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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38,401 | Type I error and type II error trade off | When the boy first pretends there is a wolf and the villagers believe him, it's a Type I error. When he claims there is a wolf again, but no one takes him seriously, though it is true, it's a type II error.
The villagers can avoid type I errors by never believing the boy, but that will always cause a Type II errors whe... | Type I error and type II error trade off | When the boy first pretends there is a wolf and the villagers believe him, it's a Type I error. When he claims there is a wolf again, but no one takes him seriously, though it is true, it's a type II | Type I error and type II error trade off
When the boy first pretends there is a wolf and the villagers believe him, it's a Type I error. When he claims there is a wolf again, but no one takes him seriously, though it is true, it's a type II error.
The villagers can avoid type I errors by never believing the boy, but th... | Type I error and type II error trade off
When the boy first pretends there is a wolf and the villagers believe him, it's a Type I error. When he claims there is a wolf again, but no one takes him seriously, though it is true, it's a type II |
38,402 | Type I error and type II error trade off | A life and death example of statistical errors
You are a paramedic and you approach the scene of a car accident. One victim is laying motionless on the road and you must assess whether the victim is dead or alive, and the victim will be treated accordingly. Based on this information which error rate results in the mos... | Type I error and type II error trade off | A life and death example of statistical errors
You are a paramedic and you approach the scene of a car accident. One victim is laying motionless on the road and you must assess whether the victim is d | Type I error and type II error trade off
A life and death example of statistical errors
You are a paramedic and you approach the scene of a car accident. One victim is laying motionless on the road and you must assess whether the victim is dead or alive, and the victim will be treated accordingly. Based on this inform... | Type I error and type II error trade off
A life and death example of statistical errors
You are a paramedic and you approach the scene of a car accident. One victim is laying motionless on the road and you must assess whether the victim is d |
38,403 | Type I error and type II error trade off | Google "illustration type 1 type 2 error" and have your pick. This site is one of many you can find a figure like the one you are asking for. | Type I error and type II error trade off | Google "illustration type 1 type 2 error" and have your pick. This site is one of many you can find a figure like the one you are asking for. | Type I error and type II error trade off
Google "illustration type 1 type 2 error" and have your pick. This site is one of many you can find a figure like the one you are asking for. | Type I error and type II error trade off
Google "illustration type 1 type 2 error" and have your pick. This site is one of many you can find a figure like the one you are asking for. |
38,404 | What does it mean for a moment generating function to exist in a neighborhood of 0? | Adding to Bey's answer, there's a reason you might care about this. The idea is that the MGF is a Laplace transform, and in this case it requires that your (continuous) probability density $f(x)$ decreases at least exponentially fast for large $x$, i.e. $e^{tx}f(x)\rightarrow 0$ for $x\rightarrow\infty$. This can be so... | What does it mean for a moment generating function to exist in a neighborhood of 0? | Adding to Bey's answer, there's a reason you might care about this. The idea is that the MGF is a Laplace transform, and in this case it requires that your (continuous) probability density $f(x)$ decr | What does it mean for a moment generating function to exist in a neighborhood of 0?
Adding to Bey's answer, there's a reason you might care about this. The idea is that the MGF is a Laplace transform, and in this case it requires that your (continuous) probability density $f(x)$ decreases at least exponentially fast fo... | What does it mean for a moment generating function to exist in a neighborhood of 0?
Adding to Bey's answer, there's a reason you might care about this. The idea is that the MGF is a Laplace transform, and in this case it requires that your (continuous) probability density $f(x)$ decr |
38,405 | What does it mean for a moment generating function to exist in a neighborhood of 0? | The MGF of a random variable $X$ is given by:
$$\mathrm{MGF}_X = \mathbb{E}[e^{tX}]$$
Where it is a function of $t$.
As you can see, the MGF at $t=0$ is always $1$, even if $X$ is, say, a Cauchy random variable, which has no moments. So, basically, when mathematicians say "a neighborhood", they mean:
$$\exists \epsilon... | What does it mean for a moment generating function to exist in a neighborhood of 0? | The MGF of a random variable $X$ is given by:
$$\mathrm{MGF}_X = \mathbb{E}[e^{tX}]$$
Where it is a function of $t$.
As you can see, the MGF at $t=0$ is always $1$, even if $X$ is, say, a Cauchy rando | What does it mean for a moment generating function to exist in a neighborhood of 0?
The MGF of a random variable $X$ is given by:
$$\mathrm{MGF}_X = \mathbb{E}[e^{tX}]$$
Where it is a function of $t$.
As you can see, the MGF at $t=0$ is always $1$, even if $X$ is, say, a Cauchy random variable, which has no moments. So... | What does it mean for a moment generating function to exist in a neighborhood of 0?
The MGF of a random variable $X$ is given by:
$$\mathrm{MGF}_X = \mathbb{E}[e^{tX}]$$
Where it is a function of $t$.
As you can see, the MGF at $t=0$ is always $1$, even if $X$ is, say, a Cauchy rando |
38,406 | What does it mean for a moment generating function to exist in a neighborhood of 0? | I thought I'd chime in with an example that illustrates when we might have to worry about this.
Suppose $X \sim Exp(\lambda)$ so that the probability density function is:
$$f(x\vert \lambda) = \lambda e^{-\lambda x}$$
Then the moment generating function is:
$$M_X(t) = E(e^{Xt}) = \int_0^\infty e^{xt} \lambda e^{-\lambd... | What does it mean for a moment generating function to exist in a neighborhood of 0? | I thought I'd chime in with an example that illustrates when we might have to worry about this.
Suppose $X \sim Exp(\lambda)$ so that the probability density function is:
$$f(x\vert \lambda) = \lambda | What does it mean for a moment generating function to exist in a neighborhood of 0?
I thought I'd chime in with an example that illustrates when we might have to worry about this.
Suppose $X \sim Exp(\lambda)$ so that the probability density function is:
$$f(x\vert \lambda) = \lambda e^{-\lambda x}$$
Then the moment ge... | What does it mean for a moment generating function to exist in a neighborhood of 0?
I thought I'd chime in with an example that illustrates when we might have to worry about this.
Suppose $X \sim Exp(\lambda)$ so that the probability density function is:
$$f(x\vert \lambda) = \lambda |
38,407 | Difference between neural network architectures | To fully answer this question, it would require a lot of pages here. Don't forget, stackexchange is not a textbook from which people read for you.
Multi-layered perceptron (MLP): are the neural networks that (probably) started everything. They are strictly feed-forward (one directional), i.e. a node from one layer can... | Difference between neural network architectures | To fully answer this question, it would require a lot of pages here. Don't forget, stackexchange is not a textbook from which people read for you.
Multi-layered perceptron (MLP): are the neural netwo | Difference between neural network architectures
To fully answer this question, it would require a lot of pages here. Don't forget, stackexchange is not a textbook from which people read for you.
Multi-layered perceptron (MLP): are the neural networks that (probably) started everything. They are strictly feed-forward (... | Difference between neural network architectures
To fully answer this question, it would require a lot of pages here. Don't forget, stackexchange is not a textbook from which people read for you.
Multi-layered perceptron (MLP): are the neural netwo |
38,408 | Is the Standard Deviation of a binomial dataset informative? | If you have a binomial random variable $X$, of size $N$, and with success probability $p$, i.e. $X \sim Bin(N;p)$, then the mean of X is $Np$ and its variance is $Np(1-p)$, so as you say the variance is a second degree polynomial in $p$. Note however that the variance is also dependent on $N$ ! The latter is important ... | Is the Standard Deviation of a binomial dataset informative? | If you have a binomial random variable $X$, of size $N$, and with success probability $p$, i.e. $X \sim Bin(N;p)$, then the mean of X is $Np$ and its variance is $Np(1-p)$, so as you say the variance | Is the Standard Deviation of a binomial dataset informative?
If you have a binomial random variable $X$, of size $N$, and with success probability $p$, i.e. $X \sim Bin(N;p)$, then the mean of X is $Np$ and its variance is $Np(1-p)$, so as you say the variance is a second degree polynomial in $p$. Note however that the... | Is the Standard Deviation of a binomial dataset informative?
If you have a binomial random variable $X$, of size $N$, and with success probability $p$, i.e. $X \sim Bin(N;p)$, then the mean of X is $Np$ and its variance is $Np(1-p)$, so as you say the variance |
38,409 | Is the Standard Deviation of a binomial dataset informative? | The family of Bernouli distributions is completely parameterized by one number, usually called $p$. So any population statistic of a Bernouli distribution must be some function of the parameter $p$. This does not mean that those statistics are descriptively useless!
For example, I can completely describe a box by giv... | Is the Standard Deviation of a binomial dataset informative? | The family of Bernouli distributions is completely parameterized by one number, usually called $p$. So any population statistic of a Bernouli distribution must be some function of the parameter $p$. | Is the Standard Deviation of a binomial dataset informative?
The family of Bernouli distributions is completely parameterized by one number, usually called $p$. So any population statistic of a Bernouli distribution must be some function of the parameter $p$. This does not mean that those statistics are descriptively... | Is the Standard Deviation of a binomial dataset informative?
The family of Bernouli distributions is completely parameterized by one number, usually called $p$. So any population statistic of a Bernouli distribution must be some function of the parameter $p$. |
38,410 | Is the Standard Deviation of a binomial dataset informative? | You might think you have a point if you already knew the true value of the binomial parameter $p$ and that you really were dealing with a binomial experiment (independent Bernoulli trials at constant $p$). With $N$ cases, the variance of the number of successes in a binomial experiment is $N p (1-p)$, and (naively) div... | Is the Standard Deviation of a binomial dataset informative? | You might think you have a point if you already knew the true value of the binomial parameter $p$ and that you really were dealing with a binomial experiment (independent Bernoulli trials at constant | Is the Standard Deviation of a binomial dataset informative?
You might think you have a point if you already knew the true value of the binomial parameter $p$ and that you really were dealing with a binomial experiment (independent Bernoulli trials at constant $p$). With $N$ cases, the variance of the number of success... | Is the Standard Deviation of a binomial dataset informative?
You might think you have a point if you already knew the true value of the binomial parameter $p$ and that you really were dealing with a binomial experiment (independent Bernoulli trials at constant |
38,411 | Why does this data throw an error in R fitdistr? | The Weibull distribution has two parameters, the scale $\lambda$ and shape $k$ (I'm following Wikipedia's notation). Both parameters are positive real numbers.
The function fitdist from the fitdistrplus package uses the optim function to find the maximum likelihood estimations of the parameters. By default, optim impos... | Why does this data throw an error in R fitdistr? | The Weibull distribution has two parameters, the scale $\lambda$ and shape $k$ (I'm following Wikipedia's notation). Both parameters are positive real numbers.
The function fitdist from the fitdistrpl | Why does this data throw an error in R fitdistr?
The Weibull distribution has two parameters, the scale $\lambda$ and shape $k$ (I'm following Wikipedia's notation). Both parameters are positive real numbers.
The function fitdist from the fitdistrplus package uses the optim function to find the maximum likelihood estim... | Why does this data throw an error in R fitdistr?
The Weibull distribution has two parameters, the scale $\lambda$ and shape $k$ (I'm following Wikipedia's notation). Both parameters are positive real numbers.
The function fitdist from the fitdistrpl |
38,412 | How to add noise to a random variable whose range is the unit interval? [closed] | A traditional way to handle constrained variables is to transform them into unconstrained variables, apply the jittering, and turn them back into the original scale.
For instance, if $d_i\in(0,1)$, one can use the logit transform
$$x_i=\text{logit}(d_i)=\log\left(\frac{d_i}{1-d_i}\right)$$
and add as much noise as nece... | How to add noise to a random variable whose range is the unit interval? [closed] | A traditional way to handle constrained variables is to transform them into unconstrained variables, apply the jittering, and turn them back into the original scale.
For instance, if $d_i\in(0,1)$, on | How to add noise to a random variable whose range is the unit interval? [closed]
A traditional way to handle constrained variables is to transform them into unconstrained variables, apply the jittering, and turn them back into the original scale.
For instance, if $d_i\in(0,1)$, one can use the logit transform
$$x_i=\te... | How to add noise to a random variable whose range is the unit interval? [closed]
A traditional way to handle constrained variables is to transform them into unconstrained variables, apply the jittering, and turn them back into the original scale.
For instance, if $d_i\in(0,1)$, on |
38,413 | How to add noise to a random variable whose range is the unit interval? [closed] | It appears there are many ways to accomplish what you are looking for. Here's one suggestion.
Treat each $d$ as if it were the value of some function $\Phi$ from the real number line to the unit interval. For example, let $\Phi$ denote the cumulative density function of the standard normal distribution, so that $d = \P... | How to add noise to a random variable whose range is the unit interval? [closed] | It appears there are many ways to accomplish what you are looking for. Here's one suggestion.
