Reinforcement Learning? | In addition to Pierre Lison's answer in favor of a reward function as $ R: S \times A \rightarrow \mathbb{R} $, Sutton and Barto touch on the topic in chapter 3.6 of their book "Reinforcement Learning: An Introduction".
Although the accepted answer is correct in terms of what is most commonly used, they prefer $ \mathc... | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Rei | In addition to Pierre Lison's answer in favor of a reward function as $ R: S \times A \rightarrow \mathbb{R} $, Sutton and Barto touch on the topic in chapter 3.6 of their book "Reinforcement Learning | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Reinforcement Learning?
In addition to Pierre Lison's answer in favor of a reward function as $ R: S \times A \rightarrow \mathbb{R} $, Sutton and Barto touch on the topic in chapter 3.6 of their book "Reinforcement Learnin... | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Rei
In addition to Pierre Lison's answer in favor of a reward function as $ R: S \times A \rightarrow \mathbb{R} $, Sutton and Barto touch on the topic in chapter 3.6 of their book "Reinforcement Learning |
34,957 | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Reinforcement Learning? | I think $R(s,a,s')$ is the same thing as $R(s,a)$ in the MDP setting because $s'$ is determined by the transition function $T(s,a)$. Therefore $R(s,a,s')$ becomes $R(s,a,T(s,a))$, which can be simplified as $R(s,a)$. | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Rei | I think $R(s,a,s')$ is the same thing as $R(s,a)$ in the MDP setting because $s'$ is determined by the transition function $T(s,a)$. Therefore $R(s,a,s')$ becomes $R(s,a,T(s,a))$, which can be simplif | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Reinforcement Learning?
I think $R(s,a,s')$ is the same thing as $R(s,a)$ in the MDP setting because $s'$ is determined by the transition function $T(s,a)$. Therefore $R(s,a,s')$ becomes $R(s,a,T(s,a))$, which can be simpli... | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Rei
I think $R(s,a,s')$ is the same thing as $R(s,a)$ in the MDP setting because $s'$ is determined by the transition function $T(s,a)$. Therefore $R(s,a,s')$ becomes $R(s,a,T(s,a))$, which can be simplif |
34,958 | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Reinforcement Learning? | They are equivalent in the following sense.
Now suppose you have an offline dataset consist of (s1,a1),(s2,a2),..,(sk,ak) with reward r1,r2,...,rk.
Based on the data, you can estimate the MDP model with transition probability T(s,a,s') and R(s,a,s'). You can also estimate the MDP model to be T(s,a,s') and R(s,a).
Solve... | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Rei | They are equivalent in the following sense.
Now suppose you have an offline dataset consist of (s1,a1),(s2,a2),..,(sk,ak) with reward r1,r2,...,rk.
Based on the data, you can estimate the MDP model wi | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Reinforcement Learning?
They are equivalent in the following sense.
Now suppose you have an offline dataset consist of (s1,a1),(s2,a2),..,(sk,ak) with reward r1,r2,...,rk.
Based on the data, you can estimate the MDP model w... | What does the Reward function depend on in a Markov Decision Processes (MDPs), in the context of Rei
They are equivalent in the following sense.
Now suppose you have an offline dataset consist of (s1,a1),(s2,a2),..,(sk,ak) with reward r1,r2,...,rk.
Based on the data, you can estimate the MDP model wi |
34,959 | Unbiased estimate of population standard deviation: is sqrt(2) a superior correction? | Maybe. What it appears that you did, is hit upon the $c_4(N)$ correction factor stated also in this wikipedia article. Specifically:
You propose the estimator
$$\tilde s = \frac 1{\sqrt {N-2^{1/2}}}\cdot (S_x)^{1/2} $$
where $S_x$ is the sum of squared deviations from the mean
The article you mention defines (although ... | Unbiased estimate of population standard deviation: is sqrt(2) a superior correction? | Maybe. What it appears that you did, is hit upon the $c_4(N)$ correction factor stated also in this wikipedia article. Specifically:
You propose the estimator
$$\tilde s = \frac 1{\sqrt {N-2^{1/2}}}\c | Unbiased estimate of population standard deviation: is sqrt(2) a superior correction?
Maybe. What it appears that you did, is hit upon the $c_4(N)$ correction factor stated also in this wikipedia article. Specifically:
You propose the estimator
$$\tilde s = \frac 1{\sqrt {N-2^{1/2}}}\cdot (S_x)^{1/2} $$
where $S_x$ is ... | Unbiased estimate of population standard deviation: is sqrt(2) a superior correction?
Maybe. What it appears that you did, is hit upon the $c_4(N)$ correction factor stated also in this wikipedia article. Specifically:
You propose the estimator
$$\tilde s = \frac 1{\sqrt {N-2^{1/2}}}\c |
34,960 | Unbiased estimate of population standard deviation: is sqrt(2) a superior correction? | For the sake of others who find this page, it is probably worth backing up a step and ask whether you really want an unbiased estimate of the population SD or an unbiased estimate of the population variance.
If you are going to use the SD to compute a confidence interval of a mean (or difference between two means) or... | Unbiased estimate of population standard deviation: is sqrt(2) a superior correction? | For the sake of others who find this page, it is probably worth backing up a step and ask whether you really want an unbiased estimate of the population SD or an unbiased estimate of the population va | Unbiased estimate of population standard deviation: is sqrt(2) a superior correction?
For the sake of others who find this page, it is probably worth backing up a step and ask whether you really want an unbiased estimate of the population SD or an unbiased estimate of the population variance.
If you are going to use ... | Unbiased estimate of population standard deviation: is sqrt(2) a superior correction?
