idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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41,501 | What would the distribution of time spent per day on a given site look like? | This type of question raises a lot of issues that would be worth talking about. I can only speak for myself, but I would want to make the following points.
The most basic properties you would expect for this distribution is that it would be continuous and have non-negative support. You could quibble with the first o... | What would the distribution of time spent per day on a given site look like? | This type of question raises a lot of issues that would be worth talking about. I can only speak for myself, but I would want to make the following points.
The most basic properties you would expect | What would the distribution of time spent per day on a given site look like?
This type of question raises a lot of issues that would be worth talking about. I can only speak for myself, but I would want to make the following points.
The most basic properties you would expect for this distribution is that it would be ... | What would the distribution of time spent per day on a given site look like?
This type of question raises a lot of issues that would be worth talking about. I can only speak for myself, but I would want to make the following points.
The most basic properties you would expect |
41,502 | Compare two Weibull distributions | My question is, what is the null hypothesis in this likelihood ratio test?
Under the null for that particular test as described, all the parameters are the same (which is why you were fitting a single Weibull to all the data under that case) -- under the shape-scale parameterization
$$f(x;\lambda,\theta) =\frac{\the... | Compare two Weibull distributions | My question is, what is the null hypothesis in this likelihood ratio test?
Under the null for that particular test as described, all the parameters are the same (which is why you were fitting a sing | Compare two Weibull distributions
My question is, what is the null hypothesis in this likelihood ratio test?
Under the null for that particular test as described, all the parameters are the same (which is why you were fitting a single Weibull to all the data under that case) -- under the shape-scale parameterization ... | Compare two Weibull distributions
My question is, what is the null hypothesis in this likelihood ratio test?
Under the null for that particular test as described, all the parameters are the same (which is why you were fitting a sing |
41,503 | What problem does Residual Nets solve that batch normalization does not solve? | "Skip connections eliminate singularities" by A. Emin Orhan, Xaq Pitkow offers an explanation: residual connections ameliorate singularities in neural networks.
Skip connections made the training of very deep networks possible and have become an indispensable component in a variety of neural architectures. A completel... | What problem does Residual Nets solve that batch normalization does not solve? | "Skip connections eliminate singularities" by A. Emin Orhan, Xaq Pitkow offers an explanation: residual connections ameliorate singularities in neural networks.
Skip connections made the training of | What problem does Residual Nets solve that batch normalization does not solve?
"Skip connections eliminate singularities" by A. Emin Orhan, Xaq Pitkow offers an explanation: residual connections ameliorate singularities in neural networks.
Skip connections made the training of very deep networks possible and have beco... | What problem does Residual Nets solve that batch normalization does not solve?
"Skip connections eliminate singularities" by A. Emin Orhan, Xaq Pitkow offers an explanation: residual connections ameliorate singularities in neural networks.
Skip connections made the training of |
41,504 | What problem does Residual Nets solve that batch normalization does not solve? | Batch normalization mitigates issues such as:
how can you use a large learning rate without 'breaking' the network, eg accidentally kill all ReLUs, push the preceeding layer so far in one direction, that their output is always negative, and thus no gradients flow
avoid having to shift all weights in one direction by a... | What problem does Residual Nets solve that batch normalization does not solve? | Batch normalization mitigates issues such as:
how can you use a large learning rate without 'breaking' the network, eg accidentally kill all ReLUs, push the preceeding layer so far in one direction, | What problem does Residual Nets solve that batch normalization does not solve?
Batch normalization mitigates issues such as:
how can you use a large learning rate without 'breaking' the network, eg accidentally kill all ReLUs, push the preceeding layer so far in one direction, that their output is always negative, and... | What problem does Residual Nets solve that batch normalization does not solve?
Batch normalization mitigates issues such as:
how can you use a large learning rate without 'breaking' the network, eg accidentally kill all ReLUs, push the preceeding layer so far in one direction, |
41,505 | What problem does Residual Nets solve that batch normalization does not solve? | I think the main reason in that deep networks forget the input data from some time thus their behavior depends from previous layers. And it the same as a broken phone. Resid connections adding some hopping over few layers, which gives better understanding what happening. | What problem does Residual Nets solve that batch normalization does not solve? | I think the main reason in that deep networks forget the input data from some time thus their behavior depends from previous layers. And it the same as a broken phone. Resid connections adding some ho | What problem does Residual Nets solve that batch normalization does not solve?
I think the main reason in that deep networks forget the input data from some time thus their behavior depends from previous layers. And it the same as a broken phone. Resid connections adding some hopping over few layers, which gives better... | What problem does Residual Nets solve that batch normalization does not solve?
I think the main reason in that deep networks forget the input data from some time thus their behavior depends from previous layers. And it the same as a broken phone. Resid connections adding some ho |
41,506 | Uniqueness for OLS linear regression | I'm going to transpose your notation so that it is consistent with how these things are usually written. You have a predictor matrix $X \in \mathbb R^{n \times p}$ (with the first column taken to be all $1$s) and a random response $Y \in \mathbb R^n$. We are going to fit the model $E(Y|X) = X\beta$. Your case correspon... | Uniqueness for OLS linear regression | I'm going to transpose your notation so that it is consistent with how these things are usually written. You have a predictor matrix $X \in \mathbb R^{n \times p}$ (with the first column taken to be a | Uniqueness for OLS linear regression
I'm going to transpose your notation so that it is consistent with how these things are usually written. You have a predictor matrix $X \in \mathbb R^{n \times p}$ (with the first column taken to be all $1$s) and a random response $Y \in \mathbb R^n$. We are going to fit the model $... | Uniqueness for OLS linear regression
I'm going to transpose your notation so that it is consistent with how these things are usually written. You have a predictor matrix $X \in \mathbb R^{n \times p}$ (with the first column taken to be a |
41,507 | Neural network regression with confidence interval implemented with Keras | You would have to output vectors of means and standard deviations rather than discrete values to achieve that.
One solution to get those vectors would be variational inference - generate those, sample w/reparametrization, then optimize so the results of the sampling match the original values like in normal regression (... | Neural network regression with confidence interval implemented with Keras | You would have to output vectors of means and standard deviations rather than discrete values to achieve that.
One solution to get those vectors would be variational inference - generate those, sample | Neural network regression with confidence interval implemented with Keras
You would have to output vectors of means and standard deviations rather than discrete values to achieve that.
One solution to get those vectors would be variational inference - generate those, sample w/reparametrization, then optimize so the res... | Neural network regression with confidence interval implemented with Keras
You would have to output vectors of means and standard deviations rather than discrete values to achieve that.
One solution to get those vectors would be variational inference - generate those, sample |
41,508 | Neural network regression with confidence interval implemented with Keras | Thanks to @jkm I was quite fascinated by the idea of implementing confidence intervals for regression in Keras. Personally, I hope it would boost my model network's performance as I have multiple supervised DL models on different datasets that are being fed into a single Reinforcement Learning Algorithm. Hence, the RL ... | Neural network regression with confidence interval implemented with Keras | Thanks to @jkm I was quite fascinated by the idea of implementing confidence intervals for regression in Keras. Personally, I hope it would boost my model network's performance as I have multiple supe | Neural network regression with confidence interval implemented with Keras
Thanks to @jkm I was quite fascinated by the idea of implementing confidence intervals for regression in Keras. Personally, I hope it would boost my model network's performance as I have multiple supervised DL models on different datasets that ar... | Neural network regression with confidence interval implemented with Keras
Thanks to @jkm I was quite fascinated by the idea of implementing confidence intervals for regression in Keras. Personally, I hope it would boost my model network's performance as I have multiple supe |
41,509 | Proving Bernoulli is the limit of Beta | The analysis can be a little messy, especially if carried out with full and elementary rigor, but the idea is simple and easily grasped. Focus on small regions very close to $0$ and $1$. As $\alpha$ and $\beta$ approach $0$, almost all the probability of a Beta$(\alpha,\beta)$ distribution becomes located within thes... | Proving Bernoulli is the limit of Beta | The analysis can be a little messy, especially if carried out with full and elementary rigor, but the idea is simple and easily grasped. Focus on small regions very close to $0$ and $1$. As $\alpha$ | Proving Bernoulli is the limit of Beta
The analysis can be a little messy, especially if carried out with full and elementary rigor, but the idea is simple and easily grasped. Focus on small regions very close to $0$ and $1$. As $\alpha$ and $\beta$ approach $0$, almost all the probability of a Beta$(\alpha,\beta)$ d... | Proving Bernoulli is the limit of Beta
The analysis can be a little messy, especially if carried out with full and elementary rigor, but the idea is simple and easily grasped. Focus on small regions very close to $0$ and $1$. As $\alpha$ |
41,510 | What's the point in neural networks for multivariate regression? | Here's a cartoon representation of the models. Model A uses a single network to predict both outputs. Model B uses separate networks to predict both outputs. Because the input to both networks is the same, we can re-frame this as the equivalent model C. In this case, the input is passed to to hidden/output layers that ... | What's the point in neural networks for multivariate regression? | Here's a cartoon representation of the models. Model A uses a single network to predict both outputs. Model B uses separate networks to predict both outputs. Because the input to both networks is the | What's the point in neural networks for multivariate regression?