Treat each $d$ as if it were the value of some function $\Phi$ from the real number line to the unit inter | How to add noise to a random variable whose range is the unit interval? [closed]
It appears there are many ways to accomplish what you are looking for. Here's one suggestion.
Treat each $d$ as if it were the value of some function $\Phi$ from the real number line to the unit interval. For example, let $\Phi$ denote the... | How to add noise to a random variable whose range is the unit interval? [closed]
It appears there are many ways to accomplish what you are looking for. Here's one suggestion.
Treat each $d$ as if it were the value of some function $\Phi$ from the real number line to the unit inter |
38,414 | Why doesn't my gamma density plot match my histogram of samples? | If $X$ has density (pdf) $f$ then $1/X$ does not have density $1/f$ (which is not even a density). Indeed, the change-of-variables formula teaches us that $Y:=h(X)$ has density
$$\bigl|{(h^{-1})}'(y)\bigr|f(h^{-1}(y))$$
when $h$ is a "nice" invertible transformation.
I gave the formula for a general $h$, because $h^{-... | Why doesn't my gamma density plot match my histogram of samples? | If $X$ has density (pdf) $f$ then $1/X$ does not have density $1/f$ (which is not even a density). Indeed, the change-of-variables formula teaches us that $Y:=h(X)$ has density
$$\bigl|{(h^{-1})}'(y) | Why doesn't my gamma density plot match my histogram of samples?
If $X$ has density (pdf) $f$ then $1/X$ does not have density $1/f$ (which is not even a density). Indeed, the change-of-variables formula teaches us that $Y:=h(X)$ has density
$$\bigl|{(h^{-1})}'(y)\bigr|f(h^{-1}(y))$$
when $h$ is a "nice" invertible tr... | Why doesn't my gamma density plot match my histogram of samples?
If $X$ has density (pdf) $f$ then $1/X$ does not have density $1/f$ (which is not even a density). Indeed, the change-of-variables formula teaches us that $Y:=h(X)$ has density
$$\bigl|{(h^{-1})}'(y) |
38,415 | Why doesn't my gamma density plot match my histogram of samples? | The problem here isn't at root anything to do with graphics.
The density of an inverse gamma distribution is not the reciprocal of the density of a gamma distribution, which is what your last syntax line implies. To see that, it's sufficient to note that such a relation would map near zero densities of the gamma to n... | Why doesn't my gamma density plot match my histogram of samples? | The problem here isn't at root anything to do with graphics.
The density of an inverse gamma distribution is not the reciprocal of the density of a gamma distribution, which is what your last syntax | Why doesn't my gamma density plot match my histogram of samples?
The problem here isn't at root anything to do with graphics.
The density of an inverse gamma distribution is not the reciprocal of the density of a gamma distribution, which is what your last syntax line implies. To see that, it's sufficient to note tha... | Why doesn't my gamma density plot match my histogram of samples?
The problem here isn't at root anything to do with graphics.
The density of an inverse gamma distribution is not the reciprocal of the density of a gamma distribution, which is what your last syntax |
38,416 | Simple non-linear regression problem | If you log-transformed your outcome variable and then fit a regression model, just exponentiate the predictions to plot it on the original scale.
In many cases, it's better to use some nonlinear functions such as polynomials or splines on the originale scale, as @hejseb mentioned. This post might be of interest.
Here i... | Simple non-linear regression problem | If you log-transformed your outcome variable and then fit a regression model, just exponentiate the predictions to plot it on the original scale.
In many cases, it's better to use some nonlinear funct | Simple non-linear regression problem
If you log-transformed your outcome variable and then fit a regression model, just exponentiate the predictions to plot it on the original scale.
In many cases, it's better to use some nonlinear functions such as polynomials or splines on the originale scale, as @hejseb mentioned. T... | Simple non-linear regression problem
If you log-transformed your outcome variable and then fit a regression model, just exponentiate the predictions to plot it on the original scale.
In many cases, it's better to use some nonlinear funct |
38,417 | Simple non-linear regression problem | If all you want is a quadratic term, you can use lm(y~x+I(x^2)). An example:
For your model that would mean predictions <- lm(price~mileage+I(mileage^2), data = ads_clean). For higher order polynomials, you can just add them in the same way. You could also try some nonparametric regression, for example locpoly.
x <- ... | Simple non-linear regression problem | If all you want is a quadratic term, you can use lm(y~x+I(x^2)). An example:
For your model that would mean predictions <- lm(price~mileage+I(mileage^2), data = ads_clean). For higher order polynomia | Simple non-linear regression problem
If all you want is a quadratic term, you can use lm(y~x+I(x^2)). An example:
For your model that would mean predictions <- lm(price~mileage+I(mileage^2), data = ads_clean). For higher order polynomials, you can just add them in the same way. You could also try some nonparametric re... | Simple non-linear regression problem
If all you want is a quadratic term, you can use lm(y~x+I(x^2)). An example:
For your model that would mean predictions <- lm(price~mileage+I(mileage^2), data = ads_clean). For higher order polynomia |
38,418 | Feature selection before neural network classification | One way to think about the process of building a predictive model (such as a neural network) is that you have a 'budget' of information to spend, much like a certain amount of money for a monthly household budget. With only 87 observations in your training set (and only 36 more in your test set), you have a very skimp... | Feature selection before neural network classification | One way to think about the process of building a predictive model (such as a neural network) is that you have a 'budget' of information to spend, much like a certain amount of money for a monthly hous | Feature selection before neural network classification
One way to think about the process of building a predictive model (such as a neural network) is that you have a 'budget' of information to spend, much like a certain amount of money for a monthly household budget. With only 87 observations in your training set (an... | Feature selection before neural network classification
One way to think about the process of building a predictive model (such as a neural network) is that you have a 'budget' of information to spend, much like a certain amount of money for a monthly hous |
38,419 | Feature selection before neural network classification | With respect to your first question, it depends on your computer.
With respect to the second, there is no single best answer. Neural networks are themselves often used for feature selection. This is the paradigm leading to deep learning. In that case it is unlikely you'd want to do any feature selection (except maybe w... | Feature selection before neural network classification | With respect to your first question, it depends on your computer.
With respect to the second, there is no single best answer. Neural networks are themselves often used for feature selection. This is t | Feature selection before neural network classification
With respect to your first question, it depends on your computer.
With respect to the second, there is no single best answer. Neural networks are themselves often used for feature selection. This is the paradigm leading to deep learning. In that case it is unlikely... | Feature selection before neural network classification
With respect to your first question, it depends on your computer.
With respect to the second, there is no single best answer. Neural networks are themselves often used for feature selection. This is t |
38,420 | Feature selection before neural network classification | Adding my own two cents to the previous answers. You have a big problem with the curse of dimensionality. This problem with the tiny corpus you have makes me think that the best option in this case would be a simple Bayesian. | Feature selection before neural network classification | Adding my own two cents to the previous answers. You have a big problem with the curse of dimensionality. This problem with the tiny corpus you have makes me think that the best option in this case wo | Feature selection before neural network classification
Adding my own two cents to the previous answers. You have a big problem with the curse of dimensionality. This problem with the tiny corpus you have makes me think that the best option in this case would be a simple Bayesian. | Feature selection before neural network classification
Adding my own two cents to the previous answers. You have a big problem with the curse of dimensionality. This problem with the tiny corpus you have makes me think that the best option in this case wo |
38,421 | Should I categorise my continuous variable for use in binary logistic regression | This can cut two ways, but mostly one. In logistic regression, as with any flavour of regression, it is fine, indeed usually better, to have continuous predictors.
Given a choice between a continuous variable as a predictor and categorising a continuous variable for predictors, the first is usually to be preferred. At... | Should I categorise my continuous variable for use in binary logistic regression | This can cut two ways, but mostly one. In logistic regression, as with any flavour of regression, it is fine, indeed usually better, to have continuous predictors.
Given a choice between a continuous | Should I categorise my continuous variable for use in binary logistic regression
This can cut two ways, but mostly one. In logistic regression, as with any flavour of regression, it is fine, indeed usually better, to have continuous predictors.
Given a choice between a continuous variable as a predictor and categorisi... | Should I categorise my continuous variable for use in binary logistic regression
This can cut two ways, but mostly one. In logistic regression, as with any flavour of regression, it is fine, indeed usually better, to have continuous predictors.
Given a choice between a continuous |
38,422 | Should I categorise my continuous variable for use in binary logistic regression | It is true that reducing an ordinal or even continuous variable to dichotomous level loses a lot of information, but this is a concern for the dependent variable (i.e. dichotomizing a continuous dependent variable) in logistic regression. For continuous predictors (independent variables), logistic regression assumes th... | Should I categorise my continuous variable for use in binary logistic regression | It is true that reducing an ordinal or even continuous variable to dichotomous level loses a lot of information, but this is a concern for the dependent variable (i.e. dichotomizing a continuous depen | Should I categorise my continuous variable for use in binary logistic regression
It is true that reducing an ordinal or even continuous variable to dichotomous level loses a lot of information, but this is a concern for the dependent variable (i.e. dichotomizing a continuous dependent variable) in logistic regression. ... | Should I categorise my continuous variable for use in binary logistic regression
It is true that reducing an ordinal or even continuous variable to dichotomous level loses a lot of information, but this is a concern for the dependent variable (i.e. dichotomizing a continuous depen |
38,423 | Interpreting p-values in Fisher vs Neyman-Pearson frameworks | Fisher uses p-values as a continuous measure of evidence against a null hypothesis?
Perhaps. What convinces you of this?
So a p-value of 0.06 would indicate that there is no difference and the null hypothesis is true?
Not at all. How did you go from 'continuous measure of evidence against' to 'there is no differenc... | Interpreting p-values in Fisher vs Neyman-Pearson frameworks | Fisher uses p-values as a continuous measure of evidence against a null hypothesis?
Perhaps. What convinces you of this?
So a p-value of 0.06 would indicate that there is no difference and the null | Interpreting p-values in Fisher vs Neyman-Pearson frameworks
Fisher uses p-values as a continuous measure of evidence against a null hypothesis?
Perhaps. What convinces you of this?
So a p-value of 0.06 would indicate that there is no difference and the null hypothesis is true?
Not at all. How did you go from 'cont... | Interpreting p-values in Fisher vs Neyman-Pearson frameworks
Fisher uses p-values as a continuous measure of evidence against a null hypothesis?
Perhaps. What convinces you of this?
So a p-value of 0.06 would indicate that there is no difference and the null |
38,424 | Interpreting p-values in Fisher vs Neyman-Pearson frameworks | The issue here is that you need to be clearer on the definitions of these terms, and what those definitions imply.
Taking the p-value as a continuous measure of evidence against the null hypothesis means that there is no 'bright line' between "no difference" and "difference". As a result of this, $p=.04$ is essentia... | Interpreting p-values in Fisher vs Neyman-Pearson frameworks | The issue here is that you need to be clearer on the definitions of these terms, and what those definitions imply.
Taking the p-value as a continuous measure of evidence against the null hypothesis | Interpreting p-values in Fisher vs Neyman-Pearson frameworks
The issue here is that you need to be clearer on the definitions of these terms, and what those definitions imply.
Taking the p-value as a continuous measure of evidence against the null hypothesis means that there is no 'bright line' between "no difference... | Interpreting p-values in Fisher vs Neyman-Pearson frameworks
The issue here is that you need to be clearer on the definitions of these terms, and what those definitions imply.
Taking the p-value as a continuous measure of evidence against the null hypothesis |
38,425 | How do I mathematically prove that k-means clustering converges to minimum squared error? | There is no k-means algorithm. K-means is the problem. Algorithms for it include MacQueen, Lloyd/Forgy, Hartigan/Wong and many more.
Most of these algorithms (all but exhaustive search I guess) will only find a local optimum, not the global optimum. They are heuristics. Fast heuristics...
It turns out the usual nearest... | How do I mathematically prove that k-means clustering converges to minimum squared error? | There is no k-means algorithm. K-means is the problem. Algorithms for it include MacQueen, Lloyd/Forgy, Hartigan/Wong and many more.
Most of these algorithms (all but exhaustive search I guess) will o | How do I mathematically prove that k-means clustering converges to minimum squared error?
There is no k-means algorithm. K-means is the problem. Algorithms for it include MacQueen, Lloyd/Forgy, Hartigan/Wong and many more.
Most of these algorithms (all but exhaustive search I guess) will only find a local optimum, not ... | How do I mathematically prove that k-means clustering converges to minimum squared error?
There is no k-means algorithm. K-means is the problem. Algorithms for it include MacQueen, Lloyd/Forgy, Hartigan/Wong and many more.
Most of these algorithms (all but exhaustive search I guess) will o |
38,426 | How do I mathematically prove that k-means clustering converges to minimum squared error? | K-means clustering does not guarantee you global optimum (although I'd not call K-means a "heuristic" technique). However you can do this: run K-means a number of times, each time with different random initial centres seed, and obtain a set of final cluster centres each time. If these sets appear similar enough - in th... | How do I mathematically prove that k-means clustering converges to minimum squared error? | K-means clustering does not guarantee you global optimum (although I'd not call K-means a "heuristic" technique). However you can do this: run K-means a number of times, each time with different rando | How do I mathematically prove that k-means clustering converges to minimum squared error?