For the sake of others who find this page, it is probably worth backing up a step and ask whether you really want an unbiased estimate of the population SD or an unbiased estimate of the population va |
34,961 | Unbiased estimate of population standard deviation: is sqrt(2) a superior correction? | If I felt that the correction is necessary beyond the standard $n-1$ why would I do the rule of a thumb? I'd go for the exact expression if it is know, such as in the case of the normal distribution. I have never seen anyone using this rule of a thumb anyways.
So, my answer is no, you didn't find anything fantastic. At... | Unbiased estimate of population standard deviation: is sqrt(2) a superior correction? | If I felt that the correction is necessary beyond the standard $n-1$ why would I do the rule of a thumb? I'd go for the exact expression if it is know, such as in the case of the normal distribution. | Unbiased estimate of population standard deviation: is sqrt(2) a superior correction?
If I felt that the correction is necessary beyond the standard $n-1$ why would I do the rule of a thumb? I'd go for the exact expression if it is know, such as in the case of the normal distribution. I have never seen anyone using thi... | Unbiased estimate of population standard deviation: is sqrt(2) a superior correction?
If I felt that the correction is necessary beyond the standard $n-1$ why would I do the rule of a thumb? I'd go for the exact expression if it is know, such as in the case of the normal distribution. |
34,962 | Connection between power law and Zipf's law | Zipf's law is generally understood to simply be a power-law distribution with integer values, that is, a probability distribution with the form
$p(x) \propto x^{-\alpha}$ for $x\geq x_{\min}>0$, $\alpha>1$ and $x\in \mathbb{N}_{>0}$
where $x_{\min}$ is the smallest value for which the power law holds, and is generally ... | Connection between power law and Zipf's law | Zipf's law is generally understood to simply be a power-law distribution with integer values, that is, a probability distribution with the form
$p(x) \propto x^{-\alpha}$ for $x\geq x_{\min}>0$, $\alp | Connection between power law and Zipf's law
Zipf's law is generally understood to simply be a power-law distribution with integer values, that is, a probability distribution with the form
$p(x) \propto x^{-\alpha}$ for $x\geq x_{\min}>0$, $\alpha>1$ and $x\in \mathbb{N}_{>0}$
where $x_{\min}$ is the smallest value for ... | Connection between power law and Zipf's law
Zipf's law is generally understood to simply be a power-law distribution with integer values, that is, a probability distribution with the form
$p(x) \propto x^{-\alpha}$ for $x\geq x_{\min}>0$, $\alp |
34,963 | Is it inappropriate to call multiple regression analysis 'correlational'? | Correlation can be two things. Correlation is a mathematical construct on one hand, which is de facto Pearson correlation. Correlation is also a counterpart to causal on the other, meaning conditional dependence between an "exposure" and "outcome" that may be mediated by 100s of unmeasured factors. Calling work (i.e. t... | Is it inappropriate to call multiple regression analysis 'correlational'? | Correlation can be two things. Correlation is a mathematical construct on one hand, which is de facto Pearson correlation. Correlation is also a counterpart to causal on the other, meaning conditional | Is it inappropriate to call multiple regression analysis 'correlational'?
Correlation can be two things. Correlation is a mathematical construct on one hand, which is de facto Pearson correlation. Correlation is also a counterpart to causal on the other, meaning conditional dependence between an "exposure" and "outcome... | Is it inappropriate to call multiple regression analysis 'correlational'?
Correlation can be two things. Correlation is a mathematical construct on one hand, which is de facto Pearson correlation. Correlation is also a counterpart to causal on the other, meaning conditional |
34,964 | Is it inappropriate to call multiple regression analysis 'correlational'? | Knowing no more than what you've said, I agree with @NickCox, @AdamO, and with you for the most part. If you have discussed this "completely mischaracterized" work in further depth than you've said here, it may not be safe to assume the objection is mostly to your characterization of it as "correlational", unless the r... | Is it inappropriate to call multiple regression analysis 'correlational'? | Knowing no more than what you've said, I agree with @NickCox, @AdamO, and with you for the most part. If you have discussed this "completely mischaracterized" work in further depth than you've said he | Is it inappropriate to call multiple regression analysis 'correlational'?
Knowing no more than what you've said, I agree with @NickCox, @AdamO, and with you for the most part. If you have discussed this "completely mischaracterized" work in further depth than you've said here, it may not be safe to assume the objection... | Is it inappropriate to call multiple regression analysis 'correlational'?
Knowing no more than what you've said, I agree with @NickCox, @AdamO, and with you for the most part. If you have discussed this "completely mischaracterized" work in further depth than you've said he |
34,965 | statistical method for spatial correlation between images | Most simplest way how to solve this in two images
is extract the values from both rasters and do correlation.
I am not sure if this solution will fit to your spacific case.
In what "format" do you have the images? (greyscale, RGB, size, resolution...).
Please give more specific details.
Two rasters in R for demonstrati... | statistical method for spatial correlation between images | Most simplest way how to solve this in two images
is extract the values from both rasters and do correlation.
I am not sure if this solution will fit to your spacific case.
In what "format" do you hav | statistical method for spatial correlation between images
Most simplest way how to solve this in two images
is extract the values from both rasters and do correlation.
I am not sure if this solution will fit to your spacific case.
In what "format" do you have the images? (greyscale, RGB, size, resolution...).
Please gi... | statistical method for spatial correlation between images
Most simplest way how to solve this in two images
is extract the values from both rasters and do correlation.
I am not sure if this solution will fit to your spacific case.