Here's a cartoon representation of the models. Model A uses a single network to predict both outputs. Model B uses separate networks to predict both outputs. Because the input to both networks is the same, we can re-frame this as the equivalent model C. I... | What's the point in neural networks for multivariate regression?
Here's a cartoon representation of the models. Model A uses a single network to predict both outputs. Model B uses separate networks to predict both outputs. Because the input to both networks is the |
41,511 | Moments of kernel density estimates | Moments are reasonably straightforward via the law of total expectation and the law of total variance:
Law of total expectation
$${\displaystyle \operatorname {E} (Y)=\operatorname {E} (\operatorname {E} (Y\mid X)),}$$
Here the $X$ is the original variable and $Y|X$ can be thought of as the kernel. The unconditional d... | Moments of kernel density estimates | Moments are reasonably straightforward via the law of total expectation and the law of total variance:
Law of total expectation
$${\displaystyle \operatorname {E} (Y)=\operatorname {E} (\operatorname | Moments of kernel density estimates
Moments are reasonably straightforward via the law of total expectation and the law of total variance:
Law of total expectation
$${\displaystyle \operatorname {E} (Y)=\operatorname {E} (\operatorname {E} (Y\mid X)),}$$
Here the $X$ is the original variable and $Y|X$ can be thought o... | Moments of kernel density estimates
Moments are reasonably straightforward via the law of total expectation and the law of total variance:
Law of total expectation
$${\displaystyle \operatorname {E} (Y)=\operatorname {E} (\operatorname |
41,512 | Hessian matrix for maximum likelihood | You have to remember that since $\pmb{\beta} \in \Re^{n \times 1}$ is a vector, partial derivatives you described are vectors, and matrices. Especially the hessian
$$H(\pmb{\beta}, \sigma^2) = \begin{pmatrix}
\frac{\partial}{\partial \boldsymbol{\beta}^{T}}[\frac{\partial l(\boldsymbol{\beta},\sigma^{2};\mathbf{y})}... | Hessian matrix for maximum likelihood | You have to remember that since $\pmb{\beta} \in \Re^{n \times 1}$ is a vector, partial derivatives you described are vectors, and matrices. Especially the hessian
$$H(\pmb{\beta}, \sigma^2) = \begin | Hessian matrix for maximum likelihood
You have to remember that since $\pmb{\beta} \in \Re^{n \times 1}$ is a vector, partial derivatives you described are vectors, and matrices. Especially the hessian
$$H(\pmb{\beta}, \sigma^2) = \begin{pmatrix}
\frac{\partial}{\partial \boldsymbol{\beta}^{T}}[\frac{\partial l(\bol... | Hessian matrix for maximum likelihood
You have to remember that since $\pmb{\beta} \in \Re^{n \times 1}$ is a vector, partial derivatives you described are vectors, and matrices. Especially the hessian
$$H(\pmb{\beta}, \sigma^2) = \begin |
41,513 | Variance of the sum of random vectors | You are asking for $\text{Var}(\sum_i X_i)$ when $\sum_i X_i$ is a vector of multiple elements, though I think what you're asking for is the covariance matrix (the generalization of variance to a vector).
You can solve this in a similar way to the univariate case.
Suppose we have two variables, $x, y \in \mathbb{R}^1$... | Variance of the sum of random vectors | You are asking for $\text{Var}(\sum_i X_i)$ when $\sum_i X_i$ is a vector of multiple elements, though I think what you're asking for is the covariance matrix (the generalization of variance to a vect | Variance of the sum of random vectors
You are asking for $\text{Var}(\sum_i X_i)$ when $\sum_i X_i$ is a vector of multiple elements, though I think what you're asking for is the covariance matrix (the generalization of variance to a vector).
You can solve this in a similar way to the univariate case.
Suppose we have ... | Variance of the sum of random vectors
You are asking for $\text{Var}(\sum_i X_i)$ when $\sum_i X_i$ is a vector of multiple elements, though I think what you're asking for is the covariance matrix (the generalization of variance to a vect |
41,514 | Variance of the sum of random vectors | Define $\mathrm{cov}(X_i, X_j) = EX_iX_j^T - EX_iEX_j^T$, which obviously reduces to the usual definition when $X_i$ is one-dimensional. Then the variance-covariance matrix of $X_i$ is $\mathrm{var}(X_i)=\mathrm{cov}(X_i, X_i)$. Thus,
\begin{align*}
\mathrm{var}\left(\sum_{i}X_i\right) &= E\left(\sum_i X_i \right)\left... | Variance of the sum of random vectors | Define $\mathrm{cov}(X_i, X_j) = EX_iX_j^T - EX_iEX_j^T$, which obviously reduces to the usual definition when $X_i$ is one-dimensional. Then the variance-covariance matrix of $X_i$ is $\mathrm{var}(X | Variance of the sum of random vectors
Define $\mathrm{cov}(X_i, X_j) = EX_iX_j^T - EX_iEX_j^T$, which obviously reduces to the usual definition when $X_i$ is one-dimensional. Then the variance-covariance matrix of $X_i$ is $\mathrm{var}(X_i)=\mathrm{cov}(X_i, X_i)$. Thus,
\begin{align*}
\mathrm{var}\left(\sum_{i}X_i\ri... | Variance of the sum of random vectors
Define $\mathrm{cov}(X_i, X_j) = EX_iX_j^T - EX_iEX_j^T$, which obviously reduces to the usual definition when $X_i$ is one-dimensional. Then the variance-covariance matrix of $X_i$ is $\mathrm{var}(X |
41,515 | What is the distribution of the (arbitrarily) weighted Maximum Likelihood Estimator? | In general, your question has no answer. There are a couple of reasons.
1) Suppose that all $w_i = 1$. Even in that case, the distribution of MLE estimate depends on the distribution of data, i.e. on the function $l(\theta;x,y)$. For instance, it is possible to prove that in the exponential family of distributions, com... | What is the distribution of the (arbitrarily) weighted Maximum Likelihood Estimator? | In general, your question has no answer. There are a couple of reasons.
1) Suppose that all $w_i = 1$. Even in that case, the distribution of MLE estimate depends on the distribution of data, i.e. on | What is the distribution of the (arbitrarily) weighted Maximum Likelihood Estimator?
In general, your question has no answer. There are a couple of reasons.
1) Suppose that all $w_i = 1$. Even in that case, the distribution of MLE estimate depends on the distribution of data, i.e. on the function $l(\theta;x,y)$. For i... | What is the distribution of the (arbitrarily) weighted Maximum Likelihood Estimator?
In general, your question has no answer. There are a couple of reasons.
1) Suppose that all $w_i = 1$. Even in that case, the distribution of MLE estimate depends on the distribution of data, i.e. on |
41,516 | What is the distribution of the (arbitrarily) weighted Maximum Likelihood Estimator? | In general the answer of Nik Tuzov is correct, but some details are not completely correct. In summary, the distribution of the WMLE is unknown. You can write down the actual equation for the MLE (weights or none) and write the complete derivative to determine the extremal point(s) maximum. Which gives you a computatio... | What is the distribution of the (arbitrarily) weighted Maximum Likelihood Estimator? | In general the answer of Nik Tuzov is correct, but some details are not completely correct. In summary, the distribution of the WMLE is unknown. You can write down the actual equation for the MLE (wei | What is the distribution of the (arbitrarily) weighted Maximum Likelihood Estimator?
In general the answer of Nik Tuzov is correct, but some details are not completely correct. In summary, the distribution of the WMLE is unknown. You can write down the actual equation for the MLE (weights or none) and write the complet... | What is the distribution of the (arbitrarily) weighted Maximum Likelihood Estimator?
In general the answer of Nik Tuzov is correct, but some details are not completely correct. In summary, the distribution of the WMLE is unknown. You can write down the actual equation for the MLE (wei |
41,517 | Most accessible introduction to directional statistics? | Batschelet is a very friendly and rich book but inevitably a little dated. It covers a lot of ground.
I find the books first authored by Fisher to have the best overall blend of statistical and scientific thinking. Fisher is best on several modern approaches, including graphics, bootstrapping and modelling.
The book ... | Most accessible introduction to directional statistics? | Batschelet is a very friendly and rich book but inevitably a little dated. It covers a lot of ground.