K-means clustering does not guarantee you global optimum (although I'd not call K-means a "heuristic" technique). However you can do this: run K-means a number of times, each time with different random initial centres seed, and ob... | How do I mathematically prove that k-means clustering converges to minimum squared error?
K-means clustering does not guarantee you global optimum (although I'd not call K-means a "heuristic" technique). However you can do this: run K-means a number of times, each time with different rando |
38,427 | How do I mathematically prove that k-means clustering converges to minimum squared error? | You can actually prove that it converges to a local minimum and that, actually, you are performing Newton minimization on the quantization error functional. All the details are in the Léon Bottou and Yoshua Bengio's paper "Convergence Properties of the K-Means Algorithms" | How do I mathematically prove that k-means clustering converges to minimum squared error? | You can actually prove that it converges to a local minimum and that, actually, you are performing Newton minimization on the quantization error functional. All the details are in the Léon Bottou and | How do I mathematically prove that k-means clustering converges to minimum squared error?
You can actually prove that it converges to a local minimum and that, actually, you are performing Newton minimization on the quantization error functional. All the details are in the Léon Bottou and Yoshua Bengio's paper "Converg... | How do I mathematically prove that k-means clustering converges to minimum squared error?
You can actually prove that it converges to a local minimum and that, actually, you are performing Newton minimization on the quantization error functional. All the details are in the Léon Bottou and |
38,428 | How do I mathematically prove that k-means clustering converges to minimum squared error? | The objective function in this type of clustering is to assign points to clusters in a way that the sum of squared distances to the centroids are minimized. However, with K-Means we (approximately) solve a different problem which has the same optimal solution as our original problem:
\begin{align}
&\min_{x} \sum_{i=1}^... | How do I mathematically prove that k-means clustering converges to minimum squared error? | The objective function in this type of clustering is to assign points to clusters in a way that the sum of squared distances to the centroids are minimized. However, with K-Means we (approximately) so | How do I mathematically prove that k-means clustering converges to minimum squared error?
The objective function in this type of clustering is to assign points to clusters in a way that the sum of squared distances to the centroids are minimized. However, with K-Means we (approximately) solve a different problem which ... | How do I mathematically prove that k-means clustering converges to minimum squared error?
The objective function in this type of clustering is to assign points to clusters in a way that the sum of squared distances to the centroids are minimized. However, with K-Means we (approximately) so |
38,429 | Why are my p-values so high? | There are many possible explanations but some of the most common are:
The explanatory variables are not related to your response. So no problem here, you just have a negative finding.
Some or all of the variables are related, but they are highly correlated so you have a problem with "variance inflation factors". If ... | Why are my p-values so high? | There are many possible explanations but some of the most common are:
The explanatory variables are not related to your response. So no problem here, you just have a negative finding.
Some or all of | Why are my p-values so high?
There are many possible explanations but some of the most common are:
The explanatory variables are not related to your response. So no problem here, you just have a negative finding.
Some or all of the variables are related, but they are highly correlated so you have a problem with "vari... | Why are my p-values so high?
There are many possible explanations but some of the most common are:
The explanatory variables are not related to your response. So no problem here, you just have a negative finding.
Some or all of |
38,430 | Why are my p-values so high? | Because your response is a ratio between 0 and 1, it might be possible there is a heterogeneous (skewness) between data. In this case, logistic regression can not take into account this heterogeneity very well. An alternative model is beta regression. Beta distribution is a good choice to consider heterogeneity and ske... | Why are my p-values so high? | Because your response is a ratio between 0 and 1, it might be possible there is a heterogeneous (skewness) between data. In this case, logistic regression can not take into account this heterogeneity | Why are my p-values so high?
Because your response is a ratio between 0 and 1, it might be possible there is a heterogeneous (skewness) between data. In this case, logistic regression can not take into account this heterogeneity very well. An alternative model is beta regression. Beta distribution is a good choice to c... | Why are my p-values so high?
Because your response is a ratio between 0 and 1, it might be possible there is a heterogeneous (skewness) between data. In this case, logistic regression can not take into account this heterogeneity |
38,431 | Why are my p-values so high? | I've seen p-values very close to 1.0 in ordinary least squares. A likely explanation is omitting an important explanatory variable. That inflates the error term making other variables look "suspiciously insignificant". A quickly constructed simulation follows but I've seen real cases that were more dramatic.
Omitted... | Why are my p-values so high? | I've seen p-values very close to 1.0 in ordinary least squares. A likely explanation is omitting an important explanatory variable. That inflates the error term making other variables look "suspicio | Why are my p-values so high?
I've seen p-values very close to 1.0 in ordinary least squares. A likely explanation is omitting an important explanatory variable. That inflates the error term making other variables look "suspiciously insignificant". A quickly constructed simulation follows but I've seen real cases tha... | Why are my p-values so high?
I've seen p-values very close to 1.0 in ordinary least squares. A likely explanation is omitting an important explanatory variable. That inflates the error term making other variables look "suspicio |
38,432 | Does ensembling (boosting) cause overfitting? | First of all, let's make sure what you mean by overfitting. I assume you mean that the algorithm has learned too many of the nuances of the training data and will not perform well when you apply it to new data it hasn't seen before (from a similar population). This would also be known as poor generalization.
All mach... | Does ensembling (boosting) cause overfitting? | First of all, let's make sure what you mean by overfitting. I assume you mean that the algorithm has learned too many of the nuances of the training data and will not perform well when you apply it t | Does ensembling (boosting) cause overfitting?
First of all, let's make sure what you mean by overfitting. I assume you mean that the algorithm has learned too many of the nuances of the training data and will not perform well when you apply it to new data it hasn't seen before (from a similar population). This would ... | Does ensembling (boosting) cause overfitting?
First of all, let's make sure what you mean by overfitting. I assume you mean that the algorithm has learned too many of the nuances of the training data and will not perform well when you apply it t |
38,433 | Does ensembling (boosting) cause overfitting? | The overfitting of boosting techniques is a topic that is not yet theoretically understood, but empirically results show that boosting seems to be very robust against overfitting.
The usual explanation for this phenomena is as follow: the samples that are incorrectly predicted in one iteration will have higher weight i... | Does ensembling (boosting) cause overfitting? | The overfitting of boosting techniques is a topic that is not yet theoretically understood, but empirically results show that boosting seems to be very robust against overfitting.
The usual explanatio | Does ensembling (boosting) cause overfitting?
The overfitting of boosting techniques is a topic that is not yet theoretically understood, but empirically results show that boosting seems to be very robust against overfitting.
The usual explanation for this phenomena is as follow: the samples that are incorrectly predic... | Does ensembling (boosting) cause overfitting?
The overfitting of boosting techniques is a topic that is not yet theoretically understood, but empirically results show that boosting seems to be very robust against overfitting.
The usual explanatio |
38,434 | Does ensembling (boosting) cause overfitting? | I think a good way to see if you are overfitting is to see the agreement between the individual nodes in the ensemble. If you get a very high agreement of 95%, there is high chance that your model may be predicting a very low accuracy of the target variable. This would definitely be a high indicator that your model has... | Does ensembling (boosting) cause overfitting? | I think a good way to see if you are overfitting is to see the agreement between the individual nodes in the ensemble. If you get a very high agreement of 95%, there is high chance that your model may | Does ensembling (boosting) cause overfitting?
I think a good way to see if you are overfitting is to see the agreement between the individual nodes in the ensemble. If you get a very high agreement of 95%, there is high chance that your model may be predicting a very low accuracy of the target variable. This would defi... | Does ensembling (boosting) cause overfitting?
I think a good way to see if you are overfitting is to see the agreement between the individual nodes in the ensemble. If you get a very high agreement of 95%, there is high chance that your model may |
38,435 | How to detect structural change in a timeseries | @Dail if you're more inclined to the applied rather than the theoretical behind detection of structural break, you might want try http://cran.r-project.org/web/packages/cpm/index.html this is the link for CPM package of R, where you can use processStream to find multiple break point in your time series. | How to detect structural change in a timeseries | @Dail if you're more inclined to the applied rather than the theoretical behind detection of structural break, you might want try http://cran.r-project.org/web/packages/cpm/index.html this is the link | How to detect structural change in a timeseries
@Dail if you're more inclined to the applied rather than the theoretical behind detection of structural break, you might want try http://cran.r-project.org/web/packages/cpm/index.html this is the link for CPM package of R, where you can use processStream to find multiple ... | How to detect structural change in a timeseries
@Dail if you're more inclined to the applied rather than the theoretical behind detection of structural break, you might want try http://cran.r-project.org/web/packages/cpm/index.html this is the link |
38,436 | How to detect structural change in a timeseries | Change Points can arise from a number of possible causes. Each of the possible causes can be evaluated. In terms of increasing complexity : 1. detecting a change in the expected value is essentially Intervention Detection. Pursue the work of Ruey Tsay to understand what you need to do. His work does not cover detecting... | How to detect structural change in a timeseries | Change Points can arise from a number of possible causes. Each of the possible causes can be evaluated. In terms of increasing complexity : 1. detecting a change in the expected value is essentially I | How to detect structural change in a timeseries
Change Points can arise from a number of possible causes. Each of the possible causes can be evaluated. In terms of increasing complexity : 1. detecting a change in the expected value is essentially Intervention Detection. Pursue the work of Ruey Tsay to understand what y... | How to detect structural change in a timeseries
Change Points can arise from a number of possible causes. Each of the possible causes can be evaluated. In terms of increasing complexity : 1. detecting a change in the expected value is essentially I |
38,437 | How to detect structural change in a timeseries | Here's some demo R code that shows how to detect (endogenously) structural breaks in time series / longitudinal data.
# assuming you have a 'ts' object in R
# 1. install package 'strucchange'
# 2. Then write down this code:
library(strucchange)
# store the breakdates
bp_ts <- breakpoints(ts)
# this will give you t... | How to detect structural change in a timeseries | Here's some demo R code that shows how to detect (endogenously) structural breaks in time series / longitudinal data.
# assuming you have a 'ts' object in R
# 1. install package 'strucchange'
# 2. T | How to detect structural change in a timeseries
Here's some demo R code that shows how to detect (endogenously) structural breaks in time series / longitudinal data.
# assuming you have a 'ts' object in R
# 1. install package 'strucchange'
# 2. Then write down this code:
library(strucchange)
# store the breakdates
... | How to detect structural change in a timeseries
Here's some demo R code that shows how to detect (endogenously) structural breaks in time series / longitudinal data.
# assuming you have a 'ts' object in R
# 1. install package 'strucchange'
# 2. T |
38,438 | How to detect structural change in a timeseries | If you care the use of R, a selection of packages available are summarized in the CRAN task view on time series (https://cran.r-project.org/web/views/TimeSeries.html). Below is the relevant portion:
Change point detection is provided in strucchange and strucchangeRcpp
(using linear regression models) and in trend (usi... | How to detect structural change in a timeseries | If you care the use of R, a selection of packages available are summarized in the CRAN task view on time series (https://cran.r-project.org/web/views/TimeSeries.html). Below is the relevant portion:
| How to detect structural change in a timeseries
If you care the use of R, a selection of packages available are summarized in the CRAN task view on time series (https://cran.r-project.org/web/views/TimeSeries.html). Below is the relevant portion:
Change point detection is provided in strucchange and strucchangeRcpp
(u... | How to detect structural change in a timeseries
If you care the use of R, a selection of packages available are summarized in the CRAN task view on time series (https://cran.r-project.org/web/views/TimeSeries.html). Below is the relevant portion:
|
38,439 | How to detect structural change in a timeseries | Searching on Google scholar for "Bayesian changepoint detection" will produce some useful references, such as Adams and MacKay, which looks very interesting and sounds the sort of thing you are looking for. There is also a good book on "Numerical Bayesian Methods Applied to Signal Processing" by O'Ruanaidh and Fitzger... | How to detect structural change in a timeseries | Searching on Google scholar for "Bayesian changepoint detection" will produce some useful references, such as Adams and MacKay, which looks very interesting and sounds the sort of thing you are lookin | How to detect structural change in a timeseries
Searching on Google scholar for "Bayesian changepoint detection" will produce some useful references, such as Adams and MacKay, which looks very interesting and sounds the sort of thing you are looking for. There is also a good book on "Numerical Bayesian Methods Applied... | How to detect structural change in a timeseries
Searching on Google scholar for "Bayesian changepoint detection" will produce some useful references, such as Adams and MacKay, which looks very interesting and sounds the sort of thing you are lookin |
38,440 | How to detect structural change in a timeseries | @Dail -- You don't need to know the date in advance. There are many options beyond the Chow Test. In practice, the Chow test can be undesirable because it assumes homoskedasticity, which is very often violated in real time series data. There is a famous paper on testing for structural breaks when the break dates are un... | How to detect structural change in a timeseries | @Dail -- You don't need to know the date in advance. There are many options beyond the Chow Test. In practice, the Chow test can be undesirable because it assumes homoskedasticity, which is very often | How to detect structural change in a timeseries
@Dail -- You don't need to know the date in advance. There are many options beyond the Chow Test. In practice, the Chow test can be undesirable because it assumes homoskedasticity, which is very often violated in real time series data. There is a famous paper on testing f... | How to detect structural change in a timeseries
@Dail -- You don't need to know the date in advance. There are many options beyond the Chow Test. In practice, the Chow test can be undesirable because it assumes homoskedasticity, which is very often |
38,441 | How to detect structural change in a timeseries | I'd like to second what IrishStat has said and point you directly to two of Ruey Tsay's books:
Analysis of Financial Time Series, Third Edition, Wiley, 2010.
