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 |
|---|---|---|---|---|---|---|
35,101 | Shapes of ROC curves for different classifiers ('steppy' for SVM and smooth for k-NN) | Diagonal lines occur in ROC curves when you have ties, that is when you have one or more observation with the exact same test value in both the positive and negative groups.
SVM classifiers output continuous probabilities. The chance to get a tie is normally very low. This is why you get a "steppy" curve.
On the other... | Shapes of ROC curves for different classifiers ('steppy' for SVM and smooth for k-NN) | Diagonal lines occur in ROC curves when you have ties, that is when you have one or more observation with the exact same test value in both the positive and negative groups.
SVM classifiers output co | Shapes of ROC curves for different classifiers ('steppy' for SVM and smooth for k-NN)
Diagonal lines occur in ROC curves when you have ties, that is when you have one or more observation with the exact same test value in both the positive and negative groups.
SVM classifiers output continuous probabilities. The chance... | Shapes of ROC curves for different classifiers ('steppy' for SVM and smooth for k-NN)
Diagonal lines occur in ROC curves when you have ties, that is when you have one or more observation with the exact same test value in both the positive and negative groups.
SVM classifiers output co |
35,102 | What's the difference between binary and binomial data? | Possibly what is meant is that binary data consists only of 0's and 1's for "failures" and "successes" (notice that what you consider as a "success" is arbitrary) and follows a Bernoulli distribution. Binomial data is data that emerged after observing $n$ Bernoulli trials, i.e. it is a sum of Bernoulli random variables... | What's the difference between binary and binomial data? | Possibly what is meant is that binary data consists only of 0's and 1's for "failures" and "successes" (notice that what you consider as a "success" is arbitrary) and follows a Bernoulli distribution. | What's the difference between binary and binomial data?
Possibly what is meant is that binary data consists only of 0's and 1's for "failures" and "successes" (notice that what you consider as a "success" is arbitrary) and follows a Bernoulli distribution. Binomial data is data that emerged after observing $n$ Bernoull... | What's the difference between binary and binomial data?
Possibly what is meant is that binary data consists only of 0's and 1's for "failures" and "successes" (notice that what you consider as a "success" is arbitrary) and follows a Bernoulli distribution. |
35,103 | Why are Type-II errors in hypothesis testing considered to be errors? | It's because we are not doing what we are supposed to do when the alternative hypothesis is true. For example, we are not using the new medicine which is actually better than the existing one but we were unable to prove it. | Why are Type-II errors in hypothesis testing considered to be errors? | It's because we are not doing what we are supposed to do when the alternative hypothesis is true. For example, we are not using the new medicine which is actually better than the existing one but we w | Why are Type-II errors in hypothesis testing considered to be errors?
It's because we are not doing what we are supposed to do when the alternative hypothesis is true. For example, we are not using the new medicine which is actually better than the existing one but we were unable to prove it. | Why are Type-II errors in hypothesis testing considered to be errors?
It's because we are not doing what we are supposed to do when the alternative hypothesis is true. For example, we are not using the new medicine which is actually better than the existing one but we w |
35,104 | Why are Type-II errors in hypothesis testing considered to be errors? | How we want to use the word "error" is ultimately a semantic issue and reasonable people could disagree on whether, and in what sense, we should consider a false negative to be an error.
On the one hand, I think you are right that a non-significant result really just means that we do not have enough information to b... | Why are Type-II errors in hypothesis testing considered to be errors? | How we want to use the word "error" is ultimately a semantic issue and reasonable people could disagree on whether, and in what sense, we should consider a false negative to be an error.
On the one | Why are Type-II errors in hypothesis testing considered to be errors?
How we want to use the word "error" is ultimately a semantic issue and reasonable people could disagree on whether, and in what sense, we should consider a false negative to be an error.
On the one hand, I think you are right that a non-significan... | Why are Type-II errors in hypothesis testing considered to be errors?
How we want to use the word "error" is ultimately a semantic issue and reasonable people could disagree on whether, and in what sense, we should consider a false negative to be an error.
On the one |
35,105 | Why are Type-II errors in hypothesis testing considered to be errors? | The word 'failure' is close to 'error'.
To me the term error makes sense since you can calculate a probability for it to occur (provided you set a certain minimal effect size that would be desirable to detect). And you want to calculate this probability in situations where you want it to be small. In those situations ... | Why are Type-II errors in hypothesis testing considered to be errors? | The word 'failure' is close to 'error'.
To me the term error makes sense since you can calculate a probability for it to occur (provided you set a certain minimal effect size that would be desirable | Why are Type-II errors in hypothesis testing considered to be errors?
The word 'failure' is close to 'error'.
To me the term error makes sense since you can calculate a probability for it to occur (provided you set a certain minimal effect size that would be desirable to detect). And you want to calculate this probabi... | Why are Type-II errors in hypothesis testing considered to be errors?
The word 'failure' is close to 'error'.
To me the term error makes sense since you can calculate a probability for it to occur (provided you set a certain minimal effect size that would be desirable |
35,106 | Is it possible to simulate logistic regression without randomness? | Logistic regression does not have an "error" term as with classical linear regression. The exception to this might be thresholded linear regression with a logistic error term, but this isn't a commonly accepted probability model which results in a logistic regression model. This is because logistic models have a mean-v... | Is it possible to simulate logistic regression without randomness? | Logistic regression does not have an "error" term as with classical linear regression. The exception to this might be thresholded linear regression with a logistic error term, but this isn't a commonl | Is it possible to simulate logistic regression without randomness?
Logistic regression does not have an "error" term as with classical linear regression. The exception to this might be thresholded linear regression with a logistic error term, but this isn't a commonly accepted probability model which results in a logis... | Is it possible to simulate logistic regression without randomness?
Logistic regression does not have an "error" term as with classical linear regression. The exception to this might be thresholded linear regression with a logistic error term, but this isn't a commonl |
35,107 | Is it possible to simulate logistic regression without randomness? | I always like to think of logistic regression as what happens if you apply a binary decision to a linear model. That is, let's assume there is some underlying relationship that follows the linear model:
$$
y = X\beta+\varepsilon
$$
where $X$ is your independent variable and $\beta$ the coefficient (or slope) on that va... | Is it possible to simulate logistic regression without randomness? | I always like to think of logistic regression as what happens if you apply a binary decision to a linear model. That is, let's assume there is some underlying relationship that follows the linear mode | Is it possible to simulate logistic regression without randomness?
I always like to think of logistic regression as what happens if you apply a binary decision to a linear model. That is, let's assume there is some underlying relationship that follows the linear model:
$$
y = X\beta+\varepsilon
$$
where $X$ is your ind... | Is it possible to simulate logistic regression without randomness?
I always like to think of logistic regression as what happens if you apply a binary decision to a linear model. That is, let's assume there is some underlying relationship that follows the linear mode |
35,108 | Why does reducing the learning rate quickly reduce the error | I think an intuitive answer goes along these lines:
Suppose you want to find a parameter that 'best explains' your data in only one dimension. 'Best explains' means to make an error function small (or a likelihood big, these are usually the same as error = -log(likelihood)). We forget for a moment that we want to talk ... | Why does reducing the learning rate quickly reduce the error | I think an intuitive answer goes along these lines:
Suppose you want to find a parameter that 'best explains' your data in only one dimension. 'Best explains' means to make an error function small (or | Why does reducing the learning rate quickly reduce the error
I think an intuitive answer goes along these lines:
Suppose you want to find a parameter that 'best explains' your data in only one dimension. 'Best explains' means to make an error function small (or a likelihood big, these are usually the same as error = -l... | Why does reducing the learning rate quickly reduce the error
I think an intuitive answer goes along these lines:
Suppose you want to find a parameter that 'best explains' your data in only one dimension. 'Best explains' means to make an error function small (or |
35,109 | Does the Central Limit Theorem hold if you replace the true variance with the sample variance? | Yes it is a result of Slutsky's Theorem since $S_n \rightarrow_p \sigma$ | Does the Central Limit Theorem hold if you replace the true variance with the sample variance? | Yes it is a result of Slutsky's Theorem since $S_n \rightarrow_p \sigma$ | Does the Central Limit Theorem hold if you replace the true variance with the sample variance?
Yes it is a result of Slutsky's Theorem since $S_n \rightarrow_p \sigma$ | Does the Central Limit Theorem hold if you replace the true variance with the sample variance?
Yes it is a result of Slutsky's Theorem since $S_n \rightarrow_p \sigma$ |
35,110 | Does the Central Limit Theorem hold if you replace the true variance with the sample variance? | You appear to be interested in a quantity like
$$
\mathcal{T}=\frac{\sqrt T(\bar{y}-\mu)}{s},
$$
with $s$ the sample standard deviation of $y_t$, $t=1,\ldots,T$.
By the CLT, $\sqrt T(\bar{y}-\mu)\to_d \mathcal{N}(0,\sigma^2)$ when (e.g.) the $y_i$ are iid with mean $\mu$ and variance $\sigma^2$.
By the WLLN, $s^2\to_p... | Does the Central Limit Theorem hold if you replace the true variance with the sample variance? | You appear to be interested in a quantity like
$$
\mathcal{T}=\frac{\sqrt T(\bar{y}-\mu)}{s},
$$
with $s$ the sample standard deviation of $y_t$, $t=1,\ldots,T$.
By the CLT, $\sqrt T(\bar{y}-\mu)\to_ | Does the Central Limit Theorem hold if you replace the true variance with the sample variance?
You appear to be interested in a quantity like
$$
\mathcal{T}=\frac{\sqrt T(\bar{y}-\mu)}{s},
$$
with $s$ the sample standard deviation of $y_t$, $t=1,\ldots,T$.
By the CLT, $\sqrt T(\bar{y}-\mu)\to_d \mathcal{N}(0,\sigma^2)... | Does the Central Limit Theorem hold if you replace the true variance with the sample variance?
You appear to be interested in a quantity like
$$
\mathcal{T}=\frac{\sqrt T(\bar{y}-\mu)}{s},
$$
with $s$ the sample standard deviation of $y_t$, $t=1,\ldots,T$.
By the CLT, $\sqrt T(\bar{y}-\mu)\to_ |
35,111 | Interaction Terms (Categorical * Continuous) [duplicate] | Yes, it's possible. Suppose your categorical model has $k$ levels, you'll need $(k-1)$ binary indicators to represent them, and you'll need another $(k-1)$ interaction terms that interact with the continuous varaible to model the interaction correctly.
In essence, it's just a regression model that allow each level of t... | Interaction Terms (Categorical * Continuous) [duplicate] | Yes, it's possible. Suppose your categorical model has $k$ levels, you'll need $(k-1)$ binary indicators to represent them, and you'll need another $(k-1)$ interaction terms that interact with the con | Interaction Terms (Categorical * Continuous) [duplicate]
Yes, it's possible. Suppose your categorical model has $k$ levels, you'll need $(k-1)$ binary indicators to represent them, and you'll need another $(k-1)$ interaction terms that interact with the continuous varaible to model the interaction correctly.
In essence... | Interaction Terms (Categorical * Continuous) [duplicate]
Yes, it's possible. Suppose your categorical model has $k$ levels, you'll need $(k-1)$ binary indicators to represent them, and you'll need another $(k-1)$ interaction terms that interact with the con |
35,112 | Interaction Terms (Categorical * Continuous) [duplicate] | I think you can do this. Say that you have k-1 categories then you can simply write the model as y = c + a$_0$ duration + a$_1$ category + a$_2$ duration(1) + a$_3$ duration(2) +...+ a$_k$ duration(k) where duration(i) is the duration for reason i and c is a constant/intercept term. If for a given y the duration corre... | Interaction Terms (Categorical * Continuous) [duplicate] | I think you can do this. Say that you have k-1 categories then you can simply write the model as y = c + a$_0$ duration + a$_1$ category + a$_2$ duration(1) + a$_3$ duration(2) +...+ a$_k$ duration(k | Interaction Terms (Categorical * Continuous) [duplicate]
I think you can do this. Say that you have k-1 categories then you can simply write the model as y = c + a$_0$ duration + a$_1$ category + a$_2$ duration(1) + a$_3$ duration(2) +...+ a$_k$ duration(k) where duration(i) is the duration for reason i and c is a con... | Interaction Terms (Categorical * Continuous) [duplicate]
I think you can do this. Say that you have k-1 categories then you can simply write the model as y = c + a$_0$ duration + a$_1$ category + a$_2$ duration(1) + a$_3$ duration(2) +...+ a$_k$ duration(k |
35,113 | Does this NYT article incorrectly assume independent increments? | Sorry, I cannot agree with the independence assumption. Fertility in women, even without contraception is a function of age, such that, without contraception the
Chances of getting pregnant without IVF (in vitro fertilization)
Starting at about age 32, a woman’s chances of conceiving decrease gradually but significantl... | Does this NYT article incorrectly assume independent increments? | Sorry, I cannot agree with the independence assumption. Fertility in women, even without contraception is a function of age, such that, without contraception the
Chances of getting pregnant without IV | Does this NYT article incorrectly assume independent increments?