I find the books first authored by Fisher to have the best overall blend of statistical and scien | Most accessible introduction to directional statistics?
Batschelet is a very friendly and rich book but inevitably a little dated. It covers a lot of ground.
I find the books first authored by Fisher to have the best overall blend of statistical and scientific thinking. Fisher is best on several modern approaches, inc... | Most accessible introduction to directional statistics?
Batschelet is a very friendly and rich book but inevitably a little dated. It covers a lot of ground.
I find the books first authored by Fisher to have the best overall blend of statistical and scien |
41,518 | Nested Cross-Validation for Feature Selection and Hyperparameter Optimization | I figured out where my understanding was off, figured I should answer my question in case anyone else stumbles upon it.
To start, sklearn makes nested cross-validation deceptively easy. I read their example over and over but never got it until I looked at the extremely helpful pseudocode given in the answer to this que... | Nested Cross-Validation for Feature Selection and Hyperparameter Optimization | I figured out where my understanding was off, figured I should answer my question in case anyone else stumbles upon it.
To start, sklearn makes nested cross-validation deceptively easy. I read their e | Nested Cross-Validation for Feature Selection and Hyperparameter Optimization
I figured out where my understanding was off, figured I should answer my question in case anyone else stumbles upon it.
To start, sklearn makes nested cross-validation deceptively easy. I read their example over and over but never got it unti... | Nested Cross-Validation for Feature Selection and Hyperparameter Optimization
I figured out where my understanding was off, figured I should answer my question in case anyone else stumbles upon it.
To start, sklearn makes nested cross-validation deceptively easy. I read their e |
41,519 | Why is boosting less likely to overfit? | The general idea is that each individual tree will over fit some parts of the data, but therefor will under fit other parts of the data. But in boosting, you don't use the individual trees, but rather "average" them all together, so for a particular data point (or group of points) the trees that over fit that point (t... | Why is boosting less likely to overfit? | The general idea is that each individual tree will over fit some parts of the data, but therefor will under fit other parts of the data. But in boosting, you don't use the individual trees, but rathe | Why is boosting less likely to overfit?
The general idea is that each individual tree will over fit some parts of the data, but therefor will under fit other parts of the data. But in boosting, you don't use the individual trees, but rather "average" them all together, so for a particular data point (or group of point... | Why is boosting less likely to overfit?
The general idea is that each individual tree will over fit some parts of the data, but therefor will under fit other parts of the data. But in boosting, you don't use the individual trees, but rathe |
41,520 | Why is boosting less likely to overfit? | This is one of those things that has been observed for a while but not necessarily theoretically explained.
In one of the original random forest papers, Breiman hypothesized that adaboost functions as a kind of random forest in its latter stage as the weights are essentially drawn from a random distribution. His full s... | Why is boosting less likely to overfit? | This is one of those things that has been observed for a while but not necessarily theoretically explained.
In one of the original random forest papers, Breiman hypothesized that adaboost functions as | Why is boosting less likely to overfit?
This is one of those things that has been observed for a while but not necessarily theoretically explained.
In one of the original random forest papers, Breiman hypothesized that adaboost functions as a kind of random forest in its latter stage as the weights are essentially draw... | Why is boosting less likely to overfit?
This is one of those things that has been observed for a while but not necessarily theoretically explained.
In one of the original random forest papers, Breiman hypothesized that adaboost functions as |
41,521 | Why is boosting less likely to overfit? | This is not a very formal justification, but the discussion in this article provides some interesting perspective on this question. I would recommend reading the article itself (it is fairly short and not too technical), but here is an overview of the basic argument:
The way boosting selects trees is algorithmically si... | Why is boosting less likely to overfit? | This is not a very formal justification, but the discussion in this article provides some interesting perspective on this question. I would recommend reading the article itself (it is fairly short and | Why is boosting less likely to overfit?
This is not a very formal justification, but the discussion in this article provides some interesting perspective on this question. I would recommend reading the article itself (it is fairly short and not too technical), but here is an overview of the basic argument:
The way boos... | Why is boosting less likely to overfit?
This is not a very formal justification, but the discussion in this article provides some interesting perspective on this question. I would recommend reading the article itself (it is fairly short and |
41,522 | Is Partitioning Around Medoids (PAM) deterministic? | PAM is close to being deterministic, but there may be ties.
In particular, PAM does not use a random generator.
The heart of PAM is the BUILD phase that tries to smartly choose the initial settings (there exist variations that use a random sample, but IIRC that is not the original PAM algorithm). If I remember correctl... | Is Partitioning Around Medoids (PAM) deterministic? | PAM is close to being deterministic, but there may be ties.
In particular, PAM does not use a random generator.
The heart of PAM is the BUILD phase that tries to smartly choose the initial settings (t | Is Partitioning Around Medoids (PAM) deterministic?
PAM is close to being deterministic, but there may be ties.
In particular, PAM does not use a random generator.
The heart of PAM is the BUILD phase that tries to smartly choose the initial settings (there exist variations that use a random sample, but IIRC that is not... | Is Partitioning Around Medoids (PAM) deterministic?
PAM is close to being deterministic, but there may be ties.
In particular, PAM does not use a random generator.
The heart of PAM is the BUILD phase that tries to smartly choose the initial settings (t |
41,523 | Is Partitioning Around Medoids (PAM) deterministic? | Short answer no. It is sensitive to the starting medoids. There could be multiple correct combinations of medoids that minimize the objective function.
Some software packages implement a smart building stage where the starting medoids are selected in a deterministic way. If the starting medoids are a deterministic the ... | Is Partitioning Around Medoids (PAM) deterministic? | Short answer no. It is sensitive to the starting medoids. There could be multiple correct combinations of medoids that minimize the objective function.
Some software packages implement a smart buildin | Is Partitioning Around Medoids (PAM) deterministic?
Short answer no. It is sensitive to the starting medoids. There could be multiple correct combinations of medoids that minimize the objective function.
Some software packages implement a smart building stage where the starting medoids are selected in a deterministic w... | Is Partitioning Around Medoids (PAM) deterministic?
Short answer no. It is sensitive to the starting medoids. There could be multiple correct combinations of medoids that minimize the objective function.
Some software packages implement a smart buildin |
41,524 | Comparing Cox proportional hazards models - AIC? | For the Cox proportional hazard model the baselinehazard (i.e. 'intercept') is not estimated and so the likelihood is only a partial one. Even though this is partial, it is possible to compare nested COX models using a likelihood ratio test (LRT) to test for a significant difference in model fit.
The Akaike's Informat... | Comparing Cox proportional hazards models - AIC? | For the Cox proportional hazard model the baselinehazard (i.e. 'intercept') is not estimated and so the likelihood is only a partial one. Even though this is partial, it is possible to compare nested | Comparing Cox proportional hazards models - AIC?
For the Cox proportional hazard model the baselinehazard (i.e. 'intercept') is not estimated and so the likelihood is only a partial one. Even though this is partial, it is possible to compare nested COX models using a likelihood ratio test (LRT) to test for a significan... | Comparing Cox proportional hazards models - AIC?
For the Cox proportional hazard model the baselinehazard (i.e. 'intercept') is not estimated and so the likelihood is only a partial one. Even though this is partial, it is possible to compare nested |
41,525 | Comparing Cox proportional hazards models - AIC? | I think that your problem is one of model selection.
If you would consider forward selection, and stop after including one variable, then you would end up with the FLAB model. As compared to the other univariate model, it is more significant and has smaller AIC. From the output, there would be no reason not to select t... | Comparing Cox proportional hazards models - AIC? | I think that your problem is one of model selection.
If you would consider forward selection, and stop after including one variable, then you would end up with the FLAB model. As compared to the other | Comparing Cox proportional hazards models - AIC?
I think that your problem is one of model selection.
If you would consider forward selection, and stop after including one variable, then you would end up with the FLAB model. As compared to the other univariate model, it is more significant and has smaller AIC. From the... | Comparing Cox proportional hazards models - AIC?
I think that your problem is one of model selection.
If you would consider forward selection, and stop after including one variable, then you would end up with the FLAB model. As compared to the other |
41,526 | Comparing Cox proportional hazards models - AIC? | With everything else being quite similar, the c-index (Concordance in the model summary) values differ and could therefore be used to compare models. Based on this, the freehand model is better (0.655 vs. 0.609). | Comparing Cox proportional hazards models - AIC? | With everything else being quite similar, the c-index (Concordance in the model summary) values differ and could therefore be used to compare models. Based on this, the freehand model is better (0.655 | Comparing Cox proportional hazards models - AIC?
With everything else being quite similar, the c-index (Concordance in the model summary) values differ and could therefore be used to compare models. Based on this, the freehand model is better (0.655 vs. 0.609). | Comparing Cox proportional hazards models - AIC?