ISBN: 0-470-41435-9; 10-digits: 978-0470414354 (book's website with some R code)
An Introduction to Analysis of Financial Data with R, Wiley, 2013
ISBN: 0-470-89... | How to detect structural change in a timeseries | I'd like to second what IrishStat has said and point you directly to two of Ruey Tsay's books:
Analysis of Financial Time Series, Third Edition, Wiley, 2010.
ISBN: 0-470-41435-9; 10-digits: 978-04704 | How to detect structural change in a timeseries
I'd like to second what IrishStat has said and point you directly to two of Ruey Tsay's books:
Analysis of Financial Time Series, Third Edition, Wiley, 2010.
ISBN: 0-470-41435-9; 10-digits: 978-0470414354 (book's website with some R code)
An Introduction to Analysis of F... | How to detect structural change in a timeseries
I'd like to second what IrishStat has said and point you directly to two of Ruey Tsay's books:
Analysis of Financial Time Series, Third Edition, Wiley, 2010.
ISBN: 0-470-41435-9; 10-digits: 978-04704 |
38,442 | How to detect structural change in a timeseries | Chow test, multiple break-point test (such as Bia Perron test), Quant-Andrews break point test etc. are different test available in Eviews.
Read description, assumptions and interpretation of each test before applying it your data set. | How to detect structural change in a timeseries | Chow test, multiple break-point test (such as Bia Perron test), Quant-Andrews break point test etc. are different test available in Eviews.
Read description, assumptions and interpretation of each tes | How to detect structural change in a timeseries
Chow test, multiple break-point test (such as Bia Perron test), Quant-Andrews break point test etc. are different test available in Eviews.
Read description, assumptions and interpretation of each test before applying it your data set. | How to detect structural change in a timeseries
Chow test, multiple break-point test (such as Bia Perron test), Quant-Andrews break point test etc. are different test available in Eviews.
Read description, assumptions and interpretation of each tes |
38,443 | What are good techniques and resources for teaching Bayes theorem? | I have to recommend the book "Doing Bayesian Data Analysis" by John Kruschke (Indiana). Having sampled a few "introductory" texts over the last while, this one really shines.
There are many really well explained points but I suppose the best lever he uses to introduce the notion of combining prior and evidence is to in... | What are good techniques and resources for teaching Bayes theorem? | I have to recommend the book "Doing Bayesian Data Analysis" by John Kruschke (Indiana). Having sampled a few "introductory" texts over the last while, this one really shines.
There are many really wel | What are good techniques and resources for teaching Bayes theorem?
I have to recommend the book "Doing Bayesian Data Analysis" by John Kruschke (Indiana). Having sampled a few "introductory" texts over the last while, this one really shines.
There are many really well explained points but I suppose the best lever he us... | What are good techniques and resources for teaching Bayes theorem?
I have to recommend the book "Doing Bayesian Data Analysis" by John Kruschke (Indiana). Having sampled a few "introductory" texts over the last while, this one really shines.
There are many really wel |
38,444 | What are good techniques and resources for teaching Bayes theorem? | For the basic Bayes Formula one common example to use is disease screening. Assume that you have a test for a disease that if used on someone who has the disease will show positive with 95% probability and if used with someone without the disease will show negative with 90% probability; further we know that 1 in 1,000... | What are good techniques and resources for teaching Bayes theorem? | For the basic Bayes Formula one common example to use is disease screening. Assume that you have a test for a disease that if used on someone who has the disease will show positive with 95% probabili | What are good techniques and resources for teaching Bayes theorem?
For the basic Bayes Formula one common example to use is disease screening. Assume that you have a test for a disease that if used on someone who has the disease will show positive with 95% probability and if used with someone without the disease will ... | What are good techniques and resources for teaching Bayes theorem?
For the basic Bayes Formula one common example to use is disease screening. Assume that you have a test for a disease that if used on someone who has the disease will show positive with 95% probabili |
38,445 | What are good techniques and resources for teaching Bayes theorem? | The LessWrong website actually has a great visual explanation of Bayes' Theorem: Bayes' Theorem Illustrated (My Way). | What are good techniques and resources for teaching Bayes theorem? | The LessWrong website actually has a great visual explanation of Bayes' Theorem: Bayes' Theorem Illustrated (My Way). | What are good techniques and resources for teaching Bayes theorem?
The LessWrong website actually has a great visual explanation of Bayes' Theorem: Bayes' Theorem Illustrated (My Way). | What are good techniques and resources for teaching Bayes theorem?
The LessWrong website actually has a great visual explanation of Bayes' Theorem: Bayes' Theorem Illustrated (My Way). |
38,446 | What are good techniques and resources for teaching Bayes theorem? | Use a deck of cards.
What are the chances this card is a spade? What are the chances this card is a spade if I know the card is black?
What are the chances this card is a king? What are the chances this card is a king if I know it is a diamond? What are the chances it is a king if I know it is a face card?
Show ... | What are good techniques and resources for teaching Bayes theorem? | Use a deck of cards.
What are the chances this card is a spade? What are the chances this card is a spade if I know the card is black?
What are the chances this card is a king? What are the chance | What are good techniques and resources for teaching Bayes theorem?
Use a deck of cards.
What are the chances this card is a spade? What are the chances this card is a spade if I know the card is black?
What are the chances this card is a king? What are the chances this card is a king if I know it is a diamond? Wha... | What are good techniques and resources for teaching Bayes theorem?
Use a deck of cards.
What are the chances this card is a spade? What are the chances this card is a spade if I know the card is black?
What are the chances this card is a king? What are the chance |
38,447 | Is there an R package with a pretty function that can deal effectively with outliers? | If you're importing your data with a command like, say,
read.table('yourfile.txt', header=TRUE, ...)
you can indicate what values are to be considered as "null" or NA values, by specifying na.strings = "999999999". We can also consider different values for indicating NA values. Consider the following file (fake.txt) w... | Is there an R package with a pretty function that can deal effectively with outliers? | If you're importing your data with a command like, say,
read.table('yourfile.txt', header=TRUE, ...)
you can indicate what values are to be considered as "null" or NA values, by specifying na.strings | Is there an R package with a pretty function that can deal effectively with outliers?
If you're importing your data with a command like, say,
read.table('yourfile.txt', header=TRUE, ...)
you can indicate what values are to be considered as "null" or NA values, by specifying na.strings = "999999999". We can also consid... | Is there an R package with a pretty function that can deal effectively with outliers?
If you're importing your data with a command like, say,
read.table('yourfile.txt', header=TRUE, ...)
you can indicate what values are to be considered as "null" or NA values, by specifying na.strings |
38,448 | Is there an R package with a pretty function that can deal effectively with outliers? | I encounter this quite frequently when dealing with customer daily time series data. It appears that many accounting systems IGNORE daily data that didn't occur i.e. no transactions were recorded for that day (time interval/bucket) and don't fill in a '0" number . Since time series analysis require a reading for every ... | Is there an R package with a pretty function that can deal effectively with outliers? | I encounter this quite frequently when dealing with customer daily time series data. It appears that many accounting systems IGNORE daily data that didn't occur i.e. no transactions were recorded for | Is there an R package with a pretty function that can deal effectively with outliers?
I encounter this quite frequently when dealing with customer daily time series data. It appears that many accounting systems IGNORE daily data that didn't occur i.e. no transactions were recorded for that day (time interval/bucket) an... | Is there an R package with a pretty function that can deal effectively with outliers?
I encounter this quite frequently when dealing with customer daily time series data. It appears that many accounting systems IGNORE daily data that didn't occur i.e. no transactions were recorded for |
38,449 | L1 & L2 double role in Regularization and Cost functions? | They are distinct notions.
Point #2 refers to the usual kind of loss function. The first example almost anyone who studies statistics or data analysis of any kind sees is the square loss in ordinary least squares linear regression: add up the squared residuals.
$$
L(y,\hat y)=\overset{n}{\underset{i=1}{\sum}}\left(
y_i... | L1 & L2 double role in Regularization and Cost functions? | They are distinct notions.
Point #2 refers to the usual kind of loss function. The first example almost anyone who studies statistics or data analysis of any kind sees is the square loss in ordinary l | L1 & L2 double role in Regularization and Cost functions?
They are distinct notions.
Point #2 refers to the usual kind of loss function. The first example almost anyone who studies statistics or data analysis of any kind sees is the square loss in ordinary least squares linear regression: add up the squared residuals.
... | L1 & L2 double role in Regularization and Cost functions?
They are distinct notions.
Point #2 refers to the usual kind of loss function. The first example almost anyone who studies statistics or data analysis of any kind sees is the square loss in ordinary l |
38,450 | L1 & L2 double role in Regularization and Cost functions? | no, they refer to two different things:
prior over parameters (that's your belief of how the parameters should be distributed)
assumption on the "noise" of the measurements (given an observation, what's the distribution that you think describes the noise)
MAE and L1 is a Laplacian prior, MSE and L2 is a Gaussian like... | L1 & L2 double role in Regularization and Cost functions? | no, they refer to two different things:
prior over parameters (that's your belief of how the parameters should be distributed)
assumption on the "noise" of the measurements (given an observation, wha | L1 & L2 double role in Regularization and Cost functions?
no, they refer to two different things:
prior over parameters (that's your belief of how the parameters should be distributed)
assumption on the "noise" of the measurements (given an observation, what's the distribution that you think describes the noise)
MAE ... | L1 & L2 double role in Regularization and Cost functions?
no, they refer to two different things:
prior over parameters (that's your belief of how the parameters should be distributed)
assumption on the "noise" of the measurements (given an observation, wha |
38,451 | L1 & L2 double role in Regularization and Cost functions? | The terms "L1" and "L2" refer to special functions called norms, which measure the length or size of a vector. You are correct in that they are used in two different contexts in statistics and machine learning, but their meanings are the same in both contexts.
In the context of regularization, the L1 and/or L2 norm re... | L1 & L2 double role in Regularization and Cost functions? | The terms "L1" and "L2" refer to special functions called norms, which measure the length or size of a vector. You are correct in that they are used in two different contexts in statistics and machine | L1 & L2 double role in Regularization and Cost functions?
The terms "L1" and "L2" refer to special functions called norms, which measure the length or size of a vector. You are correct in that they are used in two different contexts in statistics and machine learning, but their meanings are the same in both contexts.
... | L1 & L2 double role in Regularization and Cost functions?
The terms "L1" and "L2" refer to special functions called norms, which measure the length or size of a vector. You are correct in that they are used in two different contexts in statistics and machine |
38,452 | What type of regression to use when outcome is integers from 0 to 5 | @Doctor Milt's response is on the right track, but I think this is much more naturally handled using a multilevel logistic (or probit) regression, each person's response to each item (0 or 1) as the outcome variable.
You would definitely want to allow the average probability of a 1 vary across participants and across q... | What type of regression to use when outcome is integers from 0 to 5 | @Doctor Milt's response is on the right track, but I think this is much more naturally handled using a multilevel logistic (or probit) regression, each person's response to each item (0 or 1) as the o | What type of regression to use when outcome is integers from 0 to 5
@Doctor Milt's response is on the right track, but I think this is much more naturally handled using a multilevel logistic (or probit) regression, each person's response to each item (0 or 1) as the outcome variable.
You would definitely want to allow ... | What type of regression to use when outcome is integers from 0 to 5
@Doctor Milt's response is on the right track, but I think this is much more naturally handled using a multilevel logistic (or probit) regression, each person's response to each item (0 or 1) as the o |
38,453 | What type of regression to use when outcome is integers from 0 to 5 | I like the idea of a Bernoulli model, as you could start with some strong assumptions and gradually relax them.
Let $Y_{ij} \sim \mathrm{Bernoulli}(p_{ij})$, $i=1,\ldots,n$, $j=1,\ldots,5$, be the response given by the $i$th person to the $j$th question. The probability $p_{ij}$ is a function of the explanatory variabl... | What type of regression to use when outcome is integers from 0 to 5 | I like the idea of a Bernoulli model, as you could start with some strong assumptions and gradually relax them.