Sorry, I cannot agree with the independence assumption. Fertility in women, even without contraception is a function of age, such that, without contraception the
Chances of getting pregnant without IVF (in vitro fertilization)
Starting at about age 32, a ... | Does this NYT article incorrectly assume independent increments?
Sorry, I cannot agree with the independence assumption. Fertility in women, even without contraception is a function of age, such that, without contraception the
Chances of getting pregnant without IV |
35,114 | Does this NYT article incorrectly assume independent increments? | Here is an account of the probabilities relevant to the problem at hand.
Denote by $z_n$ the event 'no pregnancy after $n$ years' for a woman using some type of contraception. Then
$$
P(z_N) = P(z_N | z_{N-1}) P(z_{N-1} | z_{N-2})\cdots P(z_2 | z_1)P(z_1).
$$
The problem is that the NYT asumes $P(z_i | z_{i-1}) = P(z_1... | Does this NYT article incorrectly assume independent increments? | Here is an account of the probabilities relevant to the problem at hand.
Denote by $z_n$ the event 'no pregnancy after $n$ years' for a woman using some type of contraception. Then
$$
P(z_N) = P(z_N | | Does this NYT article incorrectly assume independent increments?
Here is an account of the probabilities relevant to the problem at hand.
Denote by $z_n$ the event 'no pregnancy after $n$ years' for a woman using some type of contraception. Then
$$
P(z_N) = P(z_N | z_{N-1}) P(z_{N-1} | z_{N-2})\cdots P(z_2 | z_1)P(z_1)... | Does this NYT article incorrectly assume independent increments?
Here is an account of the probabilities relevant to the problem at hand.
Denote by $z_n$ the event 'no pregnancy after $n$ years' for a woman using some type of contraception. Then
$$
P(z_N) = P(z_N | |
35,115 | Does this NYT article incorrectly assume independent increments? | From a probabilist perspective I would expect that
$$ \mathbb P(\text{Not pregnant after year N}) \geq \mathbb P(\text{Not pregnant after year 1})^N.$$
This expectation is motivated as follows. Assume that at time $t=0$, every woman is assigned a (potentially different) number $p\in[0,1]$, the probability that she will... | Does this NYT article incorrectly assume independent increments? | From a probabilist perspective I would expect that
$$ \mathbb P(\text{Not pregnant after year N}) \geq \mathbb P(\text{Not pregnant after year 1})^N.$$
This expectation is motivated as follows. Assume | Does this NYT article incorrectly assume independent increments?
From a probabilist perspective I would expect that
$$ \mathbb P(\text{Not pregnant after year N}) \geq \mathbb P(\text{Not pregnant after year 1})^N.$$
This expectation is motivated as follows. Assume that at time $t=0$, every woman is assigned a (potenti... | Does this NYT article incorrectly assume independent increments?
From a probabilist perspective I would expect that
$$ \mathbb P(\text{Not pregnant after year N}) \geq \mathbb P(\text{Not pregnant after year 1})^N.$$
This expectation is motivated as follows. Assume |
35,116 | Meaning of Epsilon in SVM regression | You have it backwards.
Traditional $\epsilon$-SVR works with the epsilon-insensitive hinge loss. The value of $\epsilon$ defines a margin of tolerance where no penalty is given to errors.
Remember the support vectors are the instances across the margin, i.e. the samples being penalized, which slack variables are non-z... | Meaning of Epsilon in SVM regression | You have it backwards.
Traditional $\epsilon$-SVR works with the epsilon-insensitive hinge loss. The value of $\epsilon$ defines a margin of tolerance where no penalty is given to errors.
Remember th | Meaning of Epsilon in SVM regression
You have it backwards.
Traditional $\epsilon$-SVR works with the epsilon-insensitive hinge loss. The value of $\epsilon$ defines a margin of tolerance where no penalty is given to errors.
Remember the support vectors are the instances across the margin, i.e. the samples being penal... | Meaning of Epsilon in SVM regression
You have it backwards.
Traditional $\epsilon$-SVR works with the epsilon-insensitive hinge loss. The value of $\epsilon$ defines a margin of tolerance where no penalty is given to errors.
Remember th |
35,117 | Correlation between an original variable and a principal component | Correlation coefficient between variable $X_i$ and principal component $Y_j$ is given by $$r=v_{ij}\cdot \mathrm{std}(Y_j) / \mathrm{std}(X_i)=v_{ij}\cdot \sqrt{e_{j}} / \mathrm{std}(X_i),$$
where $v_{ij}$ is an $i$-th element of the $j$-th unit-length eigenvector of the covariance matrix, $e_j=\mathrm{var}(Y_j)$ is th... | Correlation between an original variable and a principal component | Correlation coefficient between variable $X_i$ and principal component $Y_j$ is given by $$r=v_{ij}\cdot \mathrm{std}(Y_j) / \mathrm{std}(X_i)=v_{ij}\cdot \sqrt{e_{j}} / \mathrm{std}(X_i),$$
where $v_ | Correlation between an original variable and a principal component
Correlation coefficient between variable $X_i$ and principal component $Y_j$ is given by $$r=v_{ij}\cdot \mathrm{std}(Y_j) / \mathrm{std}(X_i)=v_{ij}\cdot \sqrt{e_{j}} / \mathrm{std}(X_i),$$
where $v_{ij}$ is an $i$-th element of the $j$-th unit-length ... | Correlation between an original variable and a principal component
Correlation coefficient between variable $X_i$ and principal component $Y_j$ is given by $$r=v_{ij}\cdot \mathrm{std}(Y_j) / \mathrm{std}(X_i)=v_{ij}\cdot \sqrt{e_{j}} / \mathrm{std}(X_i),$$
where $v_ |
35,118 | Correlation between an original variable and a principal component | Correlations with factors are called loadings. In PCA, eigenvectors can be scaled differently but if normalized to their eigenvalues, they are loadings (if memory serves). For other types of factor analysis, loadings and factors can differ but loadings are always refer to correlations. | Correlation between an original variable and a principal component | Correlations with factors are called loadings. In PCA, eigenvectors can be scaled differently but if normalized to their eigenvalues, they are loadings (if memory serves). For other types of factor an | Correlation between an original variable and a principal component
Correlations with factors are called loadings. In PCA, eigenvectors can be scaled differently but if normalized to their eigenvalues, they are loadings (if memory serves). For other types of factor analysis, loadings and factors can differ but loadings ... | Correlation between an original variable and a principal component
Correlations with factors are called loadings. In PCA, eigenvectors can be scaled differently but if normalized to their eigenvalues, they are loadings (if memory serves). For other types of factor an |
35,119 | Mathematical statistics (moments vs. central moments) | Two salient properties of real numbers $x, y,$ and $\mu$ are
The triangle inequalities $$|x-\mu| \le |x|+|\mu|$$ and $$|x| \le |x-\mu| + |\mu|.$$
Raising to the $r$ power for $r \gt 0$ preserves order: $$|x| \le |y| \text{ implies } |x|^r \le |y|^r$$ and (therefore) $$\max(|x|^r, |y|^r) = \max(|x|,|y|)^r.$$
Note, too... | Mathematical statistics (moments vs. central moments) | Two salient properties of real numbers $x, y,$ and $\mu$ are
The triangle inequalities $$|x-\mu| \le |x|+|\mu|$$ and $$|x| \le |x-\mu| + |\mu|.$$
Raising to the $r$ power for $r \gt 0$ preserves orde | Mathematical statistics (moments vs. central moments)
Two salient properties of real numbers $x, y,$ and $\mu$ are
The triangle inequalities $$|x-\mu| \le |x|+|\mu|$$ and $$|x| \le |x-\mu| + |\mu|.$$
Raising to the $r$ power for $r \gt 0$ preserves order: $$|x| \le |y| \text{ implies } |x|^r \le |y|^r$$ and (therefore... | Mathematical statistics (moments vs. central moments)
Two salient properties of real numbers $x, y,$ and $\mu$ are
The triangle inequalities $$|x-\mu| \le |x|+|\mu|$$ and $$|x| \le |x-\mu| + |\mu|.$$
Raising to the $r$ power for $r \gt 0$ preserves orde |
35,120 | The issue of quantile curves crossing each other | In general case, the problem of non-crossing linear quantile regresion has no solutions.
Indeed, either your quantile lines are parallel (and trivial), or they do cross somewhere.
By placing restrictions, you could ensure that the lines do not cross in the training sample, but it will in no way guarantee that crossin... | The issue of quantile curves crossing each other | In general case, the problem of non-crossing linear quantile regresion has no solutions.
Indeed, either your quantile lines are parallel (and trivial), or they do cross somewhere.
By placing restric | The issue of quantile curves crossing each other
In general case, the problem of non-crossing linear quantile regresion has no solutions.
Indeed, either your quantile lines are parallel (and trivial), or they do cross somewhere.
By placing restrictions, you could ensure that the lines do not cross in the training sam... | The issue of quantile curves crossing each other
In general case, the problem of non-crossing linear quantile regresion has no solutions.
Indeed, either your quantile lines are parallel (and trivial), or they do cross somewhere.
By placing restric |
35,121 | The issue of quantile curves crossing each other | Placing a regularizing restriction sometimes help prevent crossing.
https://ieeexplore.ieee.org/document/9548806 | The issue of quantile curves crossing each other | Placing a regularizing restriction sometimes help prevent crossing.
https://ieeexplore.ieee.org/document/9548806 | The issue of quantile curves crossing each other
Placing a regularizing restriction sometimes help prevent crossing.
https://ieeexplore.ieee.org/document/9548806 | The issue of quantile curves crossing each other
Placing a regularizing restriction sometimes help prevent crossing.
https://ieeexplore.ieee.org/document/9548806 |
35,122 | Regression when the dependent variable is between 0 and 1 | Beta regressions are used for continuous proportions (like the proportion of land with a particular soil type).
For count proportions, the most common models would be binomial regression models, a particular type of generalized linear model (GLM).
Of those, logistic regression is the most widely used though there's a n... | Regression when the dependent variable is between 0 and 1 | Beta regressions are used for continuous proportions (like the proportion of land with a particular soil type).
For count proportions, the most common models would be binomial regression models, a par | Regression when the dependent variable is between 0 and 1
Beta regressions are used for continuous proportions (like the proportion of land with a particular soil type).
For count proportions, the most common models would be binomial regression models, a particular type of generalized linear model (GLM).
Of those, logi... | Regression when the dependent variable is between 0 and 1
Beta regressions are used for continuous proportions (like the proportion of land with a particular soil type).
For count proportions, the most common models would be binomial regression models, a par |
35,123 | Use of Metropolis & Rejection & Inverse Transform sampling methods | It's not entirely correct to say that inverse methods are impossible to compute. There are perfectly good numerical approximations to the inverse Gaussian CDF. As far as I'm aware, plenty of methods use it to generate gaussian random variables. There are of course plenty of other, possibly simpler methods of generating... | Use of Metropolis & Rejection & Inverse Transform sampling methods | It's not entirely correct to say that inverse methods are impossible to compute. There are perfectly good numerical approximations to the inverse Gaussian CDF. As far as I'm aware, plenty of methods u | Use of Metropolis & Rejection & Inverse Transform sampling methods
It's not entirely correct to say that inverse methods are impossible to compute. There are perfectly good numerical approximations to the inverse Gaussian CDF. As far as I'm aware, plenty of methods use it to generate gaussian random variables. There ar... | Use of Metropolis & Rejection & Inverse Transform sampling methods
It's not entirely correct to say that inverse methods are impossible to compute. There are perfectly good numerical approximations to the inverse Gaussian CDF. As far as I'm aware, plenty of methods u |
35,124 | Use of Metropolis & Rejection & Inverse Transform sampling methods | Comparisons between simulation methods are only about efficiency as they all produce an output that is supposed to be from the same target distribution. Hence, you cannot expect one simulation method (like MCMC) to produce more rare events than another one, as those rare events are supposed to occur at the correct (and... | Use of Metropolis & Rejection & Inverse Transform sampling methods | Comparisons between simulation methods are only about efficiency as they all produce an output that is supposed to be from the same target distribution. Hence, you cannot expect one simulation method | Use of Metropolis & Rejection & Inverse Transform sampling methods
Comparisons between simulation methods are only about efficiency as they all produce an output that is supposed to be from the same target distribution. Hence, you cannot expect one simulation method (like MCMC) to produce more rare events than another ... | Use of Metropolis & Rejection & Inverse Transform sampling methods
Comparisons between simulation methods are only about efficiency as they all produce an output that is supposed to be from the same target distribution. Hence, you cannot expect one simulation method |
35,125 | What metric should I use for assessing Implicit matrix factorization recommender with ALS? | Evaluating implicit feedback based recommendations is tricky. Here are couple of approaches that I'd recommend.
Approach 1
You can use modified precision and recall metrics. Overall the procedure would be as follows,
Divide your data into train and test set by users.
For a user in test set, given their history, get th... | What metric should I use for assessing Implicit matrix factorization recommender with ALS? | Evaluating implicit feedback based recommendations is tricky. Here are couple of approaches that I'd recommend.
Approach 1
You can use modified precision and recall metrics. Overall the procedure woul | What metric should I use for assessing Implicit matrix factorization recommender with ALS?