In what "format" do you hav |
34,966 | statistical method for spatial correlation between images | This is a problem that has been analyzed most extensively in the field of astronomy or cosmology with things like galaxy spatial correlation functions. The short answer is that you probably want to compute a 2D correlation function which can be computed efficiently with the Fast Fourier Transform (if needed). You might... | statistical method for spatial correlation between images | This is a problem that has been analyzed most extensively in the field of astronomy or cosmology with things like galaxy spatial correlation functions. The short answer is that you probably want to co | statistical method for spatial correlation between images
This is a problem that has been analyzed most extensively in the field of astronomy or cosmology with things like galaxy spatial correlation functions. The short answer is that you probably want to compute a 2D correlation function which can be computed efficien... | statistical method for spatial correlation between images
This is a problem that has been analyzed most extensively in the field of astronomy or cosmology with things like galaxy spatial correlation functions. The short answer is that you probably want to co |
34,967 | statistical method for spatial correlation between images | You could manually trace the centerline or the walls of the blood vessels (or use machine learning to fill those areas. Then you could build a buffer fence around that area. As a second step, you could identify the particles on the image (either manually or by machine learning). Then you could calculate the statistics ... | statistical method for spatial correlation between images | You could manually trace the centerline or the walls of the blood vessels (or use machine learning to fill those areas. Then you could build a buffer fence around that area. As a second step, you coul | statistical method for spatial correlation between images
You could manually trace the centerline or the walls of the blood vessels (or use machine learning to fill those areas. Then you could build a buffer fence around that area. As a second step, you could identify the particles on the image (either manually or by m... | statistical method for spatial correlation between images
You could manually trace the centerline or the walls of the blood vessels (or use machine learning to fill those areas. Then you could build a buffer fence around that area. As a second step, you coul |
34,968 | statistical method for spatial correlation between images | Please see the R package SpatialPack. There you will find three different statistical approaches to address this problem | statistical method for spatial correlation between images | Please see the R package SpatialPack. There you will find three different statistical approaches to address this problem | statistical method for spatial correlation between images
Please see the R package SpatialPack. There you will find three different statistical approaches to address this problem | statistical method for spatial correlation between images
Please see the R package SpatialPack. There you will find three different statistical approaches to address this problem |
34,969 | Expected value of maximum likelihood coin parameter estimate | First of all this is a self-study question, so I'm going to go too much into each and every little technical detail, but I'm not going on a derivation frenzy either. There are many ways to do this. I'll help you by using general properties of the maximum likelihood estimator.
Background information
In order to solve yo... | Expected value of maximum likelihood coin parameter estimate | First of all this is a self-study question, so I'm going to go too much into each and every little technical detail, but I'm not going on a derivation frenzy either. There are many ways to do this. I' | Expected value of maximum likelihood coin parameter estimate
First of all this is a self-study question, so I'm going to go too much into each and every little technical detail, but I'm not going on a derivation frenzy either. There are many ways to do this. I'll help you by using general properties of the maximum like... | Expected value of maximum likelihood coin parameter estimate
First of all this is a self-study question, so I'm going to go too much into each and every little technical detail, but I'm not going on a derivation frenzy either. There are many ways to do this. I' |
34,970 | Expected value of maximum likelihood coin parameter estimate | To start you off, let's do the expected value:
If $x$ is the number of successes in $n$ throws, then $x/n$ is the proportion of successes in your sample. Consider $\mathbb{E}x$; for each throw, the probability of success is $p$ according to the assumptions, so when tossing the coin one time the expected "number of succ... | Expected value of maximum likelihood coin parameter estimate | To start you off, let's do the expected value:
If $x$ is the number of successes in $n$ throws, then $x/n$ is the proportion of successes in your sample. Consider $\mathbb{E}x$; for each throw, the pr | Expected value of maximum likelihood coin parameter estimate
To start you off, let's do the expected value:
If $x$ is the number of successes in $n$ throws, then $x/n$ is the proportion of successes in your sample. Consider $\mathbb{E}x$; for each throw, the probability of success is $p$ according to the assumptions, s... | Expected value of maximum likelihood coin parameter estimate
To start you off, let's do the expected value:
If $x$ is the number of successes in $n$ throws, then $x/n$ is the proportion of successes in your sample. Consider $\mathbb{E}x$; for each throw, the pr |
34,971 | ANCOVA in observational studies: what are the assumptions? | In an ANCOVA, you typically model
$$E(Y|T,X)=\gamma T+X \beta$$
where $Y$ is your outcome variable, $T$ is your treatment indicator ($T=0$ to indicate control, and $T=1$ to indicate treatment), and $X$ is a covariate (or a vector of covariates). Then $\gamma$ is the average treatment effect (ATE) conditional on $X$.
No... | ANCOVA in observational studies: what are the assumptions? | In an ANCOVA, you typically model
$$E(Y|T,X)=\gamma T+X \beta$$
where $Y$ is your outcome variable, $T$ is your treatment indicator ($T=0$ to indicate control, and $T=1$ to indicate treatment), and $X | ANCOVA in observational studies: what are the assumptions?
In an ANCOVA, you typically model
$$E(Y|T,X)=\gamma T+X \beta$$
where $Y$ is your outcome variable, $T$ is your treatment indicator ($T=0$ to indicate control, and $T=1$ to indicate treatment), and $X$ is a covariate (or a vector of covariates). Then $\gamma$ i... | ANCOVA in observational studies: what are the assumptions?
In an ANCOVA, you typically model
$$E(Y|T,X)=\gamma T+X \beta$$
where $Y$ is your outcome variable, $T$ is your treatment indicator ($T=0$ to indicate control, and $T=1$ to indicate treatment), and $X |
34,972 | ANCOVA in observational studies: what are the assumptions? | I think a good starting point with this issue is to think logically about the meaning of a covariate adjustment in such situations. If the expected value of the CV is conditional on the group how is there any way to remove variation associated only with the CV? Surely a CV adjustment removes group effects as well! What... | ANCOVA in observational studies: what are the assumptions? | I think a good starting point with this issue is to think logically about the meaning of a covariate adjustment in such situations. If the expected value of the CV is conditional on the group how is t | ANCOVA in observational studies: what are the assumptions?