Let $Y_{ij} \sim \mathrm{Bernoulli}(p_{ij})$, $i=1,\ldots,n$, $j=1,\ldots,5$, be the res | What type of regression to use when outcome is integers from 0 to 5
I like the idea of a Bernoulli model, as you could start with some strong assumptions and gradually relax them.
Let $Y_{ij} \sim \mathrm{Bernoulli}(p_{ij})$, $i=1,\ldots,n$, $j=1,\ldots,5$, be the response given by the $i$th person to the $j$th questio... | What type of regression to use when outcome is integers from 0 to 5
I like the idea of a Bernoulli model, as you could start with some strong assumptions and gradually relax them.
Let $Y_{ij} \sim \mathrm{Bernoulli}(p_{ij})$, $i=1,\ldots,n$, $j=1,\ldots,5$, be the res |
38,454 | Interpreting the Lambdas of Yeo Johnson Transformation? | A table adds little, but a picture can add a lot more to our understanding. I offer two pictures.
Unlike the Box-Cox transformation, which applies to positive numbers, the Yeo-Johnson transformation applies to all numbers. It does so by splitting the real line at zero, shifting the positive values by $1$ and the neg... | Interpreting the Lambdas of Yeo Johnson Transformation? | A table adds little, but a picture can add a lot more to our understanding. I offer two pictures.
Unlike the Box-Cox transformation, which applies to positive numbers, the Yeo-Johnson transformation | Interpreting the Lambdas of Yeo Johnson Transformation?
A table adds little, but a picture can add a lot more to our understanding. I offer two pictures.
Unlike the Box-Cox transformation, which applies to positive numbers, the Yeo-Johnson transformation applies to all numbers. It does so by splitting the real line ... | Interpreting the Lambdas of Yeo Johnson Transformation?
A table adds little, but a picture can add a lot more to our understanding. I offer two pictures.
Unlike the Box-Cox transformation, which applies to positive numbers, the Yeo-Johnson transformation |
38,455 | What is the 'right' slope formula of a regression? deltas or Pearson? | For only two points they are the same.
The slope of simple linear regression is
$$
\hat \beta = \frac{\sum_i (x_i - \bar x) (y_i - \bar y)}{\sum_i (x_i - \bar x)^2}
$$
that is the same form you mentioned in the second bullet. Notice that when we have two points, then things like $x_1 - \bar x$ can be written as
$$
x_1 ... | What is the 'right' slope formula of a regression? deltas or Pearson? | For only two points they are the same.
The slope of simple linear regression is
$$
\hat \beta = \frac{\sum_i (x_i - \bar x) (y_i - \bar y)}{\sum_i (x_i - \bar x)^2}
$$
that is the same form you mentio | What is the 'right' slope formula of a regression? deltas or Pearson?
For only two points they are the same.
The slope of simple linear regression is
$$
\hat \beta = \frac{\sum_i (x_i - \bar x) (y_i - \bar y)}{\sum_i (x_i - \bar x)^2}
$$
that is the same form you mentioned in the second bullet. Notice that when we have... | What is the 'right' slope formula of a regression? deltas or Pearson?
For only two points they are the same.
The slope of simple linear regression is
$$
\hat \beta = \frac{\sum_i (x_i - \bar x) (y_i - \bar y)}{\sum_i (x_i - \bar x)^2}
$$
that is the same form you mentio |
38,456 | What is the 'right' slope formula of a regression? deltas or Pearson? | These are fairly unrelated concepts.
In the first equation, that is the slope of the line connecting two points.
In the second, you are finding a line that fits multiple points best (according to a particular and common definition of best). This line is called the ordinary least squares regression line. This is what is... | What is the 'right' slope formula of a regression? deltas or Pearson? | These are fairly unrelated concepts.
In the first equation, that is the slope of the line connecting two points.
In the second, you are finding a line that fits multiple points best (according to a pa | What is the 'right' slope formula of a regression? deltas or Pearson?
These are fairly unrelated concepts.
In the first equation, that is the slope of the line connecting two points.
In the second, you are finding a line that fits multiple points best (according to a particular and common definition of best). This line... | What is the 'right' slope formula of a regression? deltas or Pearson?
These are fairly unrelated concepts.
In the first equation, that is the slope of the line connecting two points.
In the second, you are finding a line that fits multiple points best (according to a pa |
38,457 | Trying to understand Bootstrapping w/ Python | When you calculate your lower and upper bounds, you are dividing your standard deviations of your means by $\sqrt{1000}$, which I assume you are doing because you want to convert your standard deviation to a standard error. But the standard deviation you are using is the standard deviation (or standard error) of the me... | Trying to understand Bootstrapping w/ Python | When you calculate your lower and upper bounds, you are dividing your standard deviations of your means by $\sqrt{1000}$, which I assume you are doing because you want to convert your standard deviati | Trying to understand Bootstrapping w/ Python
When you calculate your lower and upper bounds, you are dividing your standard deviations of your means by $\sqrt{1000}$, which I assume you are doing because you want to convert your standard deviation to a standard error. But the standard deviation you are using is the sta... | Trying to understand Bootstrapping w/ Python
When you calculate your lower and upper bounds, you are dividing your standard deviations of your means by $\sqrt{1000}$, which I assume you are doing because you want to convert your standard deviati |
38,458 | Trying to understand Bootstrapping w/ Python | This is a comment to complement @Lynn's answer (+1) which explains the big mistake in your implementation of the bootstrap.
There is another error. It's more subtle as it doesn't have an obvious effect on the coverage of the confidence interval: You should use the sample statistic, not the average of the bootstrapped s... | Trying to understand Bootstrapping w/ Python | This is a comment to complement @Lynn's answer (+1) which explains the big mistake in your implementation of the bootstrap.
There is another error. It's more subtle as it doesn't have an obvious effec | Trying to understand Bootstrapping w/ Python
This is a comment to complement @Lynn's answer (+1) which explains the big mistake in your implementation of the bootstrap.
There is another error. It's more subtle as it doesn't have an obvious effect on the coverage of the confidence interval: You should use the sample sta... | Trying to understand Bootstrapping w/ Python
This is a comment to complement @Lynn's answer (+1) which explains the big mistake in your implementation of the bootstrap.
There is another error. It's more subtle as it doesn't have an obvious effec |
38,459 | How to find median value for five given elements based on the max min and sum of the elements | If you only know the min, max, and sum of the 5 numbers, you cannot determine the median.
E.g.
median(1, 2, 3, 4, 5)=3
median(1, 2.1, 2.8, 4.1, 5)=2.8.
But both have (min, max, sum) = (1, 5, 15). | How to find median value for five given elements based on the max min and sum of the elements | If you only know the min, max, and sum of the 5 numbers, you cannot determine the median.
E.g.
median(1, 2, 3, 4, 5)=3
median(1, 2.1, 2.8, 4.1, 5)=2.8.
But both have (min, max, sum) = (1, 5, 15). | How to find median value for five given elements based on the max min and sum of the elements
If you only know the min, max, and sum of the 5 numbers, you cannot determine the median.
E.g.
median(1, 2, 3, 4, 5)=3
median(1, 2.1, 2.8, 4.1, 5)=2.8.
But both have (min, max, sum) = (1, 5, 15). | How to find median value for five given elements based on the max min and sum of the elements
If you only know the min, max, and sum of the 5 numbers, you cannot determine the median.
E.g.
median(1, 2, 3, 4, 5)=3
median(1, 2.1, 2.8, 4.1, 5)=2.8.
But both have (min, max, sum) = (1, 5, 15). |
38,460 | How to find median value for five given elements based on the max min and sum of the elements | Find the max and min of the initial list.
Create a new list without those 2 elements.
Find the new max, min and sum and use the method you mentioned,
median = sum - min - max | How to find median value for five given elements based on the max min and sum of the elements | Find the max and min of the initial list.
Create a new list without those 2 elements.
Find the new max, min and sum and use the method you mentioned,
median = sum - min - max | How to find median value for five given elements based on the max min and sum of the elements
Find the max and min of the initial list.
Create a new list without those 2 elements.
Find the new max, min and sum and use the method you mentioned,
median = sum - min - max | How to find median value for five given elements based on the max min and sum of the elements
Find the max and min of the initial list.
Create a new list without those 2 elements.
Find the new max, min and sum and use the method you mentioned,
median = sum - min - max |
38,461 | Asymptotic Normality and Consistency | Convergence to a constant does not mean that you have an estimator that is exactly equal to this constant at any given time. It just means that given a big enough sample size, you can expect that you estimator will be close to the true value of the parameter.
Asymptotic normality most often includes some sort of a scal... | Asymptotic Normality and Consistency | Convergence to a constant does not mean that you have an estimator that is exactly equal to this constant at any given time. It just means that given a big enough sample size, you can expect that you | Asymptotic Normality and Consistency
Convergence to a constant does not mean that you have an estimator that is exactly equal to this constant at any given time. It just means that given a big enough sample size, you can expect that you estimator will be close to the true value of the parameter.
Asymptotic normality mo... | Asymptotic Normality and Consistency
Convergence to a constant does not mean that you have an estimator that is exactly equal to this constant at any given time. It just means that given a big enough sample size, you can expect that you |
38,462 | Asymptotic Normality and Consistency | I think you may either be confused with the modes of convergence associated with consistency and asymptotic normality or with the definition of consistency. It is important to note that consistency is defined as convergence to the true value of the parameter of interest. Regardless, let us begin with the definitions,
W... | Asymptotic Normality and Consistency | I think you may either be confused with the modes of convergence associated with consistency and asymptotic normality or with the definition of consistency. It is important to note that consistency is | Asymptotic Normality and Consistency
I think you may either be confused with the modes of convergence associated with consistency and asymptotic normality or with the definition of consistency. It is important to note that consistency is defined as convergence to the true value of the parameter of interest. Regardless,... | Asymptotic Normality and Consistency
I think you may either be confused with the modes of convergence associated with consistency and asymptotic normality or with the definition of consistency. It is important to note that consistency is |
38,463 | Biased estimates in logistic regression due to class imbalance | Let's find out.
To begin with, what happens with balanced datasets?
Here is a scatterplot of a dataset of $200$ observations, of which $50\%$ are zeros and the remainder are ones. On it I have graphed the underlying ("true") probabilities and the probabilities as fit with logistic regression. The two graphs agree clo... | Biased estimates in logistic regression due to class imbalance | Let's find out.
To begin with, what happens with balanced datasets?
Here is a scatterplot of a dataset of $200$ observations, of which $50\%$ are zeros and the remainder are ones. On it I have graphe | Biased estimates in logistic regression due to class imbalance
Let's find out.
To begin with, what happens with balanced datasets?
Here is a scatterplot of a dataset of $200$ observations, of which $50\%$ are zeros and the remainder are ones. On it I have graphed the underlying ("true") probabilities and the probabili... | Biased estimates in logistic regression due to class imbalance
Let's find out.
To begin with, what happens with balanced datasets?
Here is a scatterplot of a dataset of $200$ observations, of which $50\%$ are zeros and the remainder are ones. On it I have graphe |
38,464 | Number of expected pairs in a random shuffle | First, we find the probability that two adjacent individuals are of different genders. Those two people are equally likely to be any of the ${34 \choose 2}$ pairs of people, of which $18 \times 16$ are male-female pairs, so this probability is $(18 \times 16)/{34 \choose 2}$.
The total number of pairs is $X_1 + X_2 ... | Number of expected pairs in a random shuffle | First, we find the probability that two adjacent individuals are of different genders. Those two people are equally likely to be any of the ${34 \choose 2}$ pairs of people, of which $18 \times 16$ | Number of expected pairs in a random shuffle
First, we find the probability that two adjacent individuals are of different genders. Those two people are equally likely to be any of the ${34 \choose 2}$ pairs of people, of which $18 \times 16$ are male-female pairs, so this probability is $(18 \times 16)/{34 \choose ... | Number of expected pairs in a random shuffle
First, we find the probability that two adjacent individuals are of different genders. Those two people are equally likely to be any of the ${34 \choose 2}$ pairs of people, of which $18 \times 16$ |
38,465 | Number of expected pairs in a random shuffle | Someone much wiser then me will post a theoretical and exact solution. Meanwhile my attempt at a simulation:
once <- function(){
row <- sample(c(rep("m", 18), rep("f",16)))
count <- 0
for(i in 1:33){
if(row[i]!=row[i+1])
count <- count + 1
}
return(count)
}
run <- replicate(1e5, o... | Number of expected pairs in a random shuffle | Someone much wiser then me will post a theoretical and exact solution. Meanwhile my attempt at a simulation:
once <- function(){
row <- sample(c(rep("m", 18), rep("f",16)))
count <- 0
for( | Number of expected pairs in a random shuffle
Someone much wiser then me will post a theoretical and exact solution. Meanwhile my attempt at a simulation:
once <- function(){
row <- sample(c(rep("m", 18), rep("f",16)))
count <- 0
for(i in 1:33){
if(row[i]!=row[i+1])
count <- count + 1
}
... | Number of expected pairs in a random shuffle
Someone much wiser then me will post a theoretical and exact solution. Meanwhile my attempt at a simulation:
once <- function(){
row <- sample(c(rep("m", 18), rep("f",16)))
count <- 0
for( |
38,466 | What are the advantages of FC layers over Conv layers? | The strength of convolutional layers over fully connected layers is precisely that they represent a narrower range of features than fully-connected layers. A neuron in a fully connected layer is connected to every neuron in the preceding layer, and so can change if any of the neurons from the preceding layer changes. A... | What are the advantages of FC layers over Conv layers? | The strength of convolutional layers over fully connected layers is precisely that they represent a narrower range of features than fully-connected layers. A neuron in a fully connected layer is conne | What are the advantages of FC layers over Conv layers?