Evaluating implicit feedback based recommendations is tricky. Here are couple of approaches that I'd recommend.
Approach 1
You can use modified precision and recall metrics. Overall the procedure would be as follows,
Divide your... | What metric should I use for assessing Implicit matrix factorization recommender with ALS?
Evaluating implicit feedback based recommendations is tricky. Here are couple of approaches that I'd recommend.
Approach 1
You can use modified precision and recall metrics. Overall the procedure woul |
35,126 | What is the difference between VAR, Dynamic Regressive, and ARMAX models? | I will focus on ARMAX versus VAR. I am not quite sure what a dynamic regression is. (I have seen a few different interpretations. Funnily, there are textbooks and lecture notes with chapters called "Dynamic regression" that do not really delimit this class of models. Also, Rob J. Hyndman notes in his blog post "The ARI... | What is the difference between VAR, Dynamic Regressive, and ARMAX models? | I will focus on ARMAX versus VAR. I am not quite sure what a dynamic regression is. (I have seen a few different interpretations. Funnily, there are textbooks and lecture notes with chapters called "D | What is the difference between VAR, Dynamic Regressive, and ARMAX models?
I will focus on ARMAX versus VAR. I am not quite sure what a dynamic regression is. (I have seen a few different interpretations. Funnily, there are textbooks and lecture notes with chapters called "Dynamic regression" that do not really delimit ... | What is the difference between VAR, Dynamic Regressive, and ARMAX models?
I will focus on ARMAX versus VAR. I am not quite sure what a dynamic regression is. (I have seen a few different interpretations. Funnily, there are textbooks and lecture notes with chapters called "D |
35,127 | What is the difference between VAR, Dynamic Regressive, and ARMAX models? | ARMAX models are more general that VAR and Dynamic Regressive . You can see ARMAX in action here https://twitter.com/tomdireill/status/717694028104474625 where the GASX/GASY example from the Box-Jenkins text is analyzed/ | What is the difference between VAR, Dynamic Regressive, and ARMAX models? | ARMAX models are more general that VAR and Dynamic Regressive . You can see ARMAX in action here https://twitter.com/tomdireill/status/717694028104474625 where the GASX/GASY example from the Box-Jenki | What is the difference between VAR, Dynamic Regressive, and ARMAX models?
ARMAX models are more general that VAR and Dynamic Regressive . You can see ARMAX in action here https://twitter.com/tomdireill/status/717694028104474625 where the GASX/GASY example from the Box-Jenkins text is analyzed/ | What is the difference between VAR, Dynamic Regressive, and ARMAX models?
ARMAX models are more general that VAR and Dynamic Regressive . You can see ARMAX in action here https://twitter.com/tomdireill/status/717694028104474625 where the GASX/GASY example from the Box-Jenki |
35,128 | The Number of Exponential Summands in a Fixed Interval is Poisson | I propose taking, as a point of departure, the concept of a homogeneous Poisson process. This is a point process on the line (often thought of, and referred to, as a "time" line). The realizations are sets of points. Almost surely, any bounded set of real numbers will contain only finitely many points.
The fundamenta... | The Number of Exponential Summands in a Fixed Interval is Poisson | I propose taking, as a point of departure, the concept of a homogeneous Poisson process. This is a point process on the line (often thought of, and referred to, as a "time" line). The realizations a | The Number of Exponential Summands in a Fixed Interval is Poisson
I propose taking, as a point of departure, the concept of a homogeneous Poisson process. This is a point process on the line (often thought of, and referred to, as a "time" line). The realizations are sets of points. Almost surely, any bounded set of r... | The Number of Exponential Summands in a Fixed Interval is Poisson
I propose taking, as a point of departure, the concept of a homogeneous Poisson process. This is a point process on the line (often thought of, and referred to, as a "time" line). The realizations a |
35,129 | Forecasting Poisson, accuracy and prediction intervals | You have what is called intermittent demand, that is, a demand time series characterized by "many" zeros. (If your time series is not demand per se, most of what follows will still apply.) So a web search for "forecasting intermittent demand" would already be helpful. Teunter and Duncan (2009, JORS) give an overview of... | Forecasting Poisson, accuracy and prediction intervals | You have what is called intermittent demand, that is, a demand time series characterized by "many" zeros. (If your time series is not demand per se, most of what follows will still apply.) So a web se | Forecasting Poisson, accuracy and prediction intervals
You have what is called intermittent demand, that is, a demand time series characterized by "many" zeros. (If your time series is not demand per se, most of what follows will still apply.) So a web search for "forecasting intermittent demand" would already be helpf... | Forecasting Poisson, accuracy and prediction intervals
You have what is called intermittent demand, that is, a demand time series characterized by "many" zeros. (If your time series is not demand per se, most of what follows will still apply.) So a web se |
35,130 | Is Principal Component Analysis a parametric method? | We do not have to make any distributional assumptions in order to extract the Principal Component directions from a covariance or correlation matrix. To see this, recall the problem PCA solves. For a $p\times p $ covariance matrix $\mathbf{\Sigma}$ and all vectors $\mathbf{x} \in \mathbb{R}^p$ we would like to maximize... | Is Principal Component Analysis a parametric method? | We do not have to make any distributional assumptions in order to extract the Principal Component directions from a covariance or correlation matrix. To see this, recall the problem PCA solves. For a | Is Principal Component Analysis a parametric method?
We do not have to make any distributional assumptions in order to extract the Principal Component directions from a covariance or correlation matrix. To see this, recall the problem PCA solves. For a $p\times p $ covariance matrix $\mathbf{\Sigma}$ and all vectors $\... | Is Principal Component Analysis a parametric method?
We do not have to make any distributional assumptions in order to extract the Principal Component directions from a covariance or correlation matrix. To see this, recall the problem PCA solves. For a |
35,131 | Is Principal Component Analysis a parametric method? | PCA has nothing to do with the normality of your data. The principle is that you have a bunch of data points in a (high-dimensional) space and you want to see which directions or principal vectors can describe your data in an optimal way. It is virtually the same as the singular value decomposition and can be applied t... | Is Principal Component Analysis a parametric method? | PCA has nothing to do with the normality of your data. The principle is that you have a bunch of data points in a (high-dimensional) space and you want to see which directions or principal vectors can | Is Principal Component Analysis a parametric method?
PCA has nothing to do with the normality of your data. The principle is that you have a bunch of data points in a (high-dimensional) space and you want to see which directions or principal vectors can describe your data in an optimal way. It is virtually the same as ... | Is Principal Component Analysis a parametric method?
PCA has nothing to do with the normality of your data. The principle is that you have a bunch of data points in a (high-dimensional) space and you want to see which directions or principal vectors can |
35,132 | High level overview of `auto.arima` with `xreg` predictors | I think the real question is not about auto.arima but rather about regression with ARMA errors as implemented in arima with exogenous regressors.
So how does forecasting auto.arima with xreg work? Do you create a forecast for a time series based on past data and regression model based on the input time series and inp... | High level overview of `auto.arima` with `xreg` predictors | I think the real question is not about auto.arima but rather about regression with ARMA errors as implemented in arima with exogenous regressors.
So how does forecasting auto.arima with xreg work? D | High level overview of `auto.arima` with `xreg` predictors
I think the real question is not about auto.arima but rather about regression with ARMA errors as implemented in arima with exogenous regressors.
So how does forecasting auto.arima with xreg work? Do you create a forecast for a time series based on past data ... | High level overview of `auto.arima` with `xreg` predictors
I think the real question is not about auto.arima but rather about regression with ARMA errors as implemented in arima with exogenous regressors.
So how does forecasting auto.arima with xreg work? D |
35,133 | Does the intercept in a logistic regression capture the unobserved effects? | Theoretically, does the intercept term in a logistic regression model capture all unobserved effects?
This is an interesting question, and I can see how with some simple experiments, one might think that this is the case. In fact, in my first attempt to set this up, I actually created a demonstration would only incorr... | Does the intercept in a logistic regression capture the unobserved effects? | Theoretically, does the intercept term in a logistic regression model capture all unobserved effects?
This is an interesting question, and I can see how with some simple experiments, one might think | Does the intercept in a logistic regression capture the unobserved effects?
Theoretically, does the intercept term in a logistic regression model capture all unobserved effects?
This is an interesting question, and I can see how with some simple experiments, one might think that this is the case. In fact, in my first ... | Does the intercept in a logistic regression capture the unobserved effects?
Theoretically, does the intercept term in a logistic regression model capture all unobserved effects?
This is an interesting question, and I can see how with some simple experiments, one might think |
35,134 | Does the intercept in a logistic regression capture the unobserved effects? | I am not sure if any model, even a linear one, with a 'perfect' fit implies that the intercept term should be 0. It helps in these cases to think of a simple linear regression.
The way I understand the intercept is that it fixes some reasonable value for the y-variable. It just shows what value the y-variable takes eve... | Does the intercept in a logistic regression capture the unobserved effects? | I am not sure if any model, even a linear one, with a 'perfect' fit implies that the intercept term should be 0. It helps in these cases to think of a simple linear regression.
The way I understand th | Does the intercept in a logistic regression capture the unobserved effects?
I am not sure if any model, even a linear one, with a 'perfect' fit implies that the intercept term should be 0. It helps in these cases to think of a simple linear regression.
The way I understand the intercept is that it fixes some reasonable... | Does the intercept in a logistic regression capture the unobserved effects?
I am not sure if any model, even a linear one, with a 'perfect' fit implies that the intercept term should be 0. It helps in these cases to think of a simple linear regression.
The way I understand th |
35,135 | Does the intercept in a logistic regression capture the unobserved effects? | in a logistic regression model with a perfect fit (i.e. all relevant variables are included), the intercept term should be zero right?
No. The intercept captures the constant part of the hazard. | Does the intercept in a logistic regression capture the unobserved effects? | in a logistic regression model with a perfect fit (i.e. all relevant variables are included), the intercept term should be zero right?
No. The intercept captures the constant part of the hazard. | Does the intercept in a logistic regression capture the unobserved effects?
in a logistic regression model with a perfect fit (i.e. all relevant variables are included), the intercept term should be zero right?
No. The intercept captures the constant part of the hazard. | Does the intercept in a logistic regression capture the unobserved effects?
in a logistic regression model with a perfect fit (i.e. all relevant variables are included), the intercept term should be zero right?
No. The intercept captures the constant part of the hazard. |
35,136 | Does the intercept in a logistic regression capture the unobserved effects? | The intercept allows the linear hyperplane to move "sideways". For instance, in one dimension it moves the sigmoid left and right, effectively changing the place the regression activates. | Does the intercept in a logistic regression capture the unobserved effects? | The intercept allows the linear hyperplane to move "sideways". For instance, in one dimension it moves the sigmoid left and right, effectively changing the place the regression activates. | Does the intercept in a logistic regression capture the unobserved effects?
The intercept allows the linear hyperplane to move "sideways". For instance, in one dimension it moves the sigmoid left and right, effectively changing the place the regression activates. | Does the intercept in a logistic regression capture the unobserved effects?
The intercept allows the linear hyperplane to move "sideways". For instance, in one dimension it moves the sigmoid left and right, effectively changing the place the regression activates. |
35,137 | Best modeling technique for predicting waiting times? | Waiting times can often be modelled by the exponential distribution, but this better describes the time between two events of the same type, e.g. it would probably nicely model the time between two subsequent questions.
The time to answer has some more complex properties:
There is a real chance of it never being answ... | Best modeling technique for predicting waiting times? | Waiting times can often be modelled by the exponential distribution, but this better describes the time between two events of the same type, e.g. it would probably nicely model the time between two su | Best modeling technique for predicting waiting times?
Waiting times can often be modelled by the exponential distribution, but this better describes the time between two events of the same type, e.g. it would probably nicely model the time between two subsequent questions.
The time to answer has some more complex prop... | Best modeling technique for predicting waiting times?
Waiting times can often be modelled by the exponential distribution, but this better describes the time between two events of the same type, e.g. it would probably nicely model the time between two su |
35,138 | Best modeling technique for predicting waiting times? | I have accepted an answer above and am only writing this as an answer because I think my research could be beneficial to other Python users.
The comments and answers above helpfully directed me towards Survival Analysis. After exploring the modelling options in StatsModels, I then discovered the library Lifelines by C... | Best modeling technique for predicting waiting times? | I have accepted an answer above and am only writing this as an answer because I think my research could be beneficial to other Python users.
The comments and answers above helpfully directed me towar | Best modeling technique for predicting waiting times?
I have accepted an answer above and am only writing this as an answer because I think my research could be beneficial to other Python users.
The comments and answers above helpfully directed me towards Survival Analysis. After exploring the modelling options in Sta... | Best modeling technique for predicting waiting times?
I have accepted an answer above and am only writing this as an answer because I think my research could be beneficial to other Python users.