I think a good starting point with this issue is to think logically about the meaning of a covariate adjustment in such situations. If the expected value of the CV is conditional on the group how is there any way to remove variation associated only with the CV?... | ANCOVA in observational studies: what are the assumptions?
I think a good starting point with this issue is to think logically about the meaning of a covariate adjustment in such situations. If the expected value of the CV is conditional on the group how is t |
34,973 | Forecasting using Holt-Winters technique using R with less than 2 years of history | The Holt-Winters method is a poor choice for weekly data. It involves estimating a parameter for each week so the model has far too many degrees of freedom.
One approach which should work ok is to use a TBATS model which uses Fourier terms for the seasonality, and so requires fewer coefficients. In your case:
library(... | Forecasting using Holt-Winters technique using R with less than 2 years of history | The Holt-Winters method is a poor choice for weekly data. It involves estimating a parameter for each week so the model has far too many degrees of freedom.
One approach which should work ok is to us | Forecasting using Holt-Winters technique using R with less than 2 years of history
The Holt-Winters method is a poor choice for weekly data. It involves estimating a parameter for each week so the model has far too many degrees of freedom.
One approach which should work ok is to use a TBATS model which uses Fourier te... | Forecasting using Holt-Winters technique using R with less than 2 years of history
The Holt-Winters method is a poor choice for weekly data. It involves estimating a parameter for each week so the model has far too many degrees of freedom.
One approach which should work ok is to us |
34,974 | Analysis of a time series with a fixed and random factor in R | For mixed-effects modells of time series I usually use the nlme package, because it offers facilities to model auto-correlation structures. If I don't need to consider auto-correlation, I prefer the lme4 package, which offers more flexibility for specifying random effects and is also usually faster.
I recommend reading... | Analysis of a time series with a fixed and random factor in R | For mixed-effects modells of time series I usually use the nlme package, because it offers facilities to model auto-correlation structures. If I don't need to consider auto-correlation, I prefer the l | Analysis of a time series with a fixed and random factor in R
For mixed-effects modells of time series I usually use the nlme package, because it offers facilities to model auto-correlation structures. If I don't need to consider auto-correlation, I prefer the lme4 package, which offers more flexibility for specifying ... | Analysis of a time series with a fixed and random factor in R
For mixed-effects modells of time series I usually use the nlme package, because it offers facilities to model auto-correlation structures. If I don't need to consider auto-correlation, I prefer the l |
34,975 | How do SOMs reduce dimensionality of data? | The SOM grid is a 2-d manifold or topological space onto which each observation in the 10-d space is mapped via its similarity with the prototypes (code book vectors) for each cell in the SOM grid.
The SOM grid is non-linear in the full dimensional space; the "grid" is warped to more-closely fit the input data during t... | How do SOMs reduce dimensionality of data? | The SOM grid is a 2-d manifold or topological space onto which each observation in the 10-d space is mapped via its similarity with the prototypes (code book vectors) for each cell in the SOM grid.
Th | How do SOMs reduce dimensionality of data?
The SOM grid is a 2-d manifold or topological space onto which each observation in the 10-d space is mapped via its similarity with the prototypes (code book vectors) for each cell in the SOM grid.
The SOM grid is non-linear in the full dimensional space; the "grid" is warped ... | How do SOMs reduce dimensionality of data?
The SOM grid is a 2-d manifold or topological space onto which each observation in the 10-d space is mapped via its similarity with the prototypes (code book vectors) for each cell in the SOM grid.
Th |
34,976 | How do SOMs reduce dimensionality of data? | Consider your 2-dimensional SOM artificial neurons units as aiming to
have values equal to those of your high-dimensional data. It attains
this through the learning process- where a sample (a row of your data)
is taken from the data, compared for similarity with each of the units
on the map. The unit that comes closer ... | How do SOMs reduce dimensionality of data? | Consider your 2-dimensional SOM artificial neurons units as aiming to
have values equal to those of your high-dimensional data. It attains
this through the learning process- where a sample (a row of y | How do SOMs reduce dimensionality of data?
Consider your 2-dimensional SOM artificial neurons units as aiming to
have values equal to those of your high-dimensional data. It attains
this through the learning process- where a sample (a row of your data)
is taken from the data, compared for similarity with each of the un... | How do SOMs reduce dimensionality of data?
Consider your 2-dimensional SOM artificial neurons units as aiming to
have values equal to those of your high-dimensional data. It attains
this through the learning process- where a sample (a row of y |
34,977 | How to account for repeated measures in glmer? | tl;dr: Your model already accounts for the fact that you have repeated measures. Nonetheless, if it fits, you would do best to use:
glmer(y ~ x1*x2 + (x1:x2|subject), family=binomial)
but if that isn't tractable, you could try:
glmer(y ~ x1*x2 + (1|subject) + (0+x1|subject) + (0+x2|subject), family=binomial)
... | How to account for repeated measures in glmer? | tl;dr: Your model already accounts for the fact that you have repeated measures. Nonetheless, if it fits, you would do best to use:
glmer(y ~ x1*x2 + (x1:x2|subject), family=binomial)
but if that | How to account for repeated measures in glmer?
tl;dr: Your model already accounts for the fact that you have repeated measures. Nonetheless, if it fits, you would do best to use:
glmer(y ~ x1*x2 + (x1:x2|subject), family=binomial)
but if that isn't tractable, you could try:
glmer(y ~ x1*x2 + (1|subject) + (0+x1|s... | How to account for repeated measures in glmer?
tl;dr: Your model already accounts for the fact that you have repeated measures. Nonetheless, if it fits, you would do best to use:
glmer(y ~ x1*x2 + (x1:x2|subject), family=binomial)
but if that |
34,978 | Statistical test for a significant change in time series (sales) trend after policy change | Would a time series intervention analysis suit your needs? It estimates how much an intervention has changed a time series, if at all.