The strength of convolutional layers over fully connected layers is precisely that they represent a narrower range of features than fully-connected layers. A neuron in a fully connected layer is connected to every neuron in the preceding layer, and so can change if... | What are the advantages of FC layers over Conv layers?
The strength of convolutional layers over fully connected layers is precisely that they represent a narrower range of features than fully-connected layers. A neuron in a fully connected layer is conne |
38,467 | What are the advantages of FC layers over Conv layers? | As mentioned in the wiki article, convolutional layers are optimized for translationally-invariant parameters, such as pixel intensities in images and video. If your parameters represent a discretized sample of a continuous variable, such as space or time, then translational invariance means that every window of the pa... | What are the advantages of FC layers over Conv layers? | As mentioned in the wiki article, convolutional layers are optimized for translationally-invariant parameters, such as pixel intensities in images and video. If your parameters represent a discretized | What are the advantages of FC layers over Conv layers?
As mentioned in the wiki article, convolutional layers are optimized for translationally-invariant parameters, such as pixel intensities in images and video. If your parameters represent a discretized sample of a continuous variable, such as space or time, then tra... | What are the advantages of FC layers over Conv layers?
As mentioned in the wiki article, convolutional layers are optimized for translationally-invariant parameters, such as pixel intensities in images and video. If your parameters represent a discretized |
38,468 | Why is considering a maximum likelihood as a random variable a frequentist approach? | This is a frequentist approach because we are considering $\mu$ to be fixed. Thus, all the variance of $\hat \mu$ comes from the data.
Technically, a Bayesian would say that $V[\hat \mu] = V[\mu] + V[\hat \mu | \mu]$ (assuming the variance of $\hat \mu$ is independent of $\mu$).
But more over, I think the authors are... | Why is considering a maximum likelihood as a random variable a frequentist approach? | This is a frequentist approach because we are considering $\mu$ to be fixed. Thus, all the variance of $\hat \mu$ comes from the data.
Technically, a Bayesian would say that $V[\hat \mu] = V[\mu] + V | Why is considering a maximum likelihood as a random variable a frequentist approach?
This is a frequentist approach because we are considering $\mu$ to be fixed. Thus, all the variance of $\hat \mu$ comes from the data.
Technically, a Bayesian would say that $V[\hat \mu] = V[\mu] + V[\hat \mu | \mu]$ (assuming the var... | Why is considering a maximum likelihood as a random variable a frequentist approach?
This is a frequentist approach because we are considering $\mu$ to be fixed. Thus, all the variance of $\hat \mu$ comes from the data.
Technically, a Bayesian would say that $V[\hat \mu] = V[\mu] + V |
38,469 | Why is considering a maximum likelihood as a random variable a frequentist approach? | Considering an MLE as a random variable is not exclusively a frequentist approach, and indeed, the author you quote does not claim this. The operative word in the quote is "and" --- we use a frequentist approach and consider the maximum likelihood estimator as a random variable. The latter is not an exclusive consequ... | Why is considering a maximum likelihood as a random variable a frequentist approach? | Considering an MLE as a random variable is not exclusively a frequentist approach, and indeed, the author you quote does not claim this. The operative word in the quote is "and" --- we use a frequent | Why is considering a maximum likelihood as a random variable a frequentist approach?
Considering an MLE as a random variable is not exclusively a frequentist approach, and indeed, the author you quote does not claim this. The operative word in the quote is "and" --- we use a frequentist approach and consider the maxim... | Why is considering a maximum likelihood as a random variable a frequentist approach?
Considering an MLE as a random variable is not exclusively a frequentist approach, and indeed, the author you quote does not claim this. The operative word in the quote is "and" --- we use a frequent |
38,470 | Accounting for grouped random effects in lme4 | A couple of points:
If I understood correctly, your response variable is a grade, ranging from 1 to 5. This is an ordinal variable with relatively few levels. Hence, assuming a normal distribution for the residuals may not be appropriate. You could consider a mixed model for ordinal data instead, such as the continuat... | Accounting for grouped random effects in lme4 | A couple of points:
If I understood correctly, your response variable is a grade, ranging from 1 to 5. This is an ordinal variable with relatively few levels. Hence, assuming a normal distribution fo | Accounting for grouped random effects in lme4
A couple of points:
If I understood correctly, your response variable is a grade, ranging from 1 to 5. This is an ordinal variable with relatively few levels. Hence, assuming a normal distribution for the residuals may not be appropriate. You could consider a mixed model f... | Accounting for grouped random effects in lme4
A couple of points:
If I understood correctly, your response variable is a grade, ranging from 1 to 5. This is an ordinal variable with relatively few levels. Hence, assuming a normal distribution fo |
38,471 | Accounting for grouped random effects in lme4 | If you believe the different categories vary in terms of their measurement and you want to test that, you need to model the category as a random intercept with (1|category).
However, I think we need more information as to what you are actually looking to decide. For example, are you wondering if each person measures th... | Accounting for grouped random effects in lme4 | If you believe the different categories vary in terms of their measurement and you want to test that, you need to model the category as a random intercept with (1|category).
However, I think we need m | Accounting for grouped random effects in lme4
If you believe the different categories vary in terms of their measurement and you want to test that, you need to model the category as a random intercept with (1|category).
However, I think we need more information as to what you are actually looking to decide. For example... | Accounting for grouped random effects in lme4
If you believe the different categories vary in terms of their measurement and you want to test that, you need to model the category as a random intercept with (1|category).
However, I think we need m |
38,472 | Accounting for grouped random effects in lme4 | It seems that in the model:
lmer(measure ~ category + (1|subject) + (1|stimulus), data = My_data)
category is being used to denote the levels of stimulus. As such, this does not make sense, since category is not an actual variable.
Even though stimulus is random in the sense that it has (presumably) been randomly assi... | Accounting for grouped random effects in lme4 | It seems that in the model:
lmer(measure ~ category + (1|subject) + (1|stimulus), data = My_data)
category is being used to denote the levels of stimulus. As such, this does not make sense, since cat | Accounting for grouped random effects in lme4
It seems that in the model:
lmer(measure ~ category + (1|subject) + (1|stimulus), data = My_data)
category is being used to denote the levels of stimulus. As such, this does not make sense, since category is not an actual variable.
Even though stimulus is random in the sen... | Accounting for grouped random effects in lme4
It seems that in the model:
lmer(measure ~ category + (1|subject) + (1|stimulus), data = My_data)
category is being used to denote the levels of stimulus. As such, this does not make sense, since cat |
38,473 | Accounting for grouped random effects in lme4 | In your setting, subject and stimulus seem to be fully crossed random grouping factors - since each subject sees each stimulus and (I am assuming) you are using the subjects and stimuli included in your studies to represent all the subjects and all the stimuli you wish to generalize your study findings to.
The key word... | Accounting for grouped random effects in lme4 | In your setting, subject and stimulus seem to be fully crossed random grouping factors - since each subject sees each stimulus and (I am assuming) you are using the subjects and stimuli included in yo | Accounting for grouped random effects in lme4
In your setting, subject and stimulus seem to be fully crossed random grouping factors - since each subject sees each stimulus and (I am assuming) you are using the subjects and stimuli included in your studies to represent all the subjects and all the stimuli you wish to g... | Accounting for grouped random effects in lme4
In your setting, subject and stimulus seem to be fully crossed random grouping factors - since each subject sees each stimulus and (I am assuming) you are using the subjects and stimuli included in yo |
38,474 | Accounting for grouped random effects in lme4 | One important point is what you mean by "a1:c4 at day 1 are different from a1:c4 at day 2 and so on". If this means that the a1 from day 1 is not more linked to a1 from day 2 that to a2 from day 2, then you don't have 10 simulations, but 10x30= 300 simulations (90 from category A, 90 from category B and 120 from catego... | Accounting for grouped random effects in lme4 | One important point is what you mean by "a1:c4 at day 1 are different from a1:c4 at day 2 and so on". If this means that the a1 from day 1 is not more linked to a1 from day 2 that to a2 from day 2, th | Accounting for grouped random effects in lme4
One important point is what you mean by "a1:c4 at day 1 are different from a1:c4 at day 2 and so on". If this means that the a1 from day 1 is not more linked to a1 from day 2 that to a2 from day 2, then you don't have 10 simulations, but 10x30= 300 simulations (90 from cate... | Accounting for grouped random effects in lme4
One important point is what you mean by "a1:c4 at day 1 are different from a1:c4 at day 2 and so on". If this means that the a1 from day 1 is not more linked to a1 from day 2 that to a2 from day 2, th |
38,475 | Is the average of betas from Y ~ X and X ~ Y valid? | To see the connection between both representations, take a bivariate Normal vector:
$$
\begin{pmatrix}
X_1 \\
X_2
\end{pmatrix} \sim \mathcal{N} \left( \begin{pmatrix}
\mu_1 \\
\mu_2
\end{pmatrix} , \begin{pmatrix}
\sigma^2_1 & \rho \sigma_1 \sigma_2 \\
\rho \sigma_1 \sigma_2 & \sigma^2_2
\end{pmatrix} \right)... | Is the average of betas from Y ~ X and X ~ Y valid? | To see the connection between both representations, take a bivariate Normal vector:
$$
\begin{pmatrix}
X_1 \\
X_2
\end{pmatrix} \sim \mathcal{N} \left( \begin{pmatrix}
\mu_1 \\
\mu_2
\end{pmatrix | Is the average of betas from Y ~ X and X ~ Y valid?
To see the connection between both representations, take a bivariate Normal vector:
$$
\begin{pmatrix}
X_1 \\
X_2
\end{pmatrix} \sim \mathcal{N} \left( \begin{pmatrix}
\mu_1 \\
\mu_2
\end{pmatrix} , \begin{pmatrix}
\sigma^2_1 & \rho \sigma_1 \sigma_2 \\
\rho \... | Is the average of betas from Y ~ X and X ~ Y valid?
To see the connection between both representations, take a bivariate Normal vector:
$$
\begin{pmatrix}
X_1 \\
X_2
\end{pmatrix} \sim \mathcal{N} \left( \begin{pmatrix}
\mu_1 \\
\mu_2
\end{pmatrix |
38,476 | Is the average of betas from Y ~ X and X ~ Y valid? | Converted from a comment.....
The exact values of $\beta$ and $\gamma$
can be found in this answer of mine to Effect of switching responses and explanatory variables in simple linear regression, and, as you suspect,
$\beta$ is not the reciprocal of $\gamma$, and averaging $\beta$ and $\gamma$
(or averaging $\beta$ and ... | Is the average of betas from Y ~ X and X ~ Y valid? | Converted from a comment.....
The exact values of $\beta$ and $\gamma$
can be found in this answer of mine to Effect of switching responses and explanatory variables in simple linear regression, and, | Is the average of betas from Y ~ X and X ~ Y valid?
Converted from a comment.....
The exact values of $\beta$ and $\gamma$
can be found in this answer of mine to Effect of switching responses and explanatory variables in simple linear regression, and, as you suspect,
$\beta$ is not the reciprocal of $\gamma$, and avera... | Is the average of betas from Y ~ X and X ~ Y valid?
Converted from a comment.....
The exact values of $\beta$ and $\gamma$
can be found in this answer of mine to Effect of switching responses and explanatory variables in simple linear regression, and, |
38,477 | Is the average of betas from Y ~ X and X ~ Y valid? | $\beta$ and $\gamma$
As Xi'an noted in his answer the $\beta$ and $\gamma$ are related to each other by relating to the conditional means $X|Y$ and $Y|X$ (which in their turn relate to a single joint distribution) these are not symmetric in the sense that $\beta \neq 1/\gamma$. This is neither the case if you would 'kn... | Is the average of betas from Y ~ X and X ~ Y valid? | $\beta$ and $\gamma$
As Xi'an noted in his answer the $\beta$ and $\gamma$ are related to each other by relating to the conditional means $X|Y$ and $Y|X$ (which in their turn relate to a single joint | Is the average of betas from Y ~ X and X ~ Y valid?