The comments and answers above helpfully directed me towar |
35,139 | Fisher's tea tasting, binomial exact test | This is a good idea, but the lady knows that there are 4 cup of tea for each type. This is a valuable information for the lady, which makes things wrong if we model the process via a binomial distribution. The problem is that the variables (successes at each trial) you want to consider are not independent and identical... | Fisher's tea tasting, binomial exact test | This is a good idea, but the lady knows that there are 4 cup of tea for each type. This is a valuable information for the lady, which makes things wrong if we model the process via a binomial distribu | Fisher's tea tasting, binomial exact test
This is a good idea, but the lady knows that there are 4 cup of tea for each type. This is a valuable information for the lady, which makes things wrong if we model the process via a binomial distribution. The problem is that the variables (successes at each trial) you want to ... | Fisher's tea tasting, binomial exact test
This is a good idea, but the lady knows that there are 4 cup of tea for each type. This is a valuable information for the lady, which makes things wrong if we model the process via a binomial distribu |
35,140 | How large does a Poisson distribution's mean need to be to use normal distribution statistics? | Update: As @whuber has pointed out with his comments, a better way to look at this is by computing the true coverage probabilities for the Poisson. The simulation, while also with its uses, does not reveal the interesting pattern seen in the plot below.
This was based on @whuber's code (see his first comment on this a... | How large does a Poisson distribution's mean need to be to use normal distribution statistics? | Update: As @whuber has pointed out with his comments, a better way to look at this is by computing the true coverage probabilities for the Poisson. The simulation, while also with its uses, does not r | How large does a Poisson distribution's mean need to be to use normal distribution statistics?
Update: As @whuber has pointed out with his comments, a better way to look at this is by computing the true coverage probabilities for the Poisson. The simulation, while also with its uses, does not reveal the interesting pat... | How large does a Poisson distribution's mean need to be to use normal distribution statistics?
Update: As @whuber has pointed out with his comments, a better way to look at this is by computing the true coverage probabilities for the Poisson. The simulation, while also with its uses, does not r |
35,141 | How large does a Poisson distribution's mean need to be to use normal distribution statistics? | Here's another perspective. Let's say you want to approximate cdf values of a Poisson with a normal fit. You didn't specify a desired accuracy, so I'll just give an example. Suppose you want to be within 0.01 of the true cdf at all points.
Empirically, if $\lambda$ is the mean of the Poisson, I observe that $\lambda \... | How large does a Poisson distribution's mean need to be to use normal distribution statistics? | Here's another perspective. Let's say you want to approximate cdf values of a Poisson with a normal fit. You didn't specify a desired accuracy, so I'll just give an example. Suppose you want to be wit | How large does a Poisson distribution's mean need to be to use normal distribution statistics?
Here's another perspective. Let's say you want to approximate cdf values of a Poisson with a normal fit. You didn't specify a desired accuracy, so I'll just give an example. Suppose you want to be within 0.01 of the true cdf ... | How large does a Poisson distribution's mean need to be to use normal distribution statistics?
Here's another perspective. Let's say you want to approximate cdf values of a Poisson with a normal fit. You didn't specify a desired accuracy, so I'll just give an example. Suppose you want to be wit |
35,142 | How large does a Poisson distribution's mean need to be to use normal distribution statistics? | To really answer we need to know what you want to do! If you want a confidence interval, say, more might be needed than for standard errors. But why do you want a normal approximation? You can construct confidence intervals directly from the likelihood function, which probably is better.
And, note that for the poisso... | How large does a Poisson distribution's mean need to be to use normal distribution statistics? | To really answer we need to know what you want to do! If you want a confidence interval, say, more might be needed than for standard errors. But why do you want a normal approximation? You can constr | How large does a Poisson distribution's mean need to be to use normal distribution statistics?
To really answer we need to know what you want to do! If you want a confidence interval, say, more might be needed than for standard errors. But why do you want a normal approximation? You can construct confidence intervals ... | How large does a Poisson distribution's mean need to be to use normal distribution statistics?
To really answer we need to know what you want to do! If you want a confidence interval, say, more might be needed than for standard errors. But why do you want a normal approximation? You can constr |
35,143 | How to interpret modification indices output of structural equation models? | In most CFA analyses, the chi sq value will not reach p>.05, especially if you have a large N. Most people look for CMIN, i.e., chisq/df, of <3, or the change in chi sq between nested models, i.e., two models with a minor change in structure, the chi sq for this being (diff in chisq) with (diff in df) df.
The Modifica... | How to interpret modification indices output of structural equation models? | In most CFA analyses, the chi sq value will not reach p>.05, especially if you have a large N. Most people look for CMIN, i.e., chisq/df, of <3, or the change in chi sq between nested models, i.e., tw | How to interpret modification indices output of structural equation models?
In most CFA analyses, the chi sq value will not reach p>.05, especially if you have a large N. Most people look for CMIN, i.e., chisq/df, of <3, or the change in chi sq between nested models, i.e., two models with a minor change in structure, t... | How to interpret modification indices output of structural equation models?
In most CFA analyses, the chi sq value will not reach p>.05, especially if you have a large N. Most people look for CMIN, i.e., chisq/df, of <3, or the change in chi sq between nested models, i.e., tw |
35,144 | How to interpret modification indices output of structural equation models? | The model is actually not that good. See, you have a chi-square of 85.306 with p-value of 0.000. You want it to be not statistically significant instead. Also, the other fit indices are easier to interpret when comparing two different models. By themselves they mean little to nothing. Some authors have suggested that R... | How to interpret modification indices output of structural equation models? | The model is actually not that good. See, you have a chi-square of 85.306 with p-value of 0.000. You want it to be not statistically significant instead. Also, the other fit indices are easier to inte | How to interpret modification indices output of structural equation models?
The model is actually not that good. See, you have a chi-square of 85.306 with p-value of 0.000. You want it to be not statistically significant instead. Also, the other fit indices are easier to interpret when comparing two different models. B... | How to interpret modification indices output of structural equation models?
The model is actually not that good. See, you have a chi-square of 85.306 with p-value of 0.000. You want it to be not statistically significant instead. Also, the other fit indices are easier to inte |
35,145 | Regularization and projection onto the $l_*$ ball | Regularization and vector projections are connected through the idea of constrained optimization and the Karush-Kuhn (no relation)-Tucker conditions.
What are the KKT conditions?
Briefly, these state that, if $x$ is a solution to the problem "minimize $f(x)$ subject to $g(x) \le 0$", then $x$ is also a solution to the ... | Regularization and projection onto the $l_*$ ball | Regularization and vector projections are connected through the idea of constrained optimization and the Karush-Kuhn (no relation)-Tucker conditions.
What are the KKT conditions?
Briefly, these state | Regularization and projection onto the $l_*$ ball
Regularization and vector projections are connected through the idea of constrained optimization and the Karush-Kuhn (no relation)-Tucker conditions.
What are the KKT conditions?
Briefly, these state that, if $x$ is a solution to the problem "minimize $f(x)$ subject to ... | Regularization and projection onto the $l_*$ ball
Regularization and vector projections are connected through the idea of constrained optimization and the Karush-Kuhn (no relation)-Tucker conditions.
What are the KKT conditions?
Briefly, these state |
35,146 | Stopping conditions in coin flipping sequence | The probability of "success" (heads, making a basket, etc.) is the limiting ratio of the number of successes to the number of trials, $p$.
One way to run your simulation is to generate a very long sequence of independent binary trials with underlying success probability $p$. Scan across the sequence, looking for the s... | Stopping conditions in coin flipping sequence | The probability of "success" (heads, making a basket, etc.) is the limiting ratio of the number of successes to the number of trials, $p$.
One way to run your simulation is to generate a very long seq | Stopping conditions in coin flipping sequence
The probability of "success" (heads, making a basket, etc.) is the limiting ratio of the number of successes to the number of trials, $p$.
One way to run your simulation is to generate a very long sequence of independent binary trials with underlying success probability $p$... | Stopping conditions in coin flipping sequence
The probability of "success" (heads, making a basket, etc.) is the limiting ratio of the number of successes to the number of trials, $p$.
One way to run your simulation is to generate a very long seq |
35,147 | Stopping conditions in coin flipping sequence | I thought of an intuitive way to explain this (and answer my own question). It turns out that if you just ignore the stopping and see this problem as a sum of concatenated sequences, it becomes clear that it doesn't matter.
Imagine we get the following sequences stopping after 3 successive misses:
1 0 1 0 0 0
1 0 1 1 ... | Stopping conditions in coin flipping sequence | I thought of an intuitive way to explain this (and answer my own question). It turns out that if you just ignore the stopping and see this problem as a sum of concatenated sequences, it becomes clear | Stopping conditions in coin flipping sequence
I thought of an intuitive way to explain this (and answer my own question). It turns out that if you just ignore the stopping and see this problem as a sum of concatenated sequences, it becomes clear that it doesn't matter.
Imagine we get the following sequences stopping a... | Stopping conditions in coin flipping sequence
I thought of an intuitive way to explain this (and answer my own question). It turns out that if you just ignore the stopping and see this problem as a sum of concatenated sequences, it becomes clear |
35,148 | Null distribution of subspaces similarity, or what is the distribution of $\mathrm{tr}(AA'BB')$? | I have once asked a question that is essentially a special case of yours when $k=1$: Distribution of a scalar product of two random unit vectors in $\mathbb{R}^D$. @whuber gave an excellent answer, where he explains that a dot product equals $t=2u-1$, where $$u\sim \mathrm{Beta}((d-1)/2,(d-1)/2)$$ and $d$ is the dimens... | Null distribution of subspaces similarity, or what is the distribution of $\mathrm{tr}(AA'BB')$? | I have once asked a question that is essentially a special case of yours when $k=1$: Distribution of a scalar product of two random unit vectors in $\mathbb{R}^D$. @whuber gave an excellent answer, wh | Null distribution of subspaces similarity, or what is the distribution of $\mathrm{tr}(AA'BB')$?
I have once asked a question that is essentially a special case of yours when $k=1$: Distribution of a scalar product of two random unit vectors in $\mathbb{R}^D$. @whuber gave an excellent answer, where he explains that a ... | Null distribution of subspaces similarity, or what is the distribution of $\mathrm{tr}(AA'BB')$?
I have once asked a question that is essentially a special case of yours when $k=1$: Distribution of a scalar product of two random unit vectors in $\mathbb{R}^D$. @whuber gave an excellent answer, wh |
35,149 | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value? | You might want to consider an approach outside of the traditional regression approach. This is comparable to the types of problems that psychometrics is designed to resolve (well, actually your first example is precisely that, since it is a test).
In Classical Test Theory, one of the most common metrics is the item-tot... | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value? | You might want to consider an approach outside of the traditional regression approach. This is comparable to the types of problems that psychometrics is designed to resolve (well, actually your first | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value?
You might want to consider an approach outside of the traditional regression approach. This is comparable to the types of problems that psychometrics is designed to resolve (well, actually your first example is precisel... | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value?
You might want to consider an approach outside of the traditional regression approach. This is comparable to the types of problems that psychometrics is designed to resolve (well, actually your first |
35,150 | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value? | A quick mathematial way of looking at it is to expand out the formulas. Let $Z=X+Y+W$.
$$ R^2 =\left(\frac{Cov(X,Z)}{\sigma_X \sigma_Z}\right)^2 =\left(\frac{Var(X)+Cov(X,Y)+Cov(X,W)}{\sigma_X \sigma_Z}\right)^2 $$
So in a nutshell You're going to get the variance of $X$ plus its relationship with your other two variab... | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value? | A quick mathematial way of looking at it is to expand out the formulas. Let $Z=X+Y+W$.
$$ R^2 =\left(\frac{Cov(X,Z)}{\sigma_X \sigma_Z}\right)^2 =\left(\frac{Var(X)+Cov(X,Y)+Cov(X,W)}{\sigma_X \sigma_ | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value?
A quick mathematial way of looking at it is to expand out the formulas. Let $Z=X+Y+W$.
$$ R^2 =\left(\frac{Cov(X,Z)}{\sigma_X \sigma_Z}\right)^2 =\left(\frac{Var(X)+Cov(X,Y)+Cov(X,W)}{\sigma_X \sigma_Z}\right)^2 $$
So i... | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value?
A quick mathematial way of looking at it is to expand out the formulas. Let $Z=X+Y+W$.
$$ R^2 =\left(\frac{Cov(X,Z)}{\sigma_X \sigma_Z}\right)^2 =\left(\frac{Var(X)+Cov(X,Y)+Cov(X,W)}{\sigma_X \sigma_ |
35,151 | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value? | If X is one of several variables that sum to define Y, then clearly the assumptions of linear regression are broken. The P values won't be useful. The slopes and their confidence intervals can't be interpreted in the usual way. But is $R^2$ still useful? I suppose it is as a descriptive statistics. If you have three $R... | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value? | If X is one of several variables that sum to define Y, then clearly the assumptions of linear regression are broken. The P values won't be useful. The slopes and their confidence intervals can't be in | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value?
If X is one of several variables that sum to define Y, then clearly the assumptions of linear regression are broken. The P values won't be useful. The slopes and their confidence intervals can't be interpreted in the us... | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value?
If X is one of several variables that sum to define Y, then clearly the assumptions of linear regression are broken. The P values won't be useful. The slopes and their confidence intervals can't be in |
35,152 | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value? | One assumption for regression analysis is that $X$ and $Y$ are not intertwined.