how to in R: http://www.r-bloggers.com/time-series-intervention-analysis-wih-r-and-sas/
example use case: What test should I use to determine if a policy change had a statistically sig... | Statistical test for a significant change in time series (sales) trend after policy change | Would a time series intervention analysis suit your needs? It estimates how much an intervention has changed a time series, if at all.
how to in R: http://www.r-bloggers.com/time-series-intervention- | Statistical test for a significant change in time series (sales) trend after policy change
Would a time series intervention analysis suit your needs? It estimates how much an intervention has changed a time series, if at all.
how to in R: http://www.r-bloggers.com/time-series-intervention-analysis-wih-r-and-sas/
examp... | Statistical test for a significant change in time series (sales) trend after policy change
Would a time series intervention analysis suit your needs? It estimates how much an intervention has changed a time series, if at all.
how to in R: http://www.r-bloggers.com/time-series-intervention- |
34,979 | Statistical test for a significant change in time series (sales) trend after policy change | I realise this answer is a bit late for the poster of this question, but I thought it may help others reviewing this question.
There is an excellent tutorial paper on interrupted time series analysis by Bernal et al:
Bernal, J. L., Cummins, S., Gasparrini; A. (2017). Interrupted time
series regression for the evalua... | Statistical test for a significant change in time series (sales) trend after policy change | I realise this answer is a bit late for the poster of this question, but I thought it may help others reviewing this question.
There is an excellent tutorial paper on interrupted time series analysis | Statistical test for a significant change in time series (sales) trend after policy change
I realise this answer is a bit late for the poster of this question, but I thought it may help others reviewing this question.
There is an excellent tutorial paper on interrupted time series analysis by Bernal et al:
Bernal, J. ... | Statistical test for a significant change in time series (sales) trend after policy change
I realise this answer is a bit late for the poster of this question, but I thought it may help others reviewing this question.
There is an excellent tutorial paper on interrupted time series analysis |
34,980 | Statistical test for a significant change in time series (sales) trend after policy change | Without knowing more about the data, especially the independent variables (the regressors), it will be impossible to give a one-fits-all solution for anyone here.
However the issue you are adressing falls into the area of Econometrics. As such, there are a couple of good texts which will bring you further.
They easiest... | Statistical test for a significant change in time series (sales) trend after policy change | Without knowing more about the data, especially the independent variables (the regressors), it will be impossible to give a one-fits-all solution for anyone here.
However the issue you are adressing f | Statistical test for a significant change in time series (sales) trend after policy change
Without knowing more about the data, especially the independent variables (the regressors), it will be impossible to give a one-fits-all solution for anyone here.
However the issue you are adressing falls into the area of Econome... | Statistical test for a significant change in time series (sales) trend after policy change
Without knowing more about the data, especially the independent variables (the regressors), it will be impossible to give a one-fits-all solution for anyone here.
However the issue you are adressing f |
34,981 | Statistical test for a significant change in time series (sales) trend after policy change | SSD For R is a package that makes this type of intervention analysis fairly easy. You just need an value and a phase column, and ABRegres will give you the data to determine if the trends in the baseline and intervention phases are statistically significant. https://ssdanalysis.com | Statistical test for a significant change in time series (sales) trend after policy change | SSD For R is a package that makes this type of intervention analysis fairly easy. You just need an value and a phase column, and ABRegres will give you the data to determine if the trends in the basel | Statistical test for a significant change in time series (sales) trend after policy change
SSD For R is a package that makes this type of intervention analysis fairly easy. You just need an value and a phase column, and ABRegres will give you the data to determine if the trends in the baseline and intervention phases a... | Statistical test for a significant change in time series (sales) trend after policy change
SSD For R is a package that makes this type of intervention analysis fairly easy. You just need an value and a phase column, and ABRegres will give you the data to determine if the trends in the basel |
34,982 | Correlation, regression and causal modeling | Correlation vs Regression
I am still confused as to how correlation differs to regression,
technically. I understand that one is a measure of association and one a measure of causation
This is incorrect, the difference between correlation and regression is not causal. Both measures are associational measures. I will ... | Correlation, regression and causal modeling | Correlation vs Regression
I am still confused as to how correlation differs to regression,
technically. I understand that one is a measure of association and one a measure of causation
This is incor | Correlation, regression and causal modeling
Correlation vs Regression
I am still confused as to how correlation differs to regression,
technically. I understand that one is a measure of association and one a measure of causation
This is incorrect, the difference between correlation and regression is not causal. Both ... | Correlation, regression and causal modeling
Correlation vs Regression
I am still confused as to how correlation differs to regression,
technically. I understand that one is a measure of association and one a measure of causation
This is incor |
34,983 | How to choose the test statistic for permutation test? | Often there are several statistics that will all result in the same p-value/result. For example in a 2 sample case the difference of the 2 means, the mean of group A, and the sum of the values in group A will all result in the same p-value (this is because given the data values and sample sizes you can calculate the 1... | How to choose the test statistic for permutation test? | Often there are several statistics that will all result in the same p-value/result. For example in a 2 sample case the difference of the 2 means, the mean of group A, and the sum of the values in gro | How to choose the test statistic for permutation test?
Often there are several statistics that will all result in the same p-value/result. For example in a 2 sample case the difference of the 2 means, the mean of group A, and the sum of the values in group A will all result in the same p-value (this is because given t... | How to choose the test statistic for permutation test?
Often there are several statistics that will all result in the same p-value/result. For example in a 2 sample case the difference of the 2 means, the mean of group A, and the sum of the values in gro |
34,984 | How to choose the test statistic for permutation test? | You choose a test statistic that measures what you're interested in/has the properties you need.