With everything else being quite similar, the c-index (Concordance in the model summary) values differ and could therefore be used to compare models. Based on this, the freehand model is better (0.655 |
41,527 | "Smoothness" of a statistic for bootstrapping? | $\newcommand{\OLS}{\operatorname{OLS}}$This is essentially a question about mathematical, not statistical terminology, as far as I can tell.
Anyway the point is that the statistics are not a differentiable function of the sample, or are not $n-$times continuously differentiable function of the sample.
In other words ... | "Smoothness" of a statistic for bootstrapping? | $\newcommand{\OLS}{\operatorname{OLS}}$This is essentially a question about mathematical, not statistical terminology, as far as I can tell.
Anyway the point is that the statistics are not a differen | "Smoothness" of a statistic for bootstrapping?
$\newcommand{\OLS}{\operatorname{OLS}}$This is essentially a question about mathematical, not statistical terminology, as far as I can tell.
Anyway the point is that the statistics are not a differentiable function of the sample, or are not $n-$times continuously differen... | "Smoothness" of a statistic for bootstrapping?
$\newcommand{\OLS}{\operatorname{OLS}}$This is essentially a question about mathematical, not statistical terminology, as far as I can tell.
Anyway the point is that the statistics are not a differen |
41,528 | How to use isometric logratio ilr() from a package "compositions" | If your data is compositional, it means that the only relevant information available in your data is the relative information you have between parts. Therefore, you are interested in studying the relations between parts relatively. The log-ratio methodology studies this relative relations using the quotient between par... | How to use isometric logratio ilr() from a package "compositions" | If your data is compositional, it means that the only relevant information available in your data is the relative information you have between parts. Therefore, you are interested in studying the rela | How to use isometric logratio ilr() from a package "compositions"
If your data is compositional, it means that the only relevant information available in your data is the relative information you have between parts. Therefore, you are interested in studying the relations between parts relatively. The log-ratio methodol... | How to use isometric logratio ilr() from a package "compositions"
If your data is compositional, it means that the only relevant information available in your data is the relative information you have between parts. Therefore, you are interested in studying the rela |
41,529 | What is Contextual Embedding? | The contextual embedding of a word is just the corresponding hidden state of a bi-GRU:
In our model the document encoder $f$ is implemented as a bidirectional Gated Recurrent Unit (GRU) network whose hidden states form the contextual word embeddings, that is $f_i(d) = \overrightarrow{f_i}(d) \,\, ||\,\, \overleftarrow... | What is Contextual Embedding? | The contextual embedding of a word is just the corresponding hidden state of a bi-GRU:
In our model the document encoder $f$ is implemented as a bidirectional Gated Recurrent Unit (GRU) network whose | What is Contextual Embedding?
The contextual embedding of a word is just the corresponding hidden state of a bi-GRU:
In our model the document encoder $f$ is implemented as a bidirectional Gated Recurrent Unit (GRU) network whose hidden states form the contextual word embeddings, that is $f_i(d) = \overrightarrow{f_i}... | What is Contextual Embedding?
The contextual embedding of a word is just the corresponding hidden state of a bi-GRU:
In our model the document encoder $f$ is implemented as a bidirectional Gated Recurrent Unit (GRU) network whose |
41,530 | How does $\Bbb P(A) = \Bbb E(I_A)$ translate in plain English? | First let's define the indicator function:
$$
\mathbb{I_A}=\left\{
\begin{array}{ll}
1, & x \in A\\
0, & x \not \in A\\
\end{array}
\right.
$$
Now, find the expectation:
$$E(\mathbb{I_A}) = 1\times P(X \in A) + 0\times P(X \not \i... | How does $\Bbb P(A) = \Bbb E(I_A)$ translate in plain English? | First let's define the indicator function:
$$
\mathbb{I_A}=\left\{
\begin{array}{ll}
1, & x \in A\\
0, & x \not \in A\\
\end{ar | How does $\Bbb P(A) = \Bbb E(I_A)$ translate in plain English?
First let's define the indicator function:
$$
\mathbb{I_A}=\left\{
\begin{array}{ll}
1, & x \in A\\
0, & x \not \in A\\
\end{array}
\right.
$$
Now, find the expectation... | How does $\Bbb P(A) = \Bbb E(I_A)$ translate in plain English?
First let's define the indicator function:
$$
\mathbb{I_A}=\left\{
\begin{array}{ll}
1, & x \in A\\
0, & x \not \in A\\
\end{ar |
41,531 | How to report RMSE of Lasso using glmnet in R | Specifically, do I report the RMSE of the model itself (i.e., how it performs with the training data used to create it) or do I report the RMSE of the model's performance with new data (aka test data)? ...Or both?
These are called training error and test error, respectively. It's useful to report both, but test error ... | How to report RMSE of Lasso using glmnet in R | Specifically, do I report the RMSE of the model itself (i.e., how it performs with the training data used to create it) or do I report the RMSE of the model's performance with new data (aka test data) | How to report RMSE of Lasso using glmnet in R
Specifically, do I report the RMSE of the model itself (i.e., how it performs with the training data used to create it) or do I report the RMSE of the model's performance with new data (aka test data)? ...Or both?
These are called training error and test error, respectivel... | How to report RMSE of Lasso using glmnet in R
Specifically, do I report the RMSE of the model itself (i.e., how it performs with the training data used to create it) or do I report the RMSE of the model's performance with new data (aka test data) |
41,532 | Are "kernel methods" and "reproducing kernel Hilbert spaces" related? | The Wikipedia pages for "Kernel Method" and "reproducing kernel Hilbert space" both refer to Mercer's theorem, which is the connection. If the kernel used in a kernel method is a "Mercer kernel" (that is, it satisfies the Mercer condition), then the method works "as if" it was operating in the Hilbert space (a function... | Are "kernel methods" and "reproducing kernel Hilbert spaces" related? | The Wikipedia pages for "Kernel Method" and "reproducing kernel Hilbert space" both refer to Mercer's theorem, which is the connection. If the kernel used in a kernel method is a "Mercer kernel" (that | Are "kernel methods" and "reproducing kernel Hilbert spaces" related?
The Wikipedia pages for "Kernel Method" and "reproducing kernel Hilbert space" both refer to Mercer's theorem, which is the connection. If the kernel used in a kernel method is a "Mercer kernel" (that is, it satisfies the Mercer condition), then the ... | Are "kernel methods" and "reproducing kernel Hilbert spaces" related?
The Wikipedia pages for "Kernel Method" and "reproducing kernel Hilbert space" both refer to Mercer's theorem, which is the connection. If the kernel used in a kernel method is a "Mercer kernel" (that |
41,533 | Combining samples based off mean and standard error | If your first population has mean $\mu_1$ and variance $\sigma_1^2,$ then the sample mean ${\bar{x}_1}$ of your data has variance ${\sigma_1^2 \over n_1},$ where $n_1$ is the sample size. Similarly for your second sample the variance of the sample mean ${\bar{x}_2}$ is ${\sigma_2^2 \over n_2}.$
The variance of the comb... | Combining samples based off mean and standard error | If your first population has mean $\mu_1$ and variance $\sigma_1^2,$ then the sample mean ${\bar{x}_1}$ of your data has variance ${\sigma_1^2 \over n_1},$ where $n_1$ is the sample size. Similarly fo | Combining samples based off mean and standard error
If your first population has mean $\mu_1$ and variance $\sigma_1^2,$ then the sample mean ${\bar{x}_1}$ of your data has variance ${\sigma_1^2 \over n_1},$ where $n_1$ is the sample size. Similarly for your second sample the variance of the sample mean ${\bar{x}_2}$ i... | Combining samples based off mean and standard error
If your first population has mean $\mu_1$ and variance $\sigma_1^2,$ then the sample mean ${\bar{x}_1}$ of your data has variance ${\sigma_1^2 \over n_1},$ where $n_1$ is the sample size. Similarly fo |
41,534 | Combining samples based off mean and standard error | In your case it seems that you're trying to do a sort of meta-analysis where you want to act as if the two studies are one, with the commensurate larger N.
Keep in mind that the variance of a sample mean is tied to the N from which the same is taken. You can only average the variance of sample means across studies when... | Combining samples based off mean and standard error | In your case it seems that you're trying to do a sort of meta-analysis where you want to act as if the two studies are one, with the commensurate larger N.
Keep in mind that the variance of a sample m | Combining samples based off mean and standard error
In your case it seems that you're trying to do a sort of meta-analysis where you want to act as if the two studies are one, with the commensurate larger N.