$\beta$ and $\gamma$
As Xi'an noted in his answer the $\beta$ and $\gamma$ are related to each other by relating to the conditional means $X|Y$ and $Y|X$ (which in their turn relate to a single joint distribution) these are not symmetric in the sense that $\beta \neq ... | Is the average of betas from Y ~ X and X ~ Y valid?
$\beta$ and $\gamma$
As Xi'an noted in his answer the $\beta$ and $\gamma$ are related to each other by relating to the conditional means $X|Y$ and $Y|X$ (which in their turn relate to a single joint |
38,478 | Is the average of betas from Y ~ X and X ~ Y valid? | Perhaps the approach of "Granger causality" might help. This would help you to assess whether X is a good predictor of Y or whether X is a better of Y. In other words, it tells you whether beta or gamma is the thing to take more seriously. Also, considering that you are dealing with time series data, it tells you how m... | Is the average of betas from Y ~ X and X ~ Y valid? | Perhaps the approach of "Granger causality" might help. This would help you to assess whether X is a good predictor of Y or whether X is a better of Y. In other words, it tells you whether beta or gam | Is the average of betas from Y ~ X and X ~ Y valid?
Perhaps the approach of "Granger causality" might help. This would help you to assess whether X is a good predictor of Y or whether X is a better of Y. In other words, it tells you whether beta or gamma is the thing to take more seriously. Also, considering that you a... | Is the average of betas from Y ~ X and X ~ Y valid?
Perhaps the approach of "Granger causality" might help. This would help you to assess whether X is a good predictor of Y or whether X is a better of Y. In other words, it tells you whether beta or gam |
38,479 | assumptions for lmer models | Existence of variance: Do not need to check, in practice, it is always true.
Linearity: Do not need to check, because your covariates are categorical.
Homogeneity: Need to Check by plotting residuals vs predicted values.
Normality of error term: need to check by histogram, QQplot of residuals, even Kolmogorov-Smirno... | assumptions for lmer models | Existence of variance: Do not need to check, in practice, it is always true.
Linearity: Do not need to check, because your covariates are categorical.
Homogeneity: Need to Check by plotting residual | assumptions for lmer models
Existence of variance: Do not need to check, in practice, it is always true.
Linearity: Do not need to check, because your covariates are categorical.
Homogeneity: Need to Check by plotting residuals vs predicted values.
Normality of error term: need to check by histogram, QQplot of resid... | assumptions for lmer models
Existence of variance: Do not need to check, in practice, it is always true.
Linearity: Do not need to check, because your covariates are categorical.
Homogeneity: Need to Check by plotting residual |
38,480 | assumptions for lmer models | The commonly quoted assumptions (or "conditions" as I prefer to call some of them) of linear mixed effects models are:
Linearity of the predictors. This can be checked by plotting the residuals against the response and looking for any systematic shape, and by including non-linear terms (or splines) and comparing the m... | assumptions for lmer models | The commonly quoted assumptions (or "conditions" as I prefer to call some of them) of linear mixed effects models are:
Linearity of the predictors. This can be checked by plotting the residuals again | assumptions for lmer models
The commonly quoted assumptions (or "conditions" as I prefer to call some of them) of linear mixed effects models are:
Linearity of the predictors. This can be checked by plotting the residuals against the response and looking for any systematic shape, and by including non-linear terms (or ... | assumptions for lmer models
The commonly quoted assumptions (or "conditions" as I prefer to call some of them) of linear mixed effects models are:
Linearity of the predictors. This can be checked by plotting the residuals again |
38,481 | Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson? | I don't know why the book Generalized Linear Models by McCullagh and Nelder shouldn't be a top contender. It's considered the founding work on GLMs. It is a highly technical book, focused on interpretation, asymptotic theory, and general framework. A GLM is nothing more than a link function and a mean-variance relation... | Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson? | I don't know why the book Generalized Linear Models by McCullagh and Nelder shouldn't be a top contender. It's considered the founding work on GLMs. It is a highly technical book, focused on interpret | Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson?
I don't know why the book Generalized Linear Models by McCullagh and Nelder shouldn't be a top contender. It's considered the founding work on GLMs. It is a highly technical book, focused on interpretation, asymptotic theory, and general framework. A GLM is... | Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson?
I don't know why the book Generalized Linear Models by McCullagh and Nelder shouldn't be a top contender. It's considered the founding work on GLMs. It is a highly technical book, focused on interpret |
38,482 | Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson? | The book Extending the Linear Model with R by Faraway has a chapter on "other GLM", and the count regression chapter also has a Negative Binomial discussion.
Generalized Linear Modeling with H20 has something on Gamma GLMs and Tweedie GLMs. Note that Tweedie GLMs are used often by insurance companies, so you may be abl... | Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson? | The book Extending the Linear Model with R by Faraway has a chapter on "other GLM", and the count regression chapter also has a Negative Binomial discussion.
Generalized Linear Modeling with H20 has s | Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson?
The book Extending the Linear Model with R by Faraway has a chapter on "other GLM", and the count regression chapter also has a Negative Binomial discussion.
Generalized Linear Modeling with H20 has something on Gamma GLMs and Tweedie GLMs. Note that Tweedi... | Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson?
The book Extending the Linear Model with R by Faraway has a chapter on "other GLM", and the count regression chapter also has a Negative Binomial discussion.
Generalized Linear Modeling with H20 has s |
38,483 | Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson? | Hardin and Hilbe cover a bit more than the typical basic book (Dobson and Barnett, etc.); the table of contents shows that they have chapters covering Gamma, inverse Gaussian, etc.. As I recall they also have some other useful extensions for count data (like the NB1, i.e. a negative binomial with variance proportional ... | Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson? | Hardin and Hilbe cover a bit more than the typical basic book (Dobson and Barnett, etc.); the table of contents shows that they have chapters covering Gamma, inverse Gaussian, etc.. As I recall they a | Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson?
Hardin and Hilbe cover a bit more than the typical basic book (Dobson and Barnett, etc.); the table of contents shows that they have chapters covering Gamma, inverse Gaussian, etc.. As I recall they also have some other useful extensions for count data (lik... | Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson?
Hardin and Hilbe cover a bit more than the typical basic book (Dobson and Barnett, etc.); the table of contents shows that they have chapters covering Gamma, inverse Gaussian, etc.. As I recall they a |
38,484 | How to generate correlated Bernoulli variables? | I can see the problem in you experiment.
You did everything right until:
binvars <- qbinom(pvars, 4, .3)
Why? Let's try to understand what pvars represents first.
pvars is a matrix that contains Uniforms between $0$ and $1$ that have the correlation structure you specified earlier in the variable sigma.
If you feed t... | How to generate correlated Bernoulli variables? | I can see the problem in you experiment.
You did everything right until:
binvars <- qbinom(pvars, 4, .3)
Why? Let's try to understand what pvars represents first.
pvars is a matrix that contains Uni | How to generate correlated Bernoulli variables?
I can see the problem in you experiment.
You did everything right until:
binvars <- qbinom(pvars, 4, .3)
Why? Let's try to understand what pvars represents first.
pvars is a matrix that contains Uniforms between $0$ and $1$ that have the correlation structure you specif... | How to generate correlated Bernoulli variables?
I can see the problem in you experiment.
You did everything right until:
binvars <- qbinom(pvars, 4, .3)
Why? Let's try to understand what pvars represents first.
pvars is a matrix that contains Uni |
38,485 | How to generate correlated Bernoulli variables? | With the values of the correlation matrix that are proposed in the question, no simulation is needed to solve the question, as the answer is deterministic and available. Here is the reason why:
To generate two Bernoulli variates that are perfectly correlated, i.e., when$$\mathrm{corr}(C_1,C_2)=-1$$ one needs to find th... | How to generate correlated Bernoulli variables? | With the values of the correlation matrix that are proposed in the question, no simulation is needed to solve the question, as the answer is deterministic and available. Here is the reason why:
To gen | How to generate correlated Bernoulli variables?
With the values of the correlation matrix that are proposed in the question, no simulation is needed to solve the question, as the answer is deterministic and available. Here is the reason why:
To generate two Bernoulli variates that are perfectly correlated, i.e., when$$... | How to generate correlated Bernoulli variables?
With the values of the correlation matrix that are proposed in the question, no simulation is needed to solve the question, as the answer is deterministic and available. Here is the reason why:
To gen |
38,486 | How to generate correlated Bernoulli variables? | Using a mathematical method described by whuber in this related question, I have programmed a function that generates pairs of correlated binomial random variables using the standard syntax for distributions in R. You can call this function to generate any desired number of correlated Bernoulli random variables, with ... | How to generate correlated Bernoulli variables? | Using a mathematical method described by whuber in this related question, I have programmed a function that generates pairs of correlated binomial random variables using the standard syntax for distri | How to generate correlated Bernoulli variables?
Using a mathematical method described by whuber in this related question, I have programmed a function that generates pairs of correlated binomial random variables using the standard syntax for distributions in R. You can call this function to generate any desired number... | How to generate correlated Bernoulli variables?
Using a mathematical method described by whuber in this related question, I have programmed a function that generates pairs of correlated binomial random variables using the standard syntax for distri |
38,487 | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity | First, let's get a sense why this should be true. The density of a Beta$(1,n)$ variable which has been multiplied by $n$ should be proportional to
$$\left(\frac{x}{n}\right)^{1-1}\left(1 - \frac{x}{n}\right)^{n-1} \propto \left(1 - \frac{x}{n}\right)^{n-1} \approx e^{-x}$$
(for large $n$, anyway), so it surely looks e... | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity | First, let's get a sense why this should be true. The density of a Beta$(1,n)$ variable which has been multiplied by $n$ should be proportional to
$$\left(\frac{x}{n}\right)^{1-1}\left(1 - \frac{x}{n | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity
First, let's get a sense why this should be true. The density of a Beta$(1,n)$ variable which has been multiplied by $n$ should be proportional to
$$\left(\frac{x}{n}\right)^{1-1}\left(1 - \frac{x}{n}\right)^{n-1} \propto \left(1 - \frac{x}{n}\right)^{... | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity
First, let's get a sense why this should be true. The density of a Beta$(1,n)$ variable which has been multiplied by $n$ should be proportional to
$$\left(\frac{x}{n}\right)^{1-1}\left(1 - \frac{x}{n |
38,488 | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity | Here is probabilistic proof to this old problem.
Let $(X_n:n\in\mathbb{N})$ be an i.i.d sequence of exponential random variables with parameter $\theta>0$ ($\mu_{X_1}(dx)=\theta e^{-\theta x}\mathbb{1}_{(0,\infty)}(x)\,dx$). Define
$$W_n=\frac{X_1}{X_1+(X_2+\ldots + X_{n+1})}$$
As $X_1$ has $\operatorname{Gamma}(1,\the... | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity | Here is probabilistic proof to this old problem.
Let $(X_n:n\in\mathbb{N})$ be an i.i.d sequence of exponential random variables with parameter $\theta>0$ ($\mu_{X_1}(dx)=\theta e^{-\theta x}\mathbb{1 | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity
Here is probabilistic proof to this old problem.
Let $(X_n:n\in\mathbb{N})$ be an i.i.d sequence of exponential random variables with parameter $\theta>0$ ($\mu_{X_1}(dx)=\theta e^{-\theta x}\mathbb{1}_{(0,\infty)}(x)\,dx$). Define
$$W_n=\frac{X_1}{X_1+... | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity
Here is probabilistic proof to this old problem.
Let $(X_n:n\in\mathbb{N})$ be an i.i.d sequence of exponential random variables with parameter $\theta>0$ ($\mu_{X_1}(dx)=\theta e^{-\theta x}\mathbb{1 |
38,489 | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity | Another view: if $X_1, \ldots, X_n \text{ i.i.d.} \sim U(0, 1)$, then $X_{(1)} = \min(X_1, \ldots, X_n) \sim \text{Beta}(1, n)$. More generally,
\begin{align}
X_{(i)} \sim \text{Beta}(i, n + 1 - i), i = 1, \ldots, n.
\end{align}
It then follows by (for fixed $x > 0$, when $n$ is sufficiently large, $x/n$ can be bounde... | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity | Another view: if $X_1, \ldots, X_n \text{ i.i.d.} \sim U(0, 1)$, then $X_{(1)} = \min(X_1, \ldots, X_n) \sim \text{Beta}(1, n)$. More generally,
\begin{align}
X_{(i)} \sim \text{Beta}(i, n + 1 - i), | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity
Another view: if $X_1, \ldots, X_n \text{ i.i.d.} \sim U(0, 1)$, then $X_{(1)} = \min(X_1, \ldots, X_n) \sim \text{Beta}(1, n)$. More generally,
\begin{align}
X_{(i)} \sim \text{Beta}(i, n + 1 - i), i = 1, \ldots, n.