If you want to compare means, you base it on differences of means; if you want a robust comparison of location, you measure something else; if you want to compare standard deviations, you use a statistic that does that; if ... | How to choose the test statistic for permutation test? | You choose a test statistic that measures what you're interested in/has the properties you need.
If you want to compare means, you base it on differences of means; if you want a robust comparison of l | How to choose the test statistic for permutation test?
You choose a test statistic that measures what you're interested in/has the properties you need.
If you want to compare means, you base it on differences of means; if you want a robust comparison of location, you measure something else; if you want to compare stand... | How to choose the test statistic for permutation test?
You choose a test statistic that measures what you're interested in/has the properties you need.
If you want to compare means, you base it on differences of means; if you want a robust comparison of l |
34,985 | Mixed model in simple english | Here is my effort at this - imperfect, but might help.
Mixed effects models are needed when the variation in the response variable cannot be simply allocated between just a structural part and a residual individual randomness. Mixed effects models have both of these things but there is also randomness that is associat... | Mixed model in simple english | Here is my effort at this - imperfect, but might help.
Mixed effects models are needed when the variation in the response variable cannot be simply allocated between just a structural part and a resid | Mixed model in simple english
Here is my effort at this - imperfect, but might help.
Mixed effects models are needed when the variation in the response variable cannot be simply allocated between just a structural part and a residual individual randomness. Mixed effects models have both of these things but there is al... | Mixed model in simple english
Here is my effort at this - imperfect, but might help.
Mixed effects models are needed when the variation in the response variable cannot be simply allocated between just a structural part and a resid |
34,986 | Mixed model in simple english | I will provide a short response that I believe will be helpful, but won't be detailed.
I make use of mixed effects models (i.e. models with both fixed and random effects) when I believe the error in my data is not from a single source, and when I have information that could identify alternate sources. Mixed models are ... | Mixed model in simple english | I will provide a short response that I believe will be helpful, but won't be detailed.
I make use of mixed effects models (i.e. models with both fixed and random effects) when I believe the error in m | Mixed model in simple english
I will provide a short response that I believe will be helpful, but won't be detailed.
I make use of mixed effects models (i.e. models with both fixed and random effects) when I believe the error in my data is not from a single source, and when I have information that could identify altern... | Mixed model in simple english
I will provide a short response that I believe will be helpful, but won't be detailed.
I make use of mixed effects models (i.e. models with both fixed and random effects) when I believe the error in m |
34,987 | Why is a pivot quantity not necessarily a statistic? | The reason is that a pivot is a function of data and (unknown) parameters, while a statistic is only a function of data. For example, if $Z_1, \dotsc, Z_n$ is an iid sample from the distribution $\text{Normal}(\mu, 1)$, then a pivot will be $(\bar{Z} - \mu)\sqrt{n}$, since this function of data and unknown paramete... | Why is a pivot quantity not necessarily a statistic? | The reason is that a pivot is a function of data and (unknown) parameters, while a statistic is only a function of data. For example, if $Z_1, \dotsc, Z_n$ is an iid sample from the distribution $\t | Why is a pivot quantity not necessarily a statistic?
The reason is that a pivot is a function of data and (unknown) parameters, while a statistic is only a function of data. For example, if $Z_1, \dotsc, Z_n$ is an iid sample from the distribution $\text{Normal}(\mu, 1)$, then a pivot will be $(\bar{Z} - \mu)\sqrt{n... | Why is a pivot quantity not necessarily a statistic?
The reason is that a pivot is a function of data and (unknown) parameters, while a statistic is only a function of data. For example, if $Z_1, \dotsc, Z_n$ is an iid sample from the distribution $\t |
34,988 | Unbiased estimator for variance or Maximum Likelihood Estimator? | I think the answer is generally yes. If you know more about a distribution then you should use that information. For some distributions this will make very little difference, but for other it could be considerable.
As an example, consider the poisson distribution. In this case the mean and the variance are both equa... | Unbiased estimator for variance or Maximum Likelihood Estimator? | I think the answer is generally yes. If you know more about a distribution then you should use that information. For some distributions this will make very little difference, but for other it could | Unbiased estimator for variance or Maximum Likelihood Estimator?
I think the answer is generally yes. If you know more about a distribution then you should use that information. For some distributions this will make very little difference, but for other it could be considerable.
As an example, consider the poisson di... | Unbiased estimator for variance or Maximum Likelihood Estimator?
I think the answer is generally yes. If you know more about a distribution then you should use that information. For some distributions this will make very little difference, but for other it could |
34,989 | Unbiased estimator for variance or Maximum Likelihood Estimator? | I have moved my comment to an answer so I can expand on it as requested.
[If you mean the variance form $\frac{1}{n}\sum_{i=1}^{n}(X-\bar{X_{n}})^{2}$ as ML (which it is for the normal), then both forms use exactly the same information - the sums of squares of deviation from the mean. The only difference is that scalin... | Unbiased estimator for variance or Maximum Likelihood Estimator? | I have moved my comment to an answer so I can expand on it as requested.
[If you mean the variance form $\frac{1}{n}\sum_{i=1}^{n}(X-\bar{X_{n}})^{2}$ as ML (which it is for the normal), then both for | Unbiased estimator for variance or Maximum Likelihood Estimator?
I have moved my comment to an answer so I can expand on it as requested.
[If you mean the variance form $\frac{1}{n}\sum_{i=1}^{n}(X-\bar{X_{n}})^{2}$ as ML (which it is for the normal), then both forms use exactly the same information - the sums of squar... | Unbiased estimator for variance or Maximum Likelihood Estimator?
I have moved my comment to an answer so I can expand on it as requested.