Keep in mind that the variance of a sample mean is tied to the N from which the same is taken. You can only aver... | Combining samples based off mean and standard error
In your case it seems that you're trying to do a sort of meta-analysis where you want to act as if the two studies are one, with the commensurate larger N.
Keep in mind that the variance of a sample m |
41,535 | What paper introduced max norm regularization (as used in neural network training)? | This paper specifically discusses max-norm with SGD. It references Srebro and Shraibman (2005), which makes me think that it/your implementation does in fact correspond to the technique you described.
Max-norm regularization has been previously used in the context of collaborative filtering (Srebro and Shraibman, 2005... | What paper introduced max norm regularization (as used in neural network training)? | This paper specifically discusses max-norm with SGD. It references Srebro and Shraibman (2005), which makes me think that it/your implementation does in fact correspond to the technique you described. | What paper introduced max norm regularization (as used in neural network training)?
This paper specifically discusses max-norm with SGD. It references Srebro and Shraibman (2005), which makes me think that it/your implementation does in fact correspond to the technique you described.
Max-norm regularization has been p... | What paper introduced max norm regularization (as used in neural network training)?
This paper specifically discusses max-norm with SGD. It references Srebro and Shraibman (2005), which makes me think that it/your implementation does in fact correspond to the technique you described. |
41,536 | How to distinguish fixed from random effects in a model equation? | There are common notations which can be used which make it very easy to know what is fixed and random, but the equation you posted does not adopt such a notation. In your case there is no way to tell, except for the residuals (which are very commonly denoted with $e$ and since it is indexed the same way as the response... | How to distinguish fixed from random effects in a model equation? | There are common notations which can be used which make it very easy to know what is fixed and random, but the equation you posted does not adopt such a notation. In your case there is no way to tell, | How to distinguish fixed from random effects in a model equation?
There are common notations which can be used which make it very easy to know what is fixed and random, but the equation you posted does not adopt such a notation. In your case there is no way to tell, except for the residuals (which are very commonly den... | How to distinguish fixed from random effects in a model equation?
There are common notations which can be used which make it very easy to know what is fixed and random, but the equation you posted does not adopt such a notation. In your case there is no way to tell, |
41,537 | What's wrong with ''multiple testing correction'' compared to ''joint tests''? | I think you are missing @FrankHarrell's point here (I do not currently have access to the Perneger's paper discussed in the linked thread, so cannot comment on it).
The debate is not about math, it is about philosophy. Everything you wrote here is mathematically correct, and clearly Bonferroni correction allows to cont... | What's wrong with ''multiple testing correction'' compared to ''joint tests''? | I think you are missing @FrankHarrell's point here (I do not currently have access to the Perneger's paper discussed in the linked thread, so cannot comment on it).
The debate is not about math, it is | What's wrong with ''multiple testing correction'' compared to ''joint tests''?
I think you are missing @FrankHarrell's point here (I do not currently have access to the Perneger's paper discussed in the linked thread, so cannot comment on it).
The debate is not about math, it is about philosophy. Everything you wrote h... | What's wrong with ''multiple testing correction'' compared to ''joint tests''?
I think you are missing @FrankHarrell's point here (I do not currently have access to the Perneger's paper discussed in the linked thread, so cannot comment on it).
The debate is not about math, it is |
41,538 | What's wrong with ''multiple testing correction'' compared to ''joint tests''? | @amoeba: on the example with the jelly beans I would like to argue as follows (note, I just want to understand):
Let's say that there are 20 different colors of jelly beans, let's call these $c_1, c_2, \dots , c_{20}$, and let $c_{10}$ be the color 'green'.
So, with your example the p-values for color $i$ (we note th... | What's wrong with ''multiple testing correction'' compared to ''joint tests''? | @amoeba: on the example with the jelly beans I would like to argue as follows (note, I just want to understand):
Let's say that there are 20 different colors of jelly beans, let's call these $c_1, c_ | What's wrong with ''multiple testing correction'' compared to ''joint tests''?
@amoeba: on the example with the jelly beans I would like to argue as follows (note, I just want to understand):
Let's say that there are 20 different colors of jelly beans, let's call these $c_1, c_2, \dots , c_{20}$, and let $c_{10}$ be t... | What's wrong with ''multiple testing correction'' compared to ''joint tests''?
@amoeba: on the example with the jelly beans I would like to argue as follows (note, I just want to understand):
Let's say that there are 20 different colors of jelly beans, let's call these $c_1, c_ |
41,539 | What's wrong with ''multiple testing correction'' compared to ''joint tests''? | I'll leave my old answer at the end to provide context for your comment.
It seems to me that your rectangular-versus-ellipsoid thought experiment gives an interesting hint of a problem with multiple comparisons: your multiple test example is in some sense projecting information down in dimensionality, then back up, los... | What's wrong with ''multiple testing correction'' compared to ''joint tests''? | I'll leave my old answer at the end to provide context for your comment.
It seems to me that your rectangular-versus-ellipsoid thought experiment gives an interesting hint of a problem with multiple c | What's wrong with ''multiple testing correction'' compared to ''joint tests''?
I'll leave my old answer at the end to provide context for your comment.
It seems to me that your rectangular-versus-ellipsoid thought experiment gives an interesting hint of a problem with multiple comparisons: your multiple test example is... | What's wrong with ''multiple testing correction'' compared to ''joint tests''?
I'll leave my old answer at the end to provide context for your comment.
It seems to me that your rectangular-versus-ellipsoid thought experiment gives an interesting hint of a problem with multiple c |
41,540 | How do you interpret the area under the precision-recall curve? | Yes, it is average precision, where the average is taken across different thresholds for saying "yes".
The precision-recall curve typically starts out relatively high, and descends though not monotonically. On the right edge, to guarantee perfect recall you just say "yes" to everything, so precision will be down at ... | How do you interpret the area under the precision-recall curve? | Yes, it is average precision, where the average is taken across different thresholds for saying "yes".
The precision-recall curve typically starts out relatively high, and descends though not monoto | How do you interpret the area under the precision-recall curve?
Yes, it is average precision, where the average is taken across different thresholds for saying "yes".
The precision-recall curve typically starts out relatively high, and descends though not monotonically. On the right edge, to guarantee perfect recall... | How do you interpret the area under the precision-recall curve?
Yes, it is average precision, where the average is taken across different thresholds for saying "yes".
The precision-recall curve typically starts out relatively high, and descends though not monoto |
41,541 | Class imbalance in clustering | In general: yes, this could very well be problematic. Imagine you have a number of clusters of unknown, but different classes. Clustering is usually done using a distance measure between samples. Many approaches thereby implicitly assume that the clusters share certain properties, at least within certain boundaries - l... | Class imbalance in clustering | In general: yes, this could very well be problematic. Imagine you have a number of clusters of unknown, but different classes. Clustering is usually done using a distance measure between samples. Many | Class imbalance in clustering
In general: yes, this could very well be problematic. Imagine you have a number of clusters of unknown, but different classes. Clustering is usually done using a distance measure between samples. Many approaches thereby implicitly assume that the clusters share certain properties, at least... | Class imbalance in clustering
In general: yes, this could very well be problematic. Imagine you have a number of clusters of unknown, but different classes. Clustering is usually done using a distance measure between samples. Many |
41,542 | Class imbalance in clustering | https://www.researchgate.net/post/Can_anyone_recommend_algorithms_to_deal_with_unbalanced_clusters_for_classification
I think "try agglomerative ones (single link, complete link, Ward, etc.)" may be a good answer | Class imbalance in clustering | https://www.researchgate.net/post/Can_anyone_recommend_algorithms_to_deal_with_unbalanced_clusters_for_classification
I think "try agglomerative ones (single link, complete link, Ward, etc.)" may be a | Class imbalance in clustering
https://www.researchgate.net/post/Can_anyone_recommend_algorithms_to_deal_with_unbalanced_clusters_for_classification
I think "try agglomerative ones (single link, complete link, Ward, etc.)" may be a good answer | Class imbalance in clustering
https://www.researchgate.net/post/Can_anyone_recommend_algorithms_to_deal_with_unbalanced_clusters_for_classification
I think "try agglomerative ones (single link, complete link, Ward, etc.)" may be a |
41,543 | Is correlation between parameters a problem when fitting a Bayesian model using MCMC? | TLDR: There will almost always be correlation in the parameters in the Bayesian world; even if you use independent priors. Correlation might affect mixing rates, but that is going to be on a case by case basis. In general, you want to ask, "how can I account for the correlations"? Multivariate estimators of the asympto... | Is correlation between parameters a problem when fitting a Bayesian model using MCMC? | TLDR: There will almost always be correlation in the parameters in the Bayesian world; even if you use independent priors. Correlation might affect mixing rates, but that is going to be on a case by c | Is correlation between parameters a problem when fitting a Bayesian model using MCMC?