This is incorrect. One assumption for regression analysis is that the ERRORS are uncorrelated. See the wikipedia entry for the Gauss-Markov theorem.
If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a us... | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value? | One assumption for regression analysis is that $X$ and $Y$ are not intertwined.
This is incorrect. One assumption for regression analysis is that the ERRORS are uncorrelated. See the wikipedia entry | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value?
One assumption for regression analysis is that $X$ and $Y$ are not intertwined.
This is incorrect. One assumption for regression analysis is that the ERRORS are uncorrelated. See the wikipedia entry for the Gauss-Marko... | If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value?
One assumption for regression analysis is that $X$ and $Y$ are not intertwined.
This is incorrect. One assumption for regression analysis is that the ERRORS are uncorrelated. See the wikipedia entry |
35,153 | Is there a way to define a statistic similar to the z-score for the Poisson distribution? | Assuming that the typical number of spikes is large, I would suggest to use a Variance stabilizing transformation. For Poisson distribution, it goes as follows: let $X \sim \mathcal P(\lambda)$, and let $Y \sim 2 \sqrt X$. A first order approximation gives
$$Y \simeq 2 \sqrt\lambda + {1\over \sqrt\lambda}(X-\lambda),$... | Is there a way to define a statistic similar to the z-score for the Poisson distribution? | Assuming that the typical number of spikes is large, I would suggest to use a Variance stabilizing transformation. For Poisson distribution, it goes as follows: let $X \sim \mathcal P(\lambda)$, and l | Is there a way to define a statistic similar to the z-score for the Poisson distribution?
Assuming that the typical number of spikes is large, I would suggest to use a Variance stabilizing transformation. For Poisson distribution, it goes as follows: let $X \sim \mathcal P(\lambda)$, and let $Y \sim 2 \sqrt X$. A first... | Is there a way to define a statistic similar to the z-score for the Poisson distribution?
Assuming that the typical number of spikes is large, I would suggest to use a Variance stabilizing transformation. For Poisson distribution, it goes as follows: let $X \sim \mathcal P(\lambda)$, and l |
35,154 | Is there a way to define a statistic similar to the z-score for the Poisson distribution? | Is the reason that you want to test for Poisson distribution, that you think the spikes are generated by a Poisson process (that is, the instantaneous probability of seeing a spike is constant over time)? If so, and you know the length between each spike, consider testing for a Poisson process instead. This amounts to ... | Is there a way to define a statistic similar to the z-score for the Poisson distribution? | Is the reason that you want to test for Poisson distribution, that you think the spikes are generated by a Poisson process (that is, the instantaneous probability of seeing a spike is constant over ti | Is there a way to define a statistic similar to the z-score for the Poisson distribution?
Is the reason that you want to test for Poisson distribution, that you think the spikes are generated by a Poisson process (that is, the instantaneous probability of seeing a spike is constant over time)? If so, and you know the l... | Is there a way to define a statistic similar to the z-score for the Poisson distribution?
Is the reason that you want to test for Poisson distribution, that you think the spikes are generated by a Poisson process (that is, the instantaneous probability of seeing a spike is constant over ti |
35,155 | Is there a way to define a statistic similar to the z-score for the Poisson distribution? | This is similar to Ben's question, but are you just trying to test whether a multi-variate Poisson distribution fits this data? Your major problem here is that you're having to estimate the poisson mean for each cell from the data that you're trying to get a p-value/likelihood score/whatever for. Now strictly speaking ... | Is there a way to define a statistic similar to the z-score for the Poisson distribution? | This is similar to Ben's question, but are you just trying to test whether a multi-variate Poisson distribution fits this data? Your major problem here is that you're having to estimate the poisson me | Is there a way to define a statistic similar to the z-score for the Poisson distribution?
This is similar to Ben's question, but are you just trying to test whether a multi-variate Poisson distribution fits this data? Your major problem here is that you're having to estimate the poisson mean for each cell from the data... | Is there a way to define a statistic similar to the z-score for the Poisson distribution?
This is similar to Ben's question, but are you just trying to test whether a multi-variate Poisson distribution fits this data? Your major problem here is that you're having to estimate the poisson me |
35,156 | R binomial family with identity link | See Wikipedia on the linear probability model, & CV posts here & here for the statistical background. Though not "wrong", you'd want a good reason for using an identity link to model a Bernoulli probability.
According to the family manual
the binomial family [accepts] the links logit, probit, cauchit,
(corresponding... | R binomial family with identity link | See Wikipedia on the linear probability model, & CV posts here & here for the statistical background. Though not "wrong", you'd want a good reason for using an identity link to model a Bernoulli proba | R binomial family with identity link
See Wikipedia on the linear probability model, & CV posts here & here for the statistical background. Though not "wrong", you'd want a good reason for using an identity link to model a Bernoulli probability.
According to the family manual
the binomial family [accepts] the links log... | R binomial family with identity link
See Wikipedia on the linear probability model, & CV posts here & here for the statistical background. Though not "wrong", you'd want a good reason for using an identity link to model a Bernoulli proba |
35,157 | completing the square for Gaussian multivariate estimation | The essential step is along these lines:
$$(x-a)^TA(x-a) + (x-b)^TB(x-b)$$
$$=x^TAx -2a^TAx + a^TAa+ x^TBx -2b^TBx + b^TBb$$
$$=x^T(A+B)x -2(a^TA+b^TB)x + (a^TAa+ b^TBb)$$
$$=x^T(A+B)x -2(a^TA+b^TB)x + (a^TAa+ b^TBb)$$
Let $M=A+B$, let $m=(M^{-1})^T(B^Tb+A^Ta)$ and let $C=a^TAa+ b^TBb-m^TMm$
(I hope I got $m$ right the... | completing the square for Gaussian multivariate estimation | The essential step is along these lines:
$$(x-a)^TA(x-a) + (x-b)^TB(x-b)$$
$$=x^TAx -2a^TAx + a^TAa+ x^TBx -2b^TBx + b^TBb$$
$$=x^T(A+B)x -2(a^TA+b^TB)x + (a^TAa+ b^TBb)$$
$$=x^T(A+B)x -2(a^TA+b^TB)x | completing the square for Gaussian multivariate estimation
The essential step is along these lines:
$$(x-a)^TA(x-a) + (x-b)^TB(x-b)$$
$$=x^TAx -2a^TAx + a^TAa+ x^TBx -2b^TBx + b^TBb$$
$$=x^T(A+B)x -2(a^TA+b^TB)x + (a^TAa+ b^TBb)$$
$$=x^T(A+B)x -2(a^TA+b^TB)x + (a^TAa+ b^TBb)$$
Let $M=A+B$, let $m=(M^{-1})^T(B^Tb+A^Ta)$... | completing the square for Gaussian multivariate estimation
The essential step is along these lines:
$$(x-a)^TA(x-a) + (x-b)^TB(x-b)$$
$$=x^TAx -2a^TAx + a^TAa+ x^TBx -2b^TBx + b^TBb$$
$$=x^T(A+B)x -2(a^TA+b^TB)x + (a^TAa+ b^TBb)$$
$$=x^T(A+B)x -2(a^TA+b^TB)x |
35,158 | If $X$ takes on a Gamma Distribution, how can I find $X^2$, $X^3$, etc? | Your strategy will fail. Powers of $X$ follow Generalized Gamma distributions. Their densities are given by
$$f(x; k, \gamma, 1) = \frac{1}{\Gamma (k)} x^{\gamma k} e^{-x^{\gamma }} \left(\gamma \frac{dx}{x} \right).$$
(The third parameter, here set to a unit value $\sigma=1$, is a scale parameter.) For the power ... | If $X$ takes on a Gamma Distribution, how can I find $X^2$, $X^3$, etc? | Your strategy will fail. Powers of $X$ follow Generalized Gamma distributions. Their densities are given by
$$f(x; k, \gamma, 1) = \frac{1}{\Gamma (k)} x^{\gamma k} e^{-x^{\gamma }} \left(\gamma \ | If $X$ takes on a Gamma Distribution, how can I find $X^2$, $X^3$, etc?
Your strategy will fail. Powers of $X$ follow Generalized Gamma distributions. Their densities are given by
$$f(x; k, \gamma, 1) = \frac{1}{\Gamma (k)} x^{\gamma k} e^{-x^{\gamma }} \left(\gamma \frac{dx}{x} \right).$$
(The third parameter, her... | If $X$ takes on a Gamma Distribution, how can I find $X^2$, $X^3$, etc?
Your strategy will fail. Powers of $X$ follow Generalized Gamma distributions. Their densities are given by
$$f(x; k, \gamma, 1) = \frac{1}{\Gamma (k)} x^{\gamma k} e^{-x^{\gamma }} \left(\gamma \ |
35,159 | Is using error bars for means in a within-subjects study wrong? | It isn't "wrong" necessarily, and it isn't "completely uninformative". But it provides information that pertains to a largely unrelated question, and so is likely to be misleading. When you run a paired samples $t$-test, you are really conducting a one-sample $t$-test of whether the mean of the differences is equal t... | Is using error bars for means in a within-subjects study wrong? | It isn't "wrong" necessarily, and it isn't "completely uninformative". But it provides information that pertains to a largely unrelated question, and so is likely to be misleading. When you run a pa | Is using error bars for means in a within-subjects study wrong?
It isn't "wrong" necessarily, and it isn't "completely uninformative". But it provides information that pertains to a largely unrelated question, and so is likely to be misleading. When you run a paired samples $t$-test, you are really conducting a one-s... | Is using error bars for means in a within-subjects study wrong?
It isn't "wrong" necessarily, and it isn't "completely uninformative". But it provides information that pertains to a largely unrelated question, and so is likely to be misleading. When you run a pa |
35,160 | Neural network over-fitting | Overfitting is not only when test error increases with iterations. We say that there is overfitting when the performance on test set is much lower than the performance on train set (because the model fits too much to seen data, and do not generalize well).
In your second plot we can see that performances on test sets ... | Neural network over-fitting | Overfitting is not only when test error increases with iterations. We say that there is overfitting when the performance on test set is much lower than the performance on train set (because the model | Neural network over-fitting
Overfitting is not only when test error increases with iterations. We say that there is overfitting when the performance on test set is much lower than the performance on train set (because the model fits too much to seen data, and do not generalize well).
In your second plot we can see tha... | Neural network over-fitting
Overfitting is not only when test error increases with iterations. We say that there is overfitting when the performance on test set is much lower than the performance on train set (because the model |
35,161 | How to "undifference" a time series variable | I'm afraid you've already hit upon the easiest solution, which is to pick a xi, aka the constant of integration. The alternative is to phrase any question you ask about your "undifferenced" sequence such that the constant of integration doesn't matter.
The underlying problem is that "differencing" maps many sequences o... | How to "undifference" a time series variable | I'm afraid you've already hit upon the easiest solution, which is to pick a xi, aka the constant of integration. The alternative is to phrase any question you ask about your "undifferenced" sequence s | How to "undifference" a time series variable
I'm afraid you've already hit upon the easiest solution, which is to pick a xi, aka the constant of integration. The alternative is to phrase any question you ask about your "undifferenced" sequence such that the constant of integration doesn't matter.
The underlying problem... | How to "undifference" a time series variable
I'm afraid you've already hit upon the easiest solution, which is to pick a xi, aka the constant of integration. The alternative is to phrase any question you ask about your "undifferenced" sequence s |
35,162 | How to "undifference" a time series variable | Instead of doing diff() with the actual time series data, use instead the d parameter in auto.arima function to define it. lets say your data series is val.ts and you want to do differencing only until first order to make your series stationary, then instead of using auto.arima(diff(val.ts)), do auto.arima(val.ts,d=1).... | How to "undifference" a time series variable | Instead of doing diff() with the actual time series data, use instead the d parameter in auto.arima function to define it. lets say your data series is val.ts and you want to do differencing only unti | How to "undifference" a time series variable
Instead of doing diff() with the actual time series data, use instead the d parameter in auto.arima function to define it. lets say your data series is val.ts and you want to do differencing only until first order to make your series stationary, then instead of using auto.ar... | How to "undifference" a time series variable
Instead of doing diff() with the actual time series data, use instead the d parameter in auto.arima function to define it. lets say your data series is val.ts and you want to do differencing only unti |
35,163 | How to "undifference" a time series variable | Since the series was twice-differenced, you need the first two values of the original source data.
You mention that it is a money market, cash return proxy variable. Shouldn't it be possible to get the source data?
In your simulation, I'm assuming you are generating 100,000 series that have similar characteristics (usi... | How to "undifference" a time series variable | Since the series was twice-differenced, you need the first two values of the original source data.
You mention that it is a money market, cash return proxy variable. Shouldn't it be possible to get th | How to "undifference" a time series variable
Since the series was twice-differenced, you need the first two values of the original source data.
You mention that it is a money market, cash return proxy variable. Shouldn't it be possible to get the source data?
In your simulation, I'm assuming you are generating 100,000 ... | How to "undifference" a time series variable
Since the series was twice-differenced, you need the first two values of the original source data.