[If you mean the variance form $\frac{1}{n}\sum_{i=1}^{n}(X-\bar{X_{n}})^{2}$ as ML (which it is for the normal), then both for |
34,990 | How important is domain knowledge in our profession? | I make an analogy: Solving statistical problems without context is like boxing while blindfolded. You might knock your opponent out but you might bash your hand on the ringpost.
I work mostly with medical and social science researchers. There seems to be a widespread feeling there that the proper model for research is ... | How important is domain knowledge in our profession? | I make an analogy: Solving statistical problems without context is like boxing while blindfolded. You might knock your opponent out but you might bash your hand on the ringpost.
I work mostly with med | How important is domain knowledge in our profession?
I make an analogy: Solving statistical problems without context is like boxing while blindfolded. You might knock your opponent out but you might bash your hand on the ringpost.
I work mostly with medical and social science researchers. There seems to be a widespread... | How important is domain knowledge in our profession?
I make an analogy: Solving statistical problems without context is like boxing while blindfolded. You might knock your opponent out but you might bash your hand on the ringpost.
I work mostly with med |
34,991 | How important is domain knowledge in our profession? | How important is domain knowledge in our profession?
Important enough to give distinct names to the domain-oriented data analyses (e.g. -metrics: biometrics, psychometrics, chemometrics, ...)
The mix of domain knowledge and statistical knowledge is extremely important in
design of experiments, e.g. practical ./. st... | How important is domain knowledge in our profession? | How important is domain knowledge in our profession?
Important enough to give distinct names to the domain-oriented data analyses (e.g. -metrics: biometrics, psychometrics, chemometrics, ...)
The mi | How important is domain knowledge in our profession?
How important is domain knowledge in our profession?
Important enough to give distinct names to the domain-oriented data analyses (e.g. -metrics: biometrics, psychometrics, chemometrics, ...)
The mix of domain knowledge and statistical knowledge is extremely import... | How important is domain knowledge in our profession?
How important is domain knowledge in our profession?
Important enough to give distinct names to the domain-oriented data analyses (e.g. -metrics: biometrics, psychometrics, chemometrics, ...)
The mi |
34,992 | Interaction in generalized linear model | In general, the existence of an interaction means that the effect of one variable depends on the value of the other variable with which it interacts. If there isn't an interaction, then the value of the other variable doesn't matter.
This is easiest to understand in the case of linear regression. Imagine we are loo... | Interaction in generalized linear model | In general, the existence of an interaction means that the effect of one variable depends on the value of the other variable with which it interacts. If there isn't an interaction, then the value of | Interaction in generalized linear model
In general, the existence of an interaction means that the effect of one variable depends on the value of the other variable with which it interacts. If there isn't an interaction, then the value of the other variable doesn't matter.
This is easiest to understand in the case o... | Interaction in generalized linear model
In general, the existence of an interaction means that the effect of one variable depends on the value of the other variable with which it interacts. If there isn't an interaction, then the value of |
34,993 | Big Data vs multiple hypothesis testing? | This isn't the whole answer, but an important consideration is which part of your data is big.
Consider the following example. I'm doing some analysis on physical measurements of human beings. For each volunteer I measure the distance between the eyes, then length of each digit, the length of the shins, etc. And I rec... | Big Data vs multiple hypothesis testing? | This isn't the whole answer, but an important consideration is which part of your data is big.
Consider the following example. I'm doing some analysis on physical measurements of human beings. For ea | Big Data vs multiple hypothesis testing?
This isn't the whole answer, but an important consideration is which part of your data is big.
Consider the following example. I'm doing some analysis on physical measurements of human beings. For each volunteer I measure the distance between the eyes, then length of each digit... | Big Data vs multiple hypothesis testing?
This isn't the whole answer, but an important consideration is which part of your data is big.
Consider the following example. I'm doing some analysis on physical measurements of human beings. For ea |
34,994 | Big Data vs multiple hypothesis testing? | Another thing to consider is how people work with big data (as opposed to 'small' data). Big data usually requires multiple pre-processing steps before it is fed into analysis. And sometimes it is not clear what to test for exactly in these data sets to begin with. Both facts combined allow for considerable wiggle room... | Big Data vs multiple hypothesis testing? | Another thing to consider is how people work with big data (as opposed to 'small' data). Big data usually requires multiple pre-processing steps before it is fed into analysis. And sometimes it is not | Big Data vs multiple hypothesis testing?
Another thing to consider is how people work with big data (as opposed to 'small' data). Big data usually requires multiple pre-processing steps before it is fed into analysis. And sometimes it is not clear what to test for exactly in these data sets to begin with. Both facts co... | Big Data vs multiple hypothesis testing?
Another thing to consider is how people work with big data (as opposed to 'small' data). Big data usually requires multiple pre-processing steps before it is fed into analysis. And sometimes it is not |
34,995 | Big Data vs multiple hypothesis testing? | 'Big data' usually refers to data sets with gazillions of subjects, and relatively fewer measurements per subject (also called 'tall' data). For data that is wide, rather than tall, there is much work already done, a good source being Efron's recent book 'Large-Scale Inference: Empirical Bayes Methods for Estimation, T... | Big Data vs multiple hypothesis testing? | 'Big data' usually refers to data sets with gazillions of subjects, and relatively fewer measurements per subject (also called 'tall' data). For data that is wide, rather than tall, there is much work | Big Data vs multiple hypothesis testing?
'Big data' usually refers to data sets with gazillions of subjects, and relatively fewer measurements per subject (also called 'tall' data). For data that is wide, rather than tall, there is much work already done, a good source being Efron's recent book 'Large-Scale Inference: ... | Big Data vs multiple hypothesis testing?