TLDR: There will almost always be correlation in the parameters in the Bayesian world; even if you use independent priors. Correlation might affect mixing rates, but that is going to be on a case by case basis. In general, you want to... | Is correlation between parameters a problem when fitting a Bayesian model using MCMC?
TLDR: There will almost always be correlation in the parameters in the Bayesian world; even if you use independent priors. Correlation might affect mixing rates, but that is going to be on a case by c |
41,544 | Why is prewhitening important? | The reason that you pre-whiten X is to identify a filter that can transform Y and X into y and x where x is white noise i.e. serially independent or free of autocorrelation in order to IDENTIFY an appropriate model. Note that one filter (ARMA developed on X ) is used on both the Y and X. Now with y and x you can form/i... | Why is prewhitening important? | The reason that you pre-whiten X is to identify a filter that can transform Y and X into y and x where x is white noise i.e. serially independent or free of autocorrelation in order to IDENTIFY an app | Why is prewhitening important?
The reason that you pre-whiten X is to identify a filter that can transform Y and X into y and x where x is white noise i.e. serially independent or free of autocorrelation in order to IDENTIFY an appropriate model. Note that one filter (ARMA developed on X ) is used on both the Y and X. ... | Why is prewhitening important?
The reason that you pre-whiten X is to identify a filter that can transform Y and X into y and x where x is white noise i.e. serially independent or free of autocorrelation in order to IDENTIFY an app |
41,545 | Why is prewhitening important? | geophysical time series are auto-correlated, which means the measurement value at 12:00 would be similar to 13:00, but more different to 19:00, like air temperature, this is just an example. Pre-whitening is used to detrend, and make the measurement "White", namely independent between each measurement. | Why is prewhitening important? | geophysical time series are auto-correlated, which means the measurement value at 12:00 would be similar to 13:00, but more different to 19:00, like air temperature, this is just an example. Pre-white | Why is prewhitening important?
geophysical time series are auto-correlated, which means the measurement value at 12:00 would be similar to 13:00, but more different to 19:00, like air temperature, this is just an example. Pre-whitening is used to detrend, and make the measurement "White", namely independent between eac... | Why is prewhitening important?
geophysical time series are auto-correlated, which means the measurement value at 12:00 would be similar to 13:00, but more different to 19:00, like air temperature, this is just an example. Pre-white |
41,546 | Why is prewhitening important? | The need for prewhiten your time series will depend on the model that you will use to analyze your data. For example, if you want to perform Pearson correlation analysis between two-time series, the pre-whitening will be needed because the autocorrelation in the time points (if it is the case) will violate the assumpti... | Why is prewhitening important? | The need for prewhiten your time series will depend on the model that you will use to analyze your data. For example, if you want to perform Pearson correlation analysis between two-time series, the p | Why is prewhitening important?
The need for prewhiten your time series will depend on the model that you will use to analyze your data. For example, if you want to perform Pearson correlation analysis between two-time series, the pre-whitening will be needed because the autocorrelation in the time points (if it is the ... | Why is prewhitening important?
The need for prewhiten your time series will depend on the model that you will use to analyze your data. For example, if you want to perform Pearson correlation analysis between two-time series, the p |
41,547 | Pearson's correlation for non-linear data | Pearson's correlation coefficient is a measure of strength of linear relationship between the variable. So, it may provide false results for non-linear relationship.
Read a more detailed answer on Correlation and dependence | Pearson's correlation for non-linear data | Pearson's correlation coefficient is a measure of strength of linear relationship between the variable. So, it may provide false results for non-linear relationship.
Read a more detailed answer on Cor | Pearson's correlation for non-linear data
Pearson's correlation coefficient is a measure of strength of linear relationship between the variable. So, it may provide false results for non-linear relationship.
Read a more detailed answer on Correlation and dependence | Pearson's correlation for non-linear data
Pearson's correlation coefficient is a measure of strength of linear relationship between the variable. So, it may provide false results for non-linear relationship.
Read a more detailed answer on Cor |
41,548 | Pearson's correlation for non-linear data | Adding on Dr Nisha Arora's answer, the following provides a method to compute meaningful Pearson linear correlation coefficient (PLCC) in such cases.
Suppose, you have
$$y=f(x)=x^2$$
Take log on both sides
$$log(y) = 2 \ log(x)$$
Now have a linear relationship. Find Pearson's Correlation Coefficient now. Read this ans... | Pearson's correlation for non-linear data | Adding on Dr Nisha Arora's answer, the following provides a method to compute meaningful Pearson linear correlation coefficient (PLCC) in such cases.
Suppose, you have
$$y=f(x)=x^2$$
Take log on both | Pearson's correlation for non-linear data
Adding on Dr Nisha Arora's answer, the following provides a method to compute meaningful Pearson linear correlation coefficient (PLCC) in such cases.
Suppose, you have
$$y=f(x)=x^2$$
Take log on both sides
$$log(y) = 2 \ log(x)$$
Now have a linear relationship. Find Pearson's C... | Pearson's correlation for non-linear data
Adding on Dr Nisha Arora's answer, the following provides a method to compute meaningful Pearson linear correlation coefficient (PLCC) in such cases.
Suppose, you have
$$y=f(x)=x^2$$
Take log on both |
41,549 | How does batch normalization compute the population statistics after training? | Typically, the population statistics are taken from the training set.
If you include the test set, at test time, you will have information that technically, you shouldn't have access to (information about the whole dataset). For the same reason, the validation set shouldn't be used to compute those statistics.
Keep in ... | How does batch normalization compute the population statistics after training? | Typically, the population statistics are taken from the training set.
If you include the test set, at test time, you will have information that technically, you shouldn't have access to (information a | How does batch normalization compute the population statistics after training?
Typically, the population statistics are taken from the training set.
If you include the test set, at test time, you will have information that technically, you shouldn't have access to (information about the whole dataset). For the same rea... | How does batch normalization compute the population statistics after training?
Typically, the population statistics are taken from the training set.
If you include the test set, at test time, you will have information that technically, you shouldn't have access to (information a |
41,550 | How does batch normalization compute the population statistics after training? | In inference even if your batch size is not one the batch norm is also based on the whole training set(making the inference stable). | How does batch normalization compute the population statistics after training? | In inference even if your batch size is not one the batch norm is also based on the whole training set(making the inference stable). | How does batch normalization compute the population statistics after training?
In inference even if your batch size is not one the batch norm is also based on the whole training set(making the inference stable). | How does batch normalization compute the population statistics after training?
In inference even if your batch size is not one the batch norm is also based on the whole training set(making the inference stable). |
41,551 | Is the margin of error for a survey a "fake" statistic? | The level of statistical rigor your company chooses to abide by is a business question that should be answered by the people paid to answer these questions. If this person is you, think hard about where you are on that spectrum. If this person is not you, find out where your company is on this spectrum and decide wheth... | Is the margin of error for a survey a "fake" statistic? | The level of statistical rigor your company chooses to abide by is a business question that should be answered by the people paid to answer these questions. If this person is you, think hard about whe | Is the margin of error for a survey a "fake" statistic?
The level of statistical rigor your company chooses to abide by is a business question that should be answered by the people paid to answer these questions. If this person is you, think hard about where you are on that spectrum. If this person is not you, find out... | Is the margin of error for a survey a "fake" statistic?
The level of statistical rigor your company chooses to abide by is a business question that should be answered by the people paid to answer these questions. If this person is you, think hard about whe |
41,552 | Entropy of the multinomial distribution | Ok so I guess I should have done a bit of experimentation before posting this question. I just assumed that since the Wikipedia article for the multinomial distribution didn't mention entropy, and since I couldn't find anything about it on google, that it was very difficult to compute.
Let
$${\bf X}\sim \text{Multino... | Entropy of the multinomial distribution | Ok so I guess I should have done a bit of experimentation before posting this question. I just assumed that since the Wikipedia article for the multinomial distribution didn't mention entropy, and si | Entropy of the multinomial distribution
Ok so I guess I should have done a bit of experimentation before posting this question. I just assumed that since the Wikipedia article for the multinomial distribution didn't mention entropy, and since I couldn't find anything about it on google, that it was very difficult to c... | Entropy of the multinomial distribution
Ok so I guess I should have done a bit of experimentation before posting this question. I just assumed that since the Wikipedia article for the multinomial distribution didn't mention entropy, and si |
41,553 | Where do the default values in the Elo ratings formulas come from? | I found a slightly different equation for the calculation of the estimate:
E = 1/(1+10^((ra-rb)/400)).