You mention that it is a money market, cash return proxy variable. Shouldn't it be possible to get th |
35,164 | Determine the limiting distribution of Uniform Order Statistic | If you look at the cdf of $Y_n$, $$F_n(\delta)=\mathbb{P}(Y_n\le\delta)=(\delta/\theta)^n\qquad0\le\delta\le\theta\,,$$ you get that $F_n(\delta)$ converges to zero when $0\le\delta<\theta$, which means that $Y_n$ converges in probability to $\theta$:
$$Y_n\stackrel{\text{prob}}{\longrightarrow} \theta\,.$$ This implie... | Determine the limiting distribution of Uniform Order Statistic | If you look at the cdf of $Y_n$, $$F_n(\delta)=\mathbb{P}(Y_n\le\delta)=(\delta/\theta)^n\qquad0\le\delta\le\theta\,,$$ you get that $F_n(\delta)$ converges to zero when $0\le\delta<\theta$, which mea | Determine the limiting distribution of Uniform Order Statistic
If you look at the cdf of $Y_n$, $$F_n(\delta)=\mathbb{P}(Y_n\le\delta)=(\delta/\theta)^n\qquad0\le\delta\le\theta\,,$$ you get that $F_n(\delta)$ converges to zero when $0\le\delta<\theta$, which means that $Y_n$ converges in probability to $\theta$:
$$Y_n... | Determine the limiting distribution of Uniform Order Statistic
If you look at the cdf of $Y_n$, $$F_n(\delta)=\mathbb{P}(Y_n\le\delta)=(\delta/\theta)^n\qquad0\le\delta\le\theta\,,$$ you get that $F_n(\delta)$ converges to zero when $0\le\delta<\theta$, which mea |
35,165 | Determine the limiting distribution of Uniform Order Statistic | As suggested by Xi'an, work with the CDF
$$
F_n(t) = \Pr(Y_n\leq t)=\bigcap_{i=1}^n \Pr(X_i\leq t) = \prod_{i=1}^n \Pr(X_1\leq t) \, .
$$
Hence,
$$
F_n(t) = \begin{cases}
0 &,& t<0\,; \\
\left(t/\theta\right)^n &,& 0\leq t<\theta\,; \\
1 &,& t\geq\theta \, .
\end{cases}
$$
Plot a graph of this $F_n$.
For $t<0$ and... | Determine the limiting distribution of Uniform Order Statistic | As suggested by Xi'an, work with the CDF
$$
F_n(t) = \Pr(Y_n\leq t)=\bigcap_{i=1}^n \Pr(X_i\leq t) = \prod_{i=1}^n \Pr(X_1\leq t) \, .
$$
Hence,
$$
F_n(t) = \begin{cases}
0 &,& t<0\,; \\
\left(t/ | Determine the limiting distribution of Uniform Order Statistic
As suggested by Xi'an, work with the CDF
$$
F_n(t) = \Pr(Y_n\leq t)=\bigcap_{i=1}^n \Pr(X_i\leq t) = \prod_{i=1}^n \Pr(X_1\leq t) \, .
$$
Hence,
$$
F_n(t) = \begin{cases}
0 &,& t<0\,; \\
\left(t/\theta\right)^n &,& 0\leq t<\theta\,; \\
1 &,& t\geq\thet... | Determine the limiting distribution of Uniform Order Statistic
As suggested by Xi'an, work with the CDF
$$
F_n(t) = \Pr(Y_n\leq t)=\bigcap_{i=1}^n \Pr(X_i\leq t) = \prod_{i=1}^n \Pr(X_1\leq t) \, .
$$
Hence,
$$
F_n(t) = \begin{cases}
0 &,& t<0\,; \\
\left(t/ |
35,166 | Hourly predictions using time series | Well, the difference is... that they are different methods. ("Can any one explain the difference between apples and oranges?")
ARIMA models are explained in any introductory time series book. (I'll never tire of recommending this free open source online forecasting textbook.) If you want to include weather info, you'd... | Hourly predictions using time series | Well, the difference is... that they are different methods. ("Can any one explain the difference between apples and oranges?")
ARIMA models are explained in any introductory time series book. (I'll n | Hourly predictions using time series
Well, the difference is... that they are different methods. ("Can any one explain the difference between apples and oranges?")
ARIMA models are explained in any introductory time series book. (I'll never tire of recommending this free open source online forecasting textbook.) If yo... | Hourly predictions using time series
Well, the difference is... that they are different methods. ("Can any one explain the difference between apples and oranges?")
ARIMA models are explained in any introductory time series book. (I'll n |
35,167 | How to use the Hausman test for gender discrimination? | I see the reasoning behind this advice but i) this person should have explained it better to you and ii) they should have also mentioned the restrictive assumptions underlying this idea.
In the Hausman test you generally ask whether there is a difference between a consistent but inefficient model and a potential incons... | How to use the Hausman test for gender discrimination? | I see the reasoning behind this advice but i) this person should have explained it better to you and ii) they should have also mentioned the restrictive assumptions underlying this idea.
In the Hausma | How to use the Hausman test for gender discrimination?
I see the reasoning behind this advice but i) this person should have explained it better to you and ii) they should have also mentioned the restrictive assumptions underlying this idea.
In the Hausman test you generally ask whether there is a difference between a ... | How to use the Hausman test for gender discrimination?
I see the reasoning behind this advice but i) this person should have explained it better to you and ii) they should have also mentioned the restrictive assumptions underlying this idea.
In the Hausma |
35,168 | Efficient convolution (in R) | Have you taken a look at dedicated R packages for that? Like convolve, https://stat.ethz.ch/R-manual/R-devel/library/stats/html/convolve.html | Efficient convolution (in R) | Have you taken a look at dedicated R packages for that? Like convolve, https://stat.ethz.ch/R-manual/R-devel/library/stats/html/convolve.html | Efficient convolution (in R)
Have you taken a look at dedicated R packages for that? Like convolve, https://stat.ethz.ch/R-manual/R-devel/library/stats/html/convolve.html | Efficient convolution (in R)
Have you taken a look at dedicated R packages for that? Like convolve, https://stat.ethz.ch/R-manual/R-devel/library/stats/html/convolve.html |
35,169 | How to fit regression to custom model in R | You could fit a nonlinear regression. This would be suitable if - aside from the nonlinear relationship between $E(Y)$ and $x$ - your model assumptions were similar to ordinary regression (independence and constant variance, for example).
In R, see ?nls.
The difficulty with this particular model is finding suitable st... | How to fit regression to custom model in R | You could fit a nonlinear regression. This would be suitable if - aside from the nonlinear relationship between $E(Y)$ and $x$ - your model assumptions were similar to ordinary regression (independenc | How to fit regression to custom model in R
You could fit a nonlinear regression. This would be suitable if - aside from the nonlinear relationship between $E(Y)$ and $x$ - your model assumptions were similar to ordinary regression (independence and constant variance, for example).
In R, see ?nls.
The difficulty with t... | How to fit regression to custom model in R
You could fit a nonlinear regression. This would be suitable if - aside from the nonlinear relationship between $E(Y)$ and $x$ - your model assumptions were similar to ordinary regression (independenc |
35,170 | How to fit regression to custom model in R | @Glen_b provides the right path you should pursue. Here are some issues I would like to point out for this nonlinear modeling scenario.
First, the nonlinear fit @Glen_b showed has an underlying assumption that each observation, either at the same N or not, are independent. I noticed that you have a variable "R" which i... | How to fit regression to custom model in R | @Glen_b provides the right path you should pursue. Here are some issues I would like to point out for this nonlinear modeling scenario.
First, the nonlinear fit @Glen_b showed has an underlying assump | How to fit regression to custom model in R
@Glen_b provides the right path you should pursue. Here are some issues I would like to point out for this nonlinear modeling scenario.
First, the nonlinear fit @Glen_b showed has an underlying assumption that each observation, either at the same N or not, are independent. I n... | How to fit regression to custom model in R
@Glen_b provides the right path you should pursue. Here are some issues I would like to point out for this nonlinear modeling scenario.
First, the nonlinear fit @Glen_b showed has an underlying assump |
35,171 | How to fit regression to custom model in R | I assumed that since you are not statistician I will give you a simple solution.
Install SPSS and go to regression >> non linear | How to fit regression to custom model in R | I assumed that since you are not statistician I will give you a simple solution.
Install SPSS and go to regression >> non linear | How to fit regression to custom model in R
I assumed that since you are not statistician I will give you a simple solution.
Install SPSS and go to regression >> non linear | How to fit regression to custom model in R
I assumed that since you are not statistician I will give you a simple solution.
Install SPSS and go to regression >> non linear |
35,172 | What is the meaning of $\oplus$ and $\otimes$? | In statistics, $$A\oplus B:=\left[\begin{array}{cc}A & 0 \\ 0 & B \end{array} \right]$$ and (e.g. for a $2\times 2$-matrix $A$)
$$A\otimes B:=\left[\begin{array}{cc}a_{11}B & a_{12}B \\ a_{21}B & a_{22}B \end{array} \right].$$
This focuses on matrices for their use in statistics as design or hypothesis matrices etc., ... | What is the meaning of $\oplus$ and $\otimes$? | In statistics, $$A\oplus B:=\left[\begin{array}{cc}A & 0 \\ 0 & B \end{array} \right]$$ and (e.g. for a $2\times 2$-matrix $A$)
$$A\otimes B:=\left[\begin{array}{cc}a_{11}B & a_{12}B \\ a_{21}B & a_{2 | What is the meaning of $\oplus$ and $\otimes$?
In statistics, $$A\oplus B:=\left[\begin{array}{cc}A & 0 \\ 0 & B \end{array} \right]$$ and (e.g. for a $2\times 2$-matrix $A$)
$$A\otimes B:=\left[\begin{array}{cc}a_{11}B & a_{12}B \\ a_{21}B & a_{22}B \end{array} \right].$$
This focuses on matrices for their use in stat... | What is the meaning of $\oplus$ and $\otimes$?
In statistics, $$A\oplus B:=\left[\begin{array}{cc}A & 0 \\ 0 & B \end{array} \right]$$ and (e.g. for a $2\times 2$-matrix $A$)
$$A\otimes B:=\left[\begin{array}{cc}a_{11}B & a_{12}B \\ a_{21}B & a_{2 |
35,173 | What is the meaning of $\oplus$ and $\otimes$? | Suppose $A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$ and $B=\begin{pmatrix}e&f\\g&h\end{pmatrix}$
Then,
A$\otimes$B=$\begin{pmatrix}a&b\\c&d\end{pmatrix}$ $\otimes$ $\begin{pmatrix}e&f\\g&h\end{pmatrix}$=\begin{pmatrix} a {\begin{pmatrix}e&f\\g&h\end{pmatrix}}&b{\begin{pmatrix}e&f\\g&h\end{pmatrix}}\\c{\begin{pmatrix}e&f\\... | What is the meaning of $\oplus$ and $\otimes$? | Suppose $A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$ and $B=\begin{pmatrix}e&f\\g&h\end{pmatrix}$
Then,
A$\otimes$B=$\begin{pmatrix}a&b\\c&d\end{pmatrix}$ $\otimes$ $\begin{pmatrix}e&f\\g&h\end{pmatrix}$= | What is the meaning of $\oplus$ and $\otimes$?
Suppose $A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$ and $B=\begin{pmatrix}e&f\\g&h\end{pmatrix}$
Then,
A$\otimes$B=$\begin{pmatrix}a&b\\c&d\end{pmatrix}$ $\otimes$ $\begin{pmatrix}e&f\\g&h\end{pmatrix}$=\begin{pmatrix} a {\begin{pmatrix}e&f\\g&h\end{pmatrix}}&b{\begin{pmatrix... | What is the meaning of $\oplus$ and $\otimes$?