'Big data' usually refers to data sets with gazillions of subjects, and relatively fewer measurements per subject (also called 'tall' data). For data that is wide, rather than tall, there is much work |
34,996 | Simple question about the asymptotics of estimators | That's exactly how asymptotic results are being used in practice, e.g., in logistic regression. I would probably factor it differently as
$$\sqrt{N}\frac{\hat{M}-M}\sigma \overset{d}{\to}\mathcal{N}(0,1)$$
which shows the desired result more immediately, IMO (as mptikas mentioned in the comments, it is not kosher to h... | Simple question about the asymptotics of estimators | That's exactly how asymptotic results are being used in practice, e.g., in logistic regression. I would probably factor it differently as
$$\sqrt{N}\frac{\hat{M}-M}\sigma \overset{d}{\to}\mathcal{N}( | Simple question about the asymptotics of estimators
That's exactly how asymptotic results are being used in practice, e.g., in logistic regression. I would probably factor it differently as
$$\sqrt{N}\frac{\hat{M}-M}\sigma \overset{d}{\to}\mathcal{N}(0,1)$$
which shows the desired result more immediately, IMO (as mpti... | Simple question about the asymptotics of estimators
That's exactly how asymptotic results are being used in practice, e.g., in logistic regression. I would probably factor it differently as
$$\sqrt{N}\frac{\hat{M}-M}\sigma \overset{d}{\to}\mathcal{N}( |
34,997 | Simple question about the asymptotics of estimators | Taking the question at its face value, the answer is no. I offer a counterexample where $\hat{M}$ approaches its estimand in distribution while its variance diverges: in such a case, the $t$ statistic must approach zero almost surely, proving it can have neither an asymptotic Normal or t distribution.
Consider the us... | Simple question about the asymptotics of estimators | Taking the question at its face value, the answer is no. I offer a counterexample where $\hat{M}$ approaches its estimand in distribution while its variance diverges: in such a case, the $t$ statisti | Simple question about the asymptotics of estimators
Taking the question at its face value, the answer is no. I offer a counterexample where $\hat{M}$ approaches its estimand in distribution while its variance diverges: in such a case, the $t$ statistic must approach zero almost surely, proving it can have neither an a... | Simple question about the asymptotics of estimators
Taking the question at its face value, the answer is no. I offer a counterexample where $\hat{M}$ approaches its estimand in distribution while its variance diverges: in such a case, the $t$ statisti |
34,998 | Parameter estimation of exponential distribution with biased sampling | The maximum likelihood estimator for the parameter of the exponential distribution under type II censoring can be derived as follows. I assume the sample size is $m$, of which the $n < m$ smallest are observed and the $m - n$ largest are unobserved (but known to exist.)
Let us assume (for notational simplicity) that t... | Parameter estimation of exponential distribution with biased sampling | The maximum likelihood estimator for the parameter of the exponential distribution under type II censoring can be derived as follows. I assume the sample size is $m$, of which the $n < m$ smallest ar | Parameter estimation of exponential distribution with biased sampling
The maximum likelihood estimator for the parameter of the exponential distribution under type II censoring can be derived as follows. I assume the sample size is $m$, of which the $n < m$ smallest are observed and the $m - n$ largest are unobserved ... | Parameter estimation of exponential distribution with biased sampling
The maximum likelihood estimator for the parameter of the exponential distribution under type II censoring can be derived as follows. I assume the sample size is $m$, of which the $n < m$ smallest ar |
34,999 | Parameter estimation of exponential distribution with biased sampling | This links @jbowman's answer to my comment. Namely, under common working assumptions, one can use the 'standard survival likelihood' under type II censoring.
> #------seed------
> set.seed(1907)
> #----------------
>
> #------some data------
> t <- sort(rexp(n=20, rate=2)) #true sample
> t[16:20] <- t[15] ... | Parameter estimation of exponential distribution with biased sampling | This links @jbowman's answer to my comment. Namely, under common working assumptions, one can use the 'standard survival likelihood' under type II censoring.
> #------seed------
> set.seed(1907)
> #-- | Parameter estimation of exponential distribution with biased sampling
This links @jbowman's answer to my comment. Namely, under common working assumptions, one can use the 'standard survival likelihood' under type II censoring.
> #------seed------
> set.seed(1907)
> #----------------
>
> #------some data------
> t <- ... | Parameter estimation of exponential distribution with biased sampling
This links @jbowman's answer to my comment. Namely, under common working assumptions, one can use the 'standard survival likelihood' under type II censoring.
> #------seed------
> set.seed(1907)
> #-- |
35,000 | Parameter estimation of exponential distribution with biased sampling | Assuming $n$ is known, an estimate can be obtained via
$ \Phi(x_k)=1-e^{-\lambda x_k} \approx (k/n)$
where $x_k$, $0<k<m$, refers to the $k$'th smallest value in your reduced data set.
The logic is: if you had the entire set of $n$ samples, you could construct the empirical CDF, $\Phi$, from this sample. Then if you ... | Parameter estimation of exponential distribution with biased sampling | Assuming $n$ is known, an estimate can be obtained via
$ \Phi(x_k)=1-e^{-\lambda x_k} \approx (k/n)$
where $x_k$, $0<k<m$, refers to the $k$'th smallest value in your reduced data set.
The logic is: | Parameter estimation of exponential distribution with biased sampling
Assuming $n$ is known, an estimate can be obtained via
$ \Phi(x_k)=1-e^{-\lambda x_k} \approx (k/n)$
where $x_k$, $0<k<m$, refers to the $k$'th smallest value in your reduced data set.
The logic is: if you had the entire set of $n$ samples, you coul... | Parameter estimation of exponential distribution with biased sampling
Assuming $n$ is known, an estimate can be obtained via
$ \Phi(x_k)=1-e^{-\lambda x_k} \approx (k/n)$
where $x_k$, $0<k<m$, refers to the $k$'th smallest value in your reduced data set.
The logic is: |
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