And the number 400 contained in the formula was chosen by Arpad Elo so, that the Elo numbers are as compatible as possible with the numbers of the formerly used rating system by Kenneth Harkness. In fact one can see t... | Where do the default values in the Elo ratings formulas come from? | I found a slightly different equation for the calculation of the estimate:
E = 1/(1+10^((ra-rb)/400)).
And the number 400 contained in the formula was chosen by Arpad Elo so, that the Elo numbers are | Where do the default values in the Elo ratings formulas come from?
I found a slightly different equation for the calculation of the estimate:
E = 1/(1+10^((ra-rb)/400)).
And the number 400 contained in the formula was chosen by Arpad Elo so, that the Elo numbers are as compatible as possible with the numbers of the for... | Where do the default values in the Elo ratings formulas come from?
I found a slightly different equation for the calculation of the estimate:
E = 1/(1+10^((ra-rb)/400)).
And the number 400 contained in the formula was chosen by Arpad Elo so, that the Elo numbers are |
41,554 | Where do the default values in the Elo ratings formulas come from? | Regarding last question (Lastly, I've read the default average rating in the Elo system is 1500, is this connected to 400 as well?), the answer is: no.
The starting rating is arbitrary (in Elo, as in Glicko, etc. E.g. in rankade, our ranking system, players starts at 2000), it doesn't matter what number you pick.
Start... | Where do the default values in the Elo ratings formulas come from? | Regarding last question (Lastly, I've read the default average rating in the Elo system is 1500, is this connected to 400 as well?), the answer is: no.
The starting rating is arbitrary (in Elo, as in | Where do the default values in the Elo ratings formulas come from?
Regarding last question (Lastly, I've read the default average rating in the Elo system is 1500, is this connected to 400 as well?), the answer is: no.
The starting rating is arbitrary (in Elo, as in Glicko, etc. E.g. in rankade, our ranking system, pla... | Where do the default values in the Elo ratings formulas come from?
Regarding last question (Lastly, I've read the default average rating in the Elo system is 1500, is this connected to 400 as well?), the answer is: no.
The starting rating is arbitrary (in Elo, as in |
41,555 | Expectation of the maximum of two correlated normal variables | The solution is contained in the paper https://www.gwern.net/docs/conscientiousness/2008-nadarajah.pdf cited by @Lucas in his answer at Distribution of the maximum of two correlated normal variables
I will give the answer here, maybe I come back to add a proof ... Let $(X_1,X_2)$ be a bivariate random vector with a b... | Expectation of the maximum of two correlated normal variables | The solution is contained in the paper https://www.gwern.net/docs/conscientiousness/2008-nadarajah.pdf cited by @Lucas in his answer at Distribution of the maximum of two correlated normal variables | Expectation of the maximum of two correlated normal variables
The solution is contained in the paper https://www.gwern.net/docs/conscientiousness/2008-nadarajah.pdf cited by @Lucas in his answer at Distribution of the maximum of two correlated normal variables
I will give the answer here, maybe I come back to add a p... | Expectation of the maximum of two correlated normal variables
The solution is contained in the paper https://www.gwern.net/docs/conscientiousness/2008-nadarajah.pdf cited by @Lucas in his answer at Distribution of the maximum of two correlated normal variables |
41,556 | Expectation of the maximum of two correlated normal variables | About the distribution |X-Y|, the Folded normal distribution may be helpful. | Expectation of the maximum of two correlated normal variables | About the distribution |X-Y|, the Folded normal distribution may be helpful. | Expectation of the maximum of two correlated normal variables
About the distribution |X-Y|, the Folded normal distribution may be helpful. | Expectation of the maximum of two correlated normal variables
About the distribution |X-Y|, the Folded normal distribution may be helpful. |
41,557 | AIC equivalent to Mallows' Cp and Mallows' Cp unbiased for test MSE | For the Gaussian model (with variance $\sigma_{\epsilon}^2 = \hat{\sigma}_{\epsilon}^2$ assumed known), the AIC statistic is equivalent to $C_p$, and so we refer to them collectively as AIC.
Suppose a Gaussian model with variance $\sigma_{\epsilon}^2 = \hat{\sigma}_{\epsilon}^2 = \sigma^2$
Mallow's $C_p$
[
C_p = \frac{... | AIC equivalent to Mallows' Cp and Mallows' Cp unbiased for test MSE | For the Gaussian model (with variance $\sigma_{\epsilon}^2 = \hat{\sigma}_{\epsilon}^2$ assumed known), the AIC statistic is equivalent to $C_p$, and so we refer to them collectively as AIC.
Suppose a | AIC equivalent to Mallows' Cp and Mallows' Cp unbiased for test MSE
For the Gaussian model (with variance $\sigma_{\epsilon}^2 = \hat{\sigma}_{\epsilon}^2$ assumed known), the AIC statistic is equivalent to $C_p$, and so we refer to them collectively as AIC.
Suppose a Gaussian model with variance $\sigma_{\epsilon}^2 =... | AIC equivalent to Mallows' Cp and Mallows' Cp unbiased for test MSE
For the Gaussian model (with variance $\sigma_{\epsilon}^2 = \hat{\sigma}_{\epsilon}^2$ assumed known), the AIC statistic is equivalent to $C_p$, and so we refer to them collectively as AIC.
Suppose a |
41,558 | AIC equivalent to Mallows' Cp and Mallows' Cp unbiased for test MSE | Regarding showing Mallows' Cp is unbiased, use
$\text{tr}(\mathbf{A}) = \text{rank}(\mathbf{A})$ for idempotent matrices $\mathbf{A}$, and
the following technique to get expectations of quadratic forms
\begin{align*}
E\left[\mathbf{y}^\intercal \mathbf{A} \mathbf{y}\right] &= E\left[\text{tr}(\mathbf{y}^\intercal \ma... | AIC equivalent to Mallows' Cp and Mallows' Cp unbiased for test MSE | Regarding showing Mallows' Cp is unbiased, use
$\text{tr}(\mathbf{A}) = \text{rank}(\mathbf{A})$ for idempotent matrices $\mathbf{A}$, and
the following technique to get expectations of quadratic for | AIC equivalent to Mallows' Cp and Mallows' Cp unbiased for test MSE
Regarding showing Mallows' Cp is unbiased, use
$\text{tr}(\mathbf{A}) = \text{rank}(\mathbf{A})$ for idempotent matrices $\mathbf{A}$, and
the following technique to get expectations of quadratic forms
\begin{align*}
E\left[\mathbf{y}^\intercal \math... | AIC equivalent to Mallows' Cp and Mallows' Cp unbiased for test MSE
Regarding showing Mallows' Cp is unbiased, use
$\text{tr}(\mathbf{A}) = \text{rank}(\mathbf{A})$ for idempotent matrices $\mathbf{A}$, and
the following technique to get expectations of quadratic for |
41,559 | AIC equivalent to Mallows' Cp and Mallows' Cp unbiased for test MSE | They are equivalent if you use the normalized Mallows' C*p which is
$$RSS/\sigma^2+2d-n$$ since they differ by a constant which is only a function of $$\sigma^2,n$$ and so doesn't affect model selection (variance is estimated with the full population). unnormalized mallows is just an affine transorm of normalized mal... | AIC equivalent to Mallows' Cp and Mallows' Cp unbiased for test MSE | They are equivalent if you use the normalized Mallows' C*p which is
$$RSS/\sigma^2+2d-n$$ since they differ by a constant which is only a function of $$\sigma^2,n$$ and so doesn't affect model selec | AIC equivalent to Mallows' Cp and Mallows' Cp unbiased for test MSE
They are equivalent if you use the normalized Mallows' C*p which is
$$RSS/\sigma^2+2d-n$$ since they differ by a constant which is only a function of $$\sigma^2,n$$ and so doesn't affect model selection (variance is estimated with the full population... | AIC equivalent to Mallows' Cp and Mallows' Cp unbiased for test MSE
They are equivalent if you use the normalized Mallows' C*p which is
$$RSS/\sigma^2+2d-n$$ since they differ by a constant which is only a function of $$\sigma^2,n$$ and so doesn't affect model selec |
41,560 | Bayes Factor approximation | The answer to your first question is "yes": Using notation similar to Wikipedia, the Bayes factor is
$$
K
= \frac{P(D|M_1)}{P(D|M_2)}
= \frac{\int P(D|\theta_1,M_1) P(\theta_1|M_1) \,d\theta_1}
{\int P(D|\theta_2,M_2) P(\theta_2|M_2) \,d\theta_2},
$$
and the procedure you describe just replaces both nume... | Bayes Factor approximation | The answer to your first question is "yes": Using notation similar to Wikipedia, the Bayes factor is
$$
K
= \frac{P(D|M_1)}{P(D|M_2)}
= \frac{\int P(D|\theta_1,M_1) P(\theta_1|M_1) \,d\theta_1}
| Bayes Factor approximation
The answer to your first question is "yes": Using notation similar to Wikipedia, the Bayes factor is
$$
K
= \frac{P(D|M_1)}{P(D|M_2)}
= \frac{\int P(D|\theta_1,M_1) P(\theta_1|M_1) \,d\theta_1}
{\int P(D|\theta_2,M_2) P(\theta_2|M_2) \,d\theta_2},
$$
and the procedure you descr... | Bayes Factor approximation
The answer to your first question is "yes": Using notation similar to Wikipedia, the Bayes factor is
$$
K
= \frac{P(D|M_1)}{P(D|M_2)}
= \frac{\int P(D|\theta_1,M_1) P(\theta_1|M_1) \,d\theta_1}
|
41,561 | Bayes Factor approximation | The answer to your second question is yes as well if you consider the sequence of Bayes factors:
$$\mathfrak{B}_{12}^t=\dfrac{\int f_1(x_1,\ldots,x_t|\theta_1)\pi_1(\theta_1)\text{d}\theta_1}{\int f_2(x_1,\ldots,x_t|\theta_2)\pi_2(\theta_2)\text{d}\theta_2}\qquad t=1,\ldots,T$$
Then, assuming the observations are iid,
... | Bayes Factor approximation | The answer to your second question is yes as well if you consider the sequence of Bayes factors:
$$\mathfrak{B}_{12}^t=\dfrac{\int f_1(x_1,\ldots,x_t|\theta_1)\pi_1(\theta_1)\text{d}\theta_1}{\int f_2 | Bayes Factor approximation
The answer to your second question is yes as well if you consider the sequence of Bayes factors:
$$\mathfrak{B}_{12}^t=\dfrac{\int f_1(x_1,\ldots,x_t|\theta_1)\pi_1(\theta_1)\text{d}\theta_1}{\int f_2(x_1,\ldots,x_t|\theta_2)\pi_2(\theta_2)\text{d}\theta_2}\qquad t=1,\ldots,T$$
Then, assuming... | Bayes Factor approximation
The answer to your second question is yes as well if you consider the sequence of Bayes factors:
$$\mathfrak{B}_{12}^t=\dfrac{\int f_1(x_1,\ldots,x_t|\theta_1)\pi_1(\theta_1)\text{d}\theta_1}{\int f_2 |
41,562 | Is there a name for a scatter plot which compares predicted vs observed values? | A scatter plot of observed and predicted is emphatically not a quantile-quantile plot (which defines a never-decreasing sequence of points).