Suppose $A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$ and $B=\begin{pmatrix}e&f\\g&h\end{pmatrix}$
Then,
A$\otimes$B=$\begin{pmatrix}a&b\\c&d\end{pmatrix}$ $\otimes$ $\begin{pmatrix}e&f\\g&h\end{pmatrix}$= |
35,174 | Oddly large R squared values in meta regression (metafor) | The pseudo-$R^2$ value that is reported is computed with: $$R^2 = \frac{\hat{\tau}^2_{RE} - \hat{\tau}^2_{ME}}{\hat{\tau}^2_{RE}},$$ where $\hat{\tau}^2_{RE}$ is the (total) amount of heterogeneity as estimated based on a random-effects model and $\hat{\tau}^2_{ME}$ is the amount of (residual) heterogeneity as estimate... | Oddly large R squared values in meta regression (metafor) | The pseudo-$R^2$ value that is reported is computed with: $$R^2 = \frac{\hat{\tau}^2_{RE} - \hat{\tau}^2_{ME}}{\hat{\tau}^2_{RE}},$$ where $\hat{\tau}^2_{RE}$ is the (total) amount of heterogeneity as | Oddly large R squared values in meta regression (metafor)
The pseudo-$R^2$ value that is reported is computed with: $$R^2 = \frac{\hat{\tau}^2_{RE} - \hat{\tau}^2_{ME}}{\hat{\tau}^2_{RE}},$$ where $\hat{\tau}^2_{RE}$ is the (total) amount of heterogeneity as estimated based on a random-effects model and $\hat{\tau}^2_{... | Oddly large R squared values in meta regression (metafor)
The pseudo-$R^2$ value that is reported is computed with: $$R^2 = \frac{\hat{\tau}^2_{RE} - \hat{\tau}^2_{ME}}{\hat{\tau}^2_{RE}},$$ where $\hat{\tau}^2_{RE}$ is the (total) amount of heterogeneity as |
35,175 | Predict observation using Hidden Markov Models | From your question, I understood (hopefully correctly) that you want to estimate the next observation, given the observations up to now. Let $y_{1:N} = Y$ the N observations you have seen until now and let $\Theta$ be the parameters of the HMM. Then you want to infer the probability of the next observation given the al... | Predict observation using Hidden Markov Models | From your question, I understood (hopefully correctly) that you want to estimate the next observation, given the observations up to now. Let $y_{1:N} = Y$ the N observations you have seen until now an | Predict observation using Hidden Markov Models
From your question, I understood (hopefully correctly) that you want to estimate the next observation, given the observations up to now. Let $y_{1:N} = Y$ the N observations you have seen until now and let $\Theta$ be the parameters of the HMM. Then you want to infer the p... | Predict observation using Hidden Markov Models
From your question, I understood (hopefully correctly) that you want to estimate the next observation, given the observations up to now. Let $y_{1:N} = Y$ the N observations you have seen until now an |
35,176 | Predict observation using Hidden Markov Models | You can solve this problem with 2 way.
You can set new observations to your HMM model and run forward probabilities.Once you have you should focus on last column of probabilities because the forward algorithm efficiently sums over all the probabilities of all possible paths to each state for each observation in each s... | Predict observation using Hidden Markov Models | You can solve this problem with 2 way.
You can set new observations to your HMM model and run forward probabilities.Once you have you should focus on last column of probabilities because the forward | Predict observation using Hidden Markov Models
You can solve this problem with 2 way.
You can set new observations to your HMM model and run forward probabilities.Once you have you should focus on last column of probabilities because the forward algorithm efficiently sums over all the probabilities of all possible pat... | Predict observation using Hidden Markov Models
You can solve this problem with 2 way.
You can set new observations to your HMM model and run forward probabilities.Once you have you should focus on last column of probabilities because the forward |
35,177 | Question about standard deviation and central limit theorem | Yes, the sample standard deviation is asymptotically normal. Let the sample standard deviation be $\hat{\sigma} = \sqrt{\frac{1}{n} \sum_{i=1}^n (x_i - \bar{x})^2}$, and let $\sigma$ be the population standard deviation. Let's use the central limit theorem to show that
$$ \sqrt{n}(\hat{\sigma} - \sigma) \xrightarrow{d}... | Question about standard deviation and central limit theorem | Yes, the sample standard deviation is asymptotically normal. Let the sample standard deviation be $\hat{\sigma} = \sqrt{\frac{1}{n} \sum_{i=1}^n (x_i - \bar{x})^2}$, and let $\sigma$ be the population | Question about standard deviation and central limit theorem
Yes, the sample standard deviation is asymptotically normal. Let the sample standard deviation be $\hat{\sigma} = \sqrt{\frac{1}{n} \sum_{i=1}^n (x_i - \bar{x})^2}$, and let $\sigma$ be the population standard deviation. Let's use the central limit theorem to ... | Question about standard deviation and central limit theorem
Yes, the sample standard deviation is asymptotically normal. Let the sample standard deviation be $\hat{\sigma} = \sqrt{\frac{1}{n} \sum_{i=1}^n (x_i - \bar{x})^2}$, and let $\sigma$ be the population |
35,178 | Question about standard deviation and central limit theorem | In the comments on Paul's answer Whuber commented that the case of a Bernoulli variable with $p=1/2$ contradicts with his argument. In this question we look further into the Delta method with a graphic. This will provide some intuition and explanation about the (multivariate) Delta method and it explains why the Bernou... | Question about standard deviation and central limit theorem | In the comments on Paul's answer Whuber commented that the case of a Bernoulli variable with $p=1/2$ contradicts with his argument. In this question we look further into the Delta method with a graphi | Question about standard deviation and central limit theorem
In the comments on Paul's answer Whuber commented that the case of a Bernoulli variable with $p=1/2$ contradicts with his argument. In this question we look further into the Delta method with a graphic. This will provide some intuition and explanation about th... | Question about standard deviation and central limit theorem
In the comments on Paul's answer Whuber commented that the case of a Bernoulli variable with $p=1/2$ contradicts with his argument. In this question we look further into the Delta method with a graphi |
35,179 | Do kernel methods "scale" with the amount of data? | It's not necessary to hold the whole kernel matrix in memory at all times, but ofcourse you pay a price of recomputing entries if you don't. Kernel methods are very efficient in dealing with high input dimensionality thanks to the kernel trick, but as you correctly note they don't scale up that easily to large numbers ... | Do kernel methods "scale" with the amount of data? | It's not necessary to hold the whole kernel matrix in memory at all times, but ofcourse you pay a price of recomputing entries if you don't. Kernel methods are very efficient in dealing with high inpu | Do kernel methods "scale" with the amount of data?
It's not necessary to hold the whole kernel matrix in memory at all times, but ofcourse you pay a price of recomputing entries if you don't. Kernel methods are very efficient in dealing with high input dimensionality thanks to the kernel trick, but as you correctly not... | Do kernel methods "scale" with the amount of data?
It's not necessary to hold the whole kernel matrix in memory at all times, but ofcourse you pay a price of recomputing entries if you don't. Kernel methods are very efficient in dealing with high inpu |
35,180 | Do kernel methods "scale" with the amount of data? | There is a rich history of literature about dealing with large kernels.
"Random features for large-scale kernel machines" by Rahimi and Recht is an important milestone. They embed the input in a lower dimension in a randomized fashion to achieve scalability. This work has spawned further interesting works in dealing wi... | Do kernel methods "scale" with the amount of data? | There is a rich history of literature about dealing with large kernels.
"Random features for large-scale kernel machines" by Rahimi and Recht is an important milestone. They embed the input in a lower | Do kernel methods "scale" with the amount of data?
There is a rich history of literature about dealing with large kernels.
"Random features for large-scale kernel machines" by Rahimi and Recht is an important milestone. They embed the input in a lower dimension in a randomized fashion to achieve scalability. This work ... | Do kernel methods "scale" with the amount of data?
There is a rich history of literature about dealing with large kernels.
"Random features for large-scale kernel machines" by Rahimi and Recht is an important milestone. They embed the input in a lower |
35,181 | Do kernel methods "scale" with the amount of data? | I think some kernel computation can be distributed to the cluster. Then this algorithm could be regarded as scalable, since there are huge amount of memory and cpu in the computing cluster. | Do kernel methods "scale" with the amount of data? | I think some kernel computation can be distributed to the cluster. Then this algorithm could be regarded as scalable, since there are huge amount of memory and cpu in the computing cluster. | Do kernel methods "scale" with the amount of data?
I think some kernel computation can be distributed to the cluster. Then this algorithm could be regarded as scalable, since there are huge amount of memory and cpu in the computing cluster. | Do kernel methods "scale" with the amount of data?
I think some kernel computation can be distributed to the cluster. Then this algorithm could be regarded as scalable, since there are huge amount of memory and cpu in the computing cluster. |
35,182 | How to calculate the covariance between two observations of the same variable? | @AndyW has provided a nice answer. Let me throw out one small additional point relative to the "[w]hat does this mean" part of your question.
It does seem incomprehensible that there can be a covariance between two single points. What you need to bear in mind is that the two points you have are just realizations fr... | How to calculate the covariance between two observations of the same variable? | @AndyW has provided a nice answer. Let me throw out one small additional point relative to the "[w]hat does this mean" part of your question.
It does seem incomprehensible that there can be a covar | How to calculate the covariance between two observations of the same variable?
@AndyW has provided a nice answer. Let me throw out one small additional point relative to the "[w]hat does this mean" part of your question.
It does seem incomprehensible that there can be a covariance between two single points. What yo... | How to calculate the covariance between two observations of the same variable?
@AndyW has provided a nice answer. Let me throw out one small additional point relative to the "[w]hat does this mean" part of your question.
It does seem incomprehensible that there can be a covar |
35,183 | How to calculate the covariance between two observations of the same variable? | One useful way to rewrite the variance instead of square deviations from the mean is in terms of squared deviations from every other observation (via Wikipedia):
$${\rm Var}(X) = \frac{1}{n^2}\sum_{i=1}^{n}\sum_{j=1}^{n}\frac{1}{2}(x_i - x_j)^2$$
You can imagine making a figure where $x_i$ are the rows and $x_j$ are th... | How to calculate the covariance between two observations of the same variable? | One useful way to rewrite the variance instead of square deviations from the mean is in terms of squared deviations from every other observation (via Wikipedia):
$${\rm Var}(X) = \frac{1}{n^2}\sum_{i= | How to calculate the covariance between two observations of the same variable?
One useful way to rewrite the variance instead of square deviations from the mean is in terms of squared deviations from every other observation (via Wikipedia):
$${\rm Var}(X) = \frac{1}{n^2}\sum_{i=1}^{n}\sum_{j=1}^{n}\frac{1}{2}(x_i - x_j... | How to calculate the covariance between two observations of the same variable?
One useful way to rewrite the variance instead of square deviations from the mean is in terms of squared deviations from every other observation (via Wikipedia):
$${\rm Var}(X) = \frac{1}{n^2}\sum_{i= |
35,184 | Choosing a regression model | You can look at AIC, BIC or any of the other similar measures.
You could use your eyes and sense of the field.
Or you could avoid some of the problem by using splines. | Choosing a regression model | You can look at AIC, BIC or any of the other similar measures.
You could use your eyes and sense of the field.
Or you could avoid some of the problem by using splines. | Choosing a regression model
You can look at AIC, BIC or any of the other similar measures.
You could use your eyes and sense of the field.
Or you could avoid some of the problem by using splines. | Choosing a regression model
You can look at AIC, BIC or any of the other similar measures.
You could use your eyes and sense of the field.
Or you could avoid some of the problem by using splines. |
35,185 | Choosing a regression model | It's likely to be the case that you are not going to be able to find a polynomial that constitutes a correct description of the relationship no matter how much data you have.
This problem may extend to almost any class of models.
However, usually we're interested in getting a good description that suffices for some pur... | Choosing a regression model | It's likely to be the case that you are not going to be able to find a polynomial that constitutes a correct description of the relationship no matter how much data you have.
This problem may extend t | Choosing a regression model
It's likely to be the case that you are not going to be able to find a polynomial that constitutes a correct description of the relationship no matter how much data you have.
This problem may extend to almost any class of models.
However, usually we're interested in getting a good descriptio... | Choosing a regression model
It's likely to be the case that you are not going to be able to find a polynomial that constitutes a correct description of the relationship no matter how much data you have.
This problem may extend t |
35,186 | Choosing a regression model | I would say very often people align themselves with one of three different approaches:
frequentists, which make use of tests such as the F-test
bayesians, which make use of bayesian inference
information theory guys, which use the BIC and AIC, just like other examples cited above.
Frequentist analysis is probably bot... | Choosing a regression model | I would say very often people align themselves with one of three different approaches:
frequentists, which make use of tests such as the F-test
bayesians, which make use of bayesian inference
informa | Choosing a regression model
I would say very often people align themselves with one of three different approaches:
frequentists, which make use of tests such as the F-test
bayesians, which make use of bayesian inference
information theory guys, which use the BIC and AIC, just like other examples cited above.
Frequent... | Choosing a regression model
I would say very often people align themselves with one of three different approaches:
frequentists, which make use of tests such as the F-test
bayesians, which make use of bayesian inference
informa |
35,187 | Choosing a regression model | I would use restricted cubic splines which allow you to better approximate the curve. As an added refinement, may use AICc (or BIC) to chose the number of knots. | Choosing a regression model | I would use restricted cubic splines which allow you to better approximate the curve. As an added refinement, may use AICc (or BIC) to chose the number of knots. | Choosing a regression model
I would use restricted cubic splines which allow you to better approximate the curve. As an added refinement, may use AICc (or BIC) to chose the number of knots. | Choosing a regression model
I would use restricted cubic splines which allow you to better approximate the curve. As an added refinement, may use AICc (or BIC) to chose the number of knots. |
35,188 | Can a multivariate distribution with a singular covariance matrix have a density function? | A singular covariance matrix means that there exists a linear combination
$Y = \sum_{i=1}^n a_i X_i$ of the $n$ random variables such that $E[Y] = a_0$
and $\operatorname{var}(Y) = 0$. Thus,
all the probability mass lies in a hyperplane of $\mathbb R^n$ defined by
$\sum_{i=1}^n a_i x_i = a_0$ and so
the $n$ random va... | Can a multivariate distribution with a singular covariance matrix have a density function? | A singular covariance matrix means that there exists a linear combination
$Y = \sum_{i=1}^n a_i X_i$ of the $n$ random variables such that $E[Y] = a_0$
and $\operatorname{var}(Y) = 0$. Thus,
all the | Can a multivariate distribution with a singular covariance matrix have a density function?