\end{align}
It then follows by (for... | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity
Another view: if $X_1, \ldots, X_n \text{ i.i.d.} \sim U(0, 1)$, then $X_{(1)} = \min(X_1, \ldots, X_n) \sim \text{Beta}(1, n)$. More generally,
\begin{align}
X_{(i)} \sim \text{Beta}(i, n + 1 - i), |
38,490 | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity | Thanks to the comments I can now formulate the answer myself, I think:
We know that Y=nX, so we can use a general formula for the pdf of a transformed variable (link of Christoph Hanck):
$\rho_Y(y)=\frac{\rho_X(x)}{|f'(x)|}$
$f'(x)=\frac{d(nx)}{dx}=n$
$\rho_Y(y) = \frac{n(1-y/n)^{n-1}}{n}$
$\lim_{n \to \infty} (1-y/n... | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity | Thanks to the comments I can now formulate the answer myself, I think:
We know that Y=nX, so we can use a general formula for the pdf of a transformed variable (link of Christoph Hanck):
$\rho_Y(y)=\ | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity
Thanks to the comments I can now formulate the answer myself, I think:
We know that Y=nX, so we can use a general formula for the pdf of a transformed variable (link of Christoph Hanck):
$\rho_Y(y)=\frac{\rho_X(x)}{|f'(x)|}$
$f'(x)=\frac{d(nx)}{dx}=n$... | Limit of $n$ times Beta$(1,n)$ variables when $n$ goes to infinity
Thanks to the comments I can now formulate the answer myself, I think:
We know that Y=nX, so we can use a general formula for the pdf of a transformed variable (link of Christoph Hanck):
$\rho_Y(y)=\ |
38,491 | Knots in Smoothing Splines | But, in my opinion wouldn't that be overfitting?
No.
Your equation explains it all.
$$\underbrace{\sum_{i=1}^n(y_i-g(x_i))^2}_\text{residual squares}+\underbrace{\lambda\int g''(t)^2dt}_\text{roughness penalty}$$
The second part $\lambda\int g''(t)^2dt$ is often called a roughness penalty, and $\lambda$ - roughness co... | Knots in Smoothing Splines | But, in my opinion wouldn't that be overfitting?
No.
Your equation explains it all.
$$\underbrace{\sum_{i=1}^n(y_i-g(x_i))^2}_\text{residual squares}+\underbrace{\lambda\int g''(t)^2dt}_\text{roughne | Knots in Smoothing Splines
But, in my opinion wouldn't that be overfitting?
No.
Your equation explains it all.
$$\underbrace{\sum_{i=1}^n(y_i-g(x_i))^2}_\text{residual squares}+\underbrace{\lambda\int g''(t)^2dt}_\text{roughness penalty}$$
The second part $\lambda\int g''(t)^2dt$ is often called a roughness penalty, a... | Knots in Smoothing Splines
But, in my opinion wouldn't that be overfitting?
No.
Your equation explains it all.
$$\underbrace{\sum_{i=1}^n(y_i-g(x_i))^2}_\text{residual squares}+\underbrace{\lambda\int g''(t)^2dt}_\text{roughne |
38,492 | Knots in Smoothing Splines | Having read the book myself, this statement refers to a regularized model (edit: I guess all smoothing splines are like that), where every point is a knot, but you are regularizing by adding $\lambda \int g''(x)^2$ to the loss function, so you are punishing a "wiggly function", as expressed in a large absolute second d... | Knots in Smoothing Splines | Having read the book myself, this statement refers to a regularized model (edit: I guess all smoothing splines are like that), where every point is a knot, but you are regularizing by adding $\lambda | Knots in Smoothing Splines
Having read the book myself, this statement refers to a regularized model (edit: I guess all smoothing splines are like that), where every point is a knot, but you are regularizing by adding $\lambda \int g''(x)^2$ to the loss function, so you are punishing a "wiggly function", as expressed i... | Knots in Smoothing Splines
Having read the book myself, this statement refers to a regularized model (edit: I guess all smoothing splines are like that), where every point is a knot, but you are regularizing by adding $\lambda |
38,493 | Find CDF from an estimated PDF (estimated by KDE) | There's no need to integrate anything if you know the cdf of the kernel itself. I believe this is straightforward for all the common kernels.
Note that
a KDE is a mixture density
the cdf of a mixture is the mixture of the cdfs.
that is, if $\hat{f}(x)=\frac{1}{n}\sum_i f_i(x)$ is your KDE at $x$, then
$\hat{F}(x)=\f... | Find CDF from an estimated PDF (estimated by KDE) | There's no need to integrate anything if you know the cdf of the kernel itself. I believe this is straightforward for all the common kernels.
Note that
a KDE is a mixture density
the cdf of a mixtur | Find CDF from an estimated PDF (estimated by KDE)
There's no need to integrate anything if you know the cdf of the kernel itself. I believe this is straightforward for all the common kernels.
Note that
a KDE is a mixture density
the cdf of a mixture is the mixture of the cdfs.
that is, if $\hat{f}(x)=\frac{1}{n}\sum... | Find CDF from an estimated PDF (estimated by KDE)
There's no need to integrate anything if you know the cdf of the kernel itself. I believe this is straightforward for all the common kernels.
Note that
a KDE is a mixture density
the cdf of a mixtur |
38,494 | Are 1-dimensional numpy arrays equivalent to vectors? [closed] | A NumPy array is a N-dimensional container of
items of
the same type and size. As a computer programming data structure, it is limited
by resources and dtype --- there are values which are not representable by NumPy
arrays. Due to these limitations, NumPy arrays are not exactly equivalent to the
mathematical concept of... | Are 1-dimensional numpy arrays equivalent to vectors? [closed] | A NumPy array is a N-dimensional container of
items of
the same type and size. As a computer programming data structure, it is limited
by resources and dtype --- there are values which are not represe | Are 1-dimensional numpy arrays equivalent to vectors? [closed]
A NumPy array is a N-dimensional container of
items of
the same type and size. As a computer programming data structure, it is limited
by resources and dtype --- there are values which are not representable by NumPy
arrays. Due to these limitations, NumPy a... | Are 1-dimensional numpy arrays equivalent to vectors? [closed]
A NumPy array is a N-dimensional container of
items of
the same type and size. As a computer programming data structure, it is limited
by resources and dtype --- there are values which are not represe |
38,495 | Pooling data for logistic regression | This is all wrong-headed. First, note that there is no meaningful ontological status of 'winner'.
How to determine the quality of something when all you have is a set of results from head-to-head comparisons (e.g., sports teams based on the results of games in a season) is a very tricky question. In the simplest case... | Pooling data for logistic regression | This is all wrong-headed. First, note that there is no meaningful ontological status of 'winner'.
How to determine the quality of something when all you have is a set of results from head-to-head com | Pooling data for logistic regression
This is all wrong-headed. First, note that there is no meaningful ontological status of 'winner'.
How to determine the quality of something when all you have is a set of results from head-to-head comparisons (e.g., sports teams based on the results of games in a season) is a very t... | Pooling data for logistic regression
This is all wrong-headed. First, note that there is no meaningful ontological status of 'winner'.
How to determine the quality of something when all you have is a set of results from head-to-head com |
38,496 | Pooling data for logistic regression | That is fine way to structure the data, yes. Your trepidation comes from your data taking on a multilevel structure: Dogs are nested within races. You can test if you "need" to account for this multilevel structure by doing multilevel modeling. You can specify a model with a random intercept at the race level (Level 2)... | Pooling data for logistic regression | That is fine way to structure the data, yes. Your trepidation comes from your data taking on a multilevel structure: Dogs are nested within races. You can test if you "need" to account for this multil | Pooling data for logistic regression
That is fine way to structure the data, yes. Your trepidation comes from your data taking on a multilevel structure: Dogs are nested within races. You can test if you "need" to account for this multilevel structure by doing multilevel modeling. You can specify a model with a random ... | Pooling data for logistic regression
That is fine way to structure the data, yes. Your trepidation comes from your data taking on a multilevel structure: Dogs are nested within races. You can test if you "need" to account for this multil |
38,497 | Pooling data for logistic regression | I don't quite understand what you mean by "pool" here. What you described will certainly get your data in a format that makes it easy to work with in R or Python (although putting it in a data.frame object is cleaner imo).
The fact that different numbers of dogs racing probably won't be a problem. What will be a prob... | Pooling data for logistic regression | I don't quite understand what you mean by "pool" here. What you described will certainly get your data in a format that makes it easy to work with in R or Python (although putting it in a data.frame | Pooling data for logistic regression
I don't quite understand what you mean by "pool" here. What you described will certainly get your data in a format that makes it easy to work with in R or Python (although putting it in a data.frame object is cleaner imo).
The fact that different numbers of dogs racing probably won... | Pooling data for logistic regression
I don't quite understand what you mean by "pool" here. What you described will certainly get your data in a format that makes it easy to work with in R or Python (although putting it in a data.frame |
38,498 | Why does variance-covariance matrix of $\hat{\beta}$ have transpose inside? | You quote the definition of covariance of two variables, while the form with transpose is the definition of covariance matrix. In first case we are talking about two random variables $X$ and $Y$,
$$ \operatorname{cov}(X,Y) = \operatorname{E}{\big[(X - \operatorname{E}[X])(Y - \operatorname{E}[Y])\big]} $$
while in the ... | Why does variance-covariance matrix of $\hat{\beta}$ have transpose inside? | You quote the definition of covariance of two variables, while the form with transpose is the definition of covariance matrix. In first case we are talking about two random variables $X$ and $Y$,
$$ \ | Why does variance-covariance matrix of $\hat{\beta}$ have transpose inside?
You quote the definition of covariance of two variables, while the form with transpose is the definition of covariance matrix. In first case we are talking about two random variables $X$ and $Y$,
$$ \operatorname{cov}(X,Y) = \operatorname{E}{\b... | Why does variance-covariance matrix of $\hat{\beta}$ have transpose inside?
You quote the definition of covariance of two variables, while the form with transpose is the definition of covariance matrix. In first case we are talking about two random variables $X$ and $Y$,
$$ \ |
38,499 | Why does variance-covariance matrix of $\hat{\beta}$ have transpose inside? | A covariance matrix is matrix-valued. Covariance of two random variables is an element in that matrix, i.e. a scalar. Hence the covariance formula that you list yields a scalar, while computing $xx^T$ for vector-valued $x$ yields a matrix. | Why does variance-covariance matrix of $\hat{\beta}$ have transpose inside? | A covariance matrix is matrix-valued. Covariance of two random variables is an element in that matrix, i.e. a scalar. Hence the covariance formula that you list yields a scalar, while computing $xx^T$ | Why does variance-covariance matrix of $\hat{\beta}$ have transpose inside?
A covariance matrix is matrix-valued. Covariance of two random variables is an element in that matrix, i.e. a scalar. Hence the covariance formula that you list yields a scalar, while computing $xx^T$ for vector-valued $x$ yields a matrix. | Why does variance-covariance matrix of $\hat{\beta}$ have transpose inside?
A covariance matrix is matrix-valued. Covariance of two random variables is an element in that matrix, i.e. a scalar. Hence the covariance formula that you list yields a scalar, while computing $xx^T$ |
38,500 | Why does variance-covariance matrix of $\hat{\beta}$ have transpose inside? | Small example: Consider a 2x1
$$v = \begin{bmatrix}
7\\
6
\end{bmatrix}$$
Note that
$$v'v = \begin{bmatrix}
7&6
\end{bmatrix}\begin{bmatrix}
7\\
6
\end{bmatrix}$$
is a scalar (or 1x1 matrix?)
But
$$vv' = \begin{bmatrix}
7\\
6
\end{bmatrix} \begin{bmatrix}
7&6
\end{bmatrix}$$
is a matrix | Why does variance-covariance matrix of $\hat{\beta}$ have transpose inside? | Small example: Consider a 2x1
$$v = \begin{bmatrix}
7\\
6
\end{bmatrix}$$
Note that
$$v'v = \begin{bmatrix}
7&6
\end{bmatrix}\begin{bmatrix}
7\\
6
\end{bmatrix}$$
is a scalar (or 1x1 matrix?)
But
$$ | Why does variance-covariance matrix of $\hat{\beta}$ have transpose inside?
Small example: Consider a 2x1
$$v = \begin{bmatrix}
7\\
6
\end{bmatrix}$$
Note that
$$v'v = \begin{bmatrix}
7&6
\end{bmatrix}\begin{bmatrix}
7\\
6
\end{bmatrix}$$
is a scalar (or 1x1 matrix?)
But
$$vv' = \begin{bmatrix}
7\\
6
\end{bmatrix} \... | Why does variance-covariance matrix of $\hat{\beta}$ have transpose inside?
Small example: Consider a 2x1
$$v = \begin{bmatrix}
7\\
6
\end{bmatrix}$$
Note that
$$v'v = \begin{bmatrix}
7&6
\end{bmatrix}\begin{bmatrix}
7\\
6
\end{bmatrix}$$
is a scalar (or 1x1 matrix?)
But
$$ |
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