A singular covariance matrix means that there exists a linear combination
$Y = \sum_{i=1}^n a_i X_i$ of the $n$ random variables such that $E[Y] = a_0$
and $\operatorname{var}(Y) = 0$. Thus,
all the probability mass lies in a h... | Can a multivariate distribution with a singular covariance matrix have a density function?
A singular covariance matrix means that there exists a linear combination
$Y = \sum_{i=1}^n a_i X_i$ of the $n$ random variables such that $E[Y] = a_0$
and $\operatorname{var}(Y) = 0$. Thus,
all the |
35,189 | Can a multivariate distribution with a singular covariance matrix have a density function? | Yes, but it will be a probability distribution over a lower dimensional subspace. You could argue that it is a probability distribution in R^N if you allow things like dirac delta functions. That's a subtle mathematical issue but physicists, for example, do it all the time. | Can a multivariate distribution with a singular covariance matrix have a density function? | Yes, but it will be a probability distribution over a lower dimensional subspace. You could argue that it is a probability distribution in R^N if you allow things like dirac delta functions. That's a | Can a multivariate distribution with a singular covariance matrix have a density function?
Yes, but it will be a probability distribution over a lower dimensional subspace. You could argue that it is a probability distribution in R^N if you allow things like dirac delta functions. That's a subtle mathematical issue but... | Can a multivariate distribution with a singular covariance matrix have a density function?
Yes, but it will be a probability distribution over a lower dimensional subspace. You could argue that it is a probability distribution in R^N if you allow things like dirac delta functions. That's a |
35,190 | Can a multivariate distribution with a singular covariance matrix have a density function? | Although this is alluded to above, I want to make it clearer that whilst it may not have a meaningful density on $\mathbb{R}^{n}$ you can define the density on a Rank($\Sigma$)-dimensional subspace, where $\Sigma$ denotes the covariance matrix. | Can a multivariate distribution with a singular covariance matrix have a density function? | Although this is alluded to above, I want to make it clearer that whilst it may not have a meaningful density on $\mathbb{R}^{n}$ you can define the density on a Rank($\Sigma$)-dimensional subspace, w | Can a multivariate distribution with a singular covariance matrix have a density function?
Although this is alluded to above, I want to make it clearer that whilst it may not have a meaningful density on $\mathbb{R}^{n}$ you can define the density on a Rank($\Sigma$)-dimensional subspace, where $\Sigma$ denotes the cov... | Can a multivariate distribution with a singular covariance matrix have a density function?
Although this is alluded to above, I want to make it clearer that whilst it may not have a meaningful density on $\mathbb{R}^{n}$ you can define the density on a Rank($\Sigma$)-dimensional subspace, w |
35,191 | Why use rejection sampling if it still uses the distribution? | Therefore we still use the distribution of p for the randomly generated values x.
Computing the density, $p$, isn't the same as sampling random variables from the distribution $p$ is the density for.
Why don't we sample directly from p?
I'm uncertain what you mean by "sample directly". How do you propose to sample ... | Why use rejection sampling if it still uses the distribution? | Therefore we still use the distribution of p for the randomly generated values x.
Computing the density, $p$, isn't the same as sampling random variables from the distribution $p$ is the density for. | Why use rejection sampling if it still uses the distribution?
Therefore we still use the distribution of p for the randomly generated values x.
Computing the density, $p$, isn't the same as sampling random variables from the distribution $p$ is the density for.
Why don't we sample directly from p?
I'm uncertain wha... | Why use rejection sampling if it still uses the distribution?
Therefore we still use the distribution of p for the randomly generated values x.
Computing the density, $p$, isn't the same as sampling random variables from the distribution $p$ is the density for. |
35,192 | Why use rejection sampling if it still uses the distribution? | Sampling from a distribution means getting a sample with its probability matching the pdf of that distribution. In rejection sampling, we take random samples and select such that the pdf of these samples donot exceed the pdf of given distribution. This is the rejection criteria.
This way we have appropriate samples a... | Why use rejection sampling if it still uses the distribution? | Sampling from a distribution means getting a sample with its probability matching the pdf of that distribution. In rejection sampling, we take random samples and select such that the pdf of these sam | Why use rejection sampling if it still uses the distribution?
Sampling from a distribution means getting a sample with its probability matching the pdf of that distribution. In rejection sampling, we take random samples and select such that the pdf of these samples donot exceed the pdf of given distribution. This is t... | Why use rejection sampling if it still uses the distribution?
Sampling from a distribution means getting a sample with its probability matching the pdf of that distribution. In rejection sampling, we take random samples and select such that the pdf of these sam |
35,193 | Why use rejection sampling if it still uses the distribution? | So why do we use rejection sampling exactly?
There are a few reasons to use rejection sampling.
Historically, computation was the bottleneck in random variate generation. Calculation of functions like $log(\cdot)$, $exp(\cdot)$ and $sin(\cdot$) were time consuming. Some rejection techniques enabled avoiding the comput... | Why use rejection sampling if it still uses the distribution? | So why do we use rejection sampling exactly?
There are a few reasons to use rejection sampling.
Historically, computation was the bottleneck in random variate generation. Calculation of functions lik | Why use rejection sampling if it still uses the distribution?
So why do we use rejection sampling exactly?
There are a few reasons to use rejection sampling.
Historically, computation was the bottleneck in random variate generation. Calculation of functions like $log(\cdot)$, $exp(\cdot)$ and $sin(\cdot$) were time co... | Why use rejection sampling if it still uses the distribution?
So why do we use rejection sampling exactly?
There are a few reasons to use rejection sampling.
Historically, computation was the bottleneck in random variate generation. Calculation of functions lik |
35,194 | When correlation turns too high? | Some correlation is not a problem. Actually, it is the very reason why we add control variables. Consider what would happen when all explanatory variables are not correlated with one another. In that case there would be no added value to adding them all in one model: you could just look at a series of bivariate regress... | When correlation turns too high? | Some correlation is not a problem. Actually, it is the very reason why we add control variables. Consider what would happen when all explanatory variables are not correlated with one another. In that | When correlation turns too high?
Some correlation is not a problem. Actually, it is the very reason why we add control variables. Consider what would happen when all explanatory variables are not correlated with one another. In that case there would be no added value to adding them all in one model: you could just look... | When correlation turns too high?
Some correlation is not a problem. Actually, it is the very reason why we add control variables. Consider what would happen when all explanatory variables are not correlated with one another. In that |
35,195 | What does "$\sim$" mean and $A | B \sim C$? | Usually ~ means "has the distribution...", so you are correct.
A ~ B, means that the random variable A has the distribution B (or is distributed equal to B).
In the article you mentioned DP is described as a distribution (see page 05, Dirichlet Processes):
A Dirichlet process DP($\alpha_0$;$G_0$) is defined to be the ... | What does "$\sim$" mean and $A | B \sim C$? | Usually ~ means "has the distribution...", so you are correct.
A ~ B, means that the random variable A has the distribution B (or is distributed equal to B).
In the article you mentioned DP is describ | What does "$\sim$" mean and $A | B \sim C$?
Usually ~ means "has the distribution...", so you are correct.
A ~ B, means that the random variable A has the distribution B (or is distributed equal to B).
In the article you mentioned DP is described as a distribution (see page 05, Dirichlet Processes):
A Dirichlet proces... | What does "$\sim$" mean and $A | B \sim C$?
Usually ~ means "has the distribution...", so you are correct.
A ~ B, means that the random variable A has the distribution B (or is distributed equal to B).
In the article you mentioned DP is describ |
35,196 | What does "$\sim$" mean and $A | B \sim C$? | The ~ symbol means 'distributed according to'. So $a \sim G$ means the random variable $a$ is distributed according to the distribution $G$.
The bar symbol, as in $x_i|\theta_i \sim F(\theta_i)$, means "given". You shouldn't let it confuse you. It's often used in hierarchical models to emphasize that the lower stage o... | What does "$\sim$" mean and $A | B \sim C$? | The ~ symbol means 'distributed according to'. So $a \sim G$ means the random variable $a$ is distributed according to the distribution $G$.
The bar symbol, as in $x_i|\theta_i \sim F(\theta_i)$, mea | What does "$\sim$" mean and $A | B \sim C$?
The ~ symbol means 'distributed according to'. So $a \sim G$ means the random variable $a$ is distributed according to the distribution $G$.
The bar symbol, as in $x_i|\theta_i \sim F(\theta_i)$, means "given". You shouldn't let it confuse you. It's often used in hierarchica... | What does "$\sim$" mean and $A | B \sim C$?
The ~ symbol means 'distributed according to'. So $a \sim G$ means the random variable $a$ is distributed according to the distribution $G$.
The bar symbol, as in $x_i|\theta_i \sim F(\theta_i)$, mea |
35,197 | How to calculate ratings/rankings from Paired comparison / Pairwise comparison of large data-sets? | Hopefully this isn't too late, but your data is still valuable using the Bradley-Terry model. This paper is a nice reference MM Algorithms for generalized Bradley-Terry models. Equation 4 is the one you want.
Brief explanation as I guess you are not a mathematition, and I'm being nice as I'd really like a copy of your ... | How to calculate ratings/rankings from Paired comparison / Pairwise comparison of large data-sets? | Hopefully this isn't too late, but your data is still valuable using the Bradley-Terry model. This paper is a nice reference MM Algorithms for generalized Bradley-Terry models. Equation 4 is the one y | How to calculate ratings/rankings from Paired comparison / Pairwise comparison of large data-sets?
Hopefully this isn't too late, but your data is still valuable using the Bradley-Terry model. This paper is a nice reference MM Algorithms for generalized Bradley-Terry models. Equation 4 is the one you want.
Brief explan... | How to calculate ratings/rankings from Paired comparison / Pairwise comparison of large data-sets?
Hopefully this isn't too late, but your data is still valuable using the Bradley-Terry model. This paper is a nice reference MM Algorithms for generalized Bradley-Terry models. Equation 4 is the one y |
35,198 | Translate R's glm command into mathematical notation | For a binary logistic regression, the usual use case for the binomial GLM with a logit link, you're modeling the probability that your dependent variable is a "success" (or "yes"), conventionally coded as $1$. The way that you're doing this is by modeling the log odds. So rather than modeling the mean of the response a... | Translate R's glm command into mathematical notation | For a binary logistic regression, the usual use case for the binomial GLM with a logit link, you're modeling the probability that your dependent variable is a "success" (or "yes"), conventionally code | Translate R's glm command into mathematical notation
For a binary logistic regression, the usual use case for the binomial GLM with a logit link, you're modeling the probability that your dependent variable is a "success" (or "yes"), conventionally coded as $1$. The way that you're doing this is by modeling the log odd... | Translate R's glm command into mathematical notation
For a binary logistic regression, the usual use case for the binomial GLM with a logit link, you're modeling the probability that your dependent variable is a "success" (or "yes"), conventionally code |
35,199 | Does ARIMA require normally distributed errors or normally distributed input data? | First, having normally distributed errors is equivalent to having normally distributed observations for any linear time series model.
Second, it is not necessary to assume normality of errors. Often, maximum likelihood is used to estimate the parameters of the model, and then a Gaussian likelihood is used, but it gives... | Does ARIMA require normally distributed errors or normally distributed input data? | First, having normally distributed errors is equivalent to having normally distributed observations for any linear time series model.
Second, it is not necessary to assume normality of errors. Often, | Does ARIMA require normally distributed errors or normally distributed input data?
First, having normally distributed errors is equivalent to having normally distributed observations for any linear time series model.
Second, it is not necessary to assume normality of errors. Often, maximum likelihood is used to estimat... | Does ARIMA require normally distributed errors or normally distributed input data?
First, having normally distributed errors is equivalent to having normally distributed observations for any linear time series model.
Second, it is not necessary to assume normality of errors. Often, |
35,200 | Does ARIMA require normally distributed errors or normally distributed input data? | No -- the paper Maximum Likelihood Estimates of Non-Gaussian ARMA Models studies ARMA models with Student-t and Laplace distributed errors. Here is the abstract:
"We consider an approximate maximum likelihood algorithm for estimating parameters of possibly non-causal and non-invertible autoregressive moving average pro... | Does ARIMA require normally distributed errors or normally distributed input data? | No -- the paper Maximum Likelihood Estimates of Non-Gaussian ARMA Models studies ARMA models with Student-t and Laplace distributed errors. Here is the abstract:
"We consider an approximate maximum li | Does ARIMA require normally distributed errors or normally distributed input data?
No -- the paper Maximum Likelihood Estimates of Non-Gaussian ARMA Models studies ARMA models with Student-t and Laplace distributed errors. Here is the abstract:
"We consider an approximate maximum likelihood algorithm for estimating par... | Does ARIMA require normally distributed errors or normally distributed input data?
No -- the paper Maximum Likelihood Estimates of Non-Gaussian ARMA Models studies ARMA models with Student-t and Laplace distributed errors. Here is the abstract:
"We consider an approximate maximum li |
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