People often just talk informally in terms of what is on which axis, say observed versus or against predicted or fitted (e.g. Chambers et al. 1983).
I'd suggest that plotting obs... | Is there a name for a scatter plot which compares predicted vs observed values? | A scatter plot of observed and predicted is emphatically not a quantile-quantile plot (which defines a never-decreasing sequence of points).
People often just talk informally in terms of what is on w | Is there a name for a scatter plot which compares predicted vs observed values?
A scatter plot of observed and predicted is emphatically not a quantile-quantile plot (which defines a never-decreasing sequence of points).
People often just talk informally in terms of what is on which axis, say observed versus or agains... | Is there a name for a scatter plot which compares predicted vs observed values?
A scatter plot of observed and predicted is emphatically not a quantile-quantile plot (which defines a never-decreasing sequence of points).
People often just talk informally in terms of what is on w |
41,563 | Quadratic terms in logistic regression | After building a model based on general linear model (as you would typically be doing when you have a binary outcome), you have several methods available for checking for violations of the assumptions supporting statistical validity. The assumption that would be violated when the prediction relationship was polynomial ... | Quadratic terms in logistic regression | After building a model based on general linear model (as you would typically be doing when you have a binary outcome), you have several methods available for checking for violations of the assumptions | Quadratic terms in logistic regression
After building a model based on general linear model (as you would typically be doing when you have a binary outcome), you have several methods available for checking for violations of the assumptions supporting statistical validity. The assumption that would be violated when the ... | Quadratic terms in logistic regression
After building a model based on general linear model (as you would typically be doing when you have a binary outcome), you have several methods available for checking for violations of the assumptions |
41,564 | Quadratic terms in logistic regression | During EDA, you can take the (continuous) predictor and discretize it by either creating equal-sized or equal-spaced bins. Then you can plot the event rates across all bins to visually detect a linear or quadratic relationship (if it exists). E.g., an inverted U-shaped curve would suggest the presence of a quadratic re... | Quadratic terms in logistic regression | During EDA, you can take the (continuous) predictor and discretize it by either creating equal-sized or equal-spaced bins. Then you can plot the event rates across all bins to visually detect a linear | Quadratic terms in logistic regression
During EDA, you can take the (continuous) predictor and discretize it by either creating equal-sized or equal-spaced bins. Then you can plot the event rates across all bins to visually detect a linear or quadratic relationship (if it exists). E.g., an inverted U-shaped curve would... | Quadratic terms in logistic regression
During EDA, you can take the (continuous) predictor and discretize it by either creating equal-sized or equal-spaced bins. Then you can plot the event rates across all bins to visually detect a linear |
41,565 | Simulating a stochastic integral | You have two sources of divergence from 0.5, and you're only making changes to one of them; as a result you won't expect to see the sort of convergence you suggest. [Instead you'd expect to see a slight improvement at the smallest $n$ values which then disappears into noise as you increase $n$ further.]
The first sourc... | Simulating a stochastic integral | You have two sources of divergence from 0.5, and you're only making changes to one of them; as a result you won't expect to see the sort of convergence you suggest. [Instead you'd expect to see a slig | Simulating a stochastic integral
You have two sources of divergence from 0.5, and you're only making changes to one of them; as a result you won't expect to see the sort of convergence you suggest. [Instead you'd expect to see a slight improvement at the smallest $n$ values which then disappears into noise as you incre... | Simulating a stochastic integral
You have two sources of divergence from 0.5, and you're only making changes to one of them; as a result you won't expect to see the sort of convergence you suggest. [Instead you'd expect to see a slig |
41,566 | Simulating a stochastic integral | Let $X_i := B(t_i) [B(t_{i+1}) - B(t_i)]$ for $i=0$ to $n-1$. The rv.s
$X_i$ are gaussian and independent due to the independence of the
increments of $B(t)$. Moreover $\mathbb{E}(X_i) = 0$ and
$$
\text{Var}(X_i) = E[X_i^2] =
\mathbb{E}[B(t_i)^2] \, \mathbb{E}[(B(t_{i+1}) - B(t_i))^2] = t_i \, (t_{i+1} - t_i),
... | Simulating a stochastic integral | Let $X_i := B(t_i) [B(t_{i+1}) - B(t_i)]$ for $i=0$ to $n-1$. The rv.s
$X_i$ are gaussian and independent due to the independence of the
increments of $B(t)$. Moreover $\mathbb{E}(X_i) = 0$ and
$$
| Simulating a stochastic integral
Let $X_i := B(t_i) [B(t_{i+1}) - B(t_i)]$ for $i=0$ to $n-1$. The rv.s
$X_i$ are gaussian and independent due to the independence of the
increments of $B(t)$. Moreover $\mathbb{E}(X_i) = 0$ and
$$
\text{Var}(X_i) = E[X_i^2] =
\mathbb{E}[B(t_i)^2] \, \mathbb{E}[(B(t_{i+1}) - B(t_i... | Simulating a stochastic integral
Let $X_i := B(t_i) [B(t_{i+1}) - B(t_i)]$ for $i=0$ to $n-1$. The rv.s
$X_i$ are gaussian and independent due to the independence of the
increments of $B(t)$. Moreover $\mathbb{E}(X_i) = 0$ and
$$
|
41,567 | Simulating a stochastic integral | To simulate the convergence, simulate the mean of the squared DIFFERENCE between the integral based on n steps and the integral based on 2n steps. Then the same for the difference between the integrals for 2n steps and 4n steps. Then the difference between 4n steps and 8n steps. Use the SAME Brownian motion trajectory ... | Simulating a stochastic integral | To simulate the convergence, simulate the mean of the squared DIFFERENCE between the integral based on n steps and the integral based on 2n steps. Then the same for the difference between the integral | Simulating a stochastic integral
To simulate the convergence, simulate the mean of the squared DIFFERENCE between the integral based on n steps and the integral based on 2n steps. Then the same for the difference between the integrals for 2n steps and 4n steps. Then the difference between 4n steps and 8n steps. Use the... | Simulating a stochastic integral
To simulate the convergence, simulate the mean of the squared DIFFERENCE between the integral based on n steps and the integral based on 2n steps. Then the same for the difference between the integral |
41,568 | Simulating a stochastic integral | 3.9.10 BdB.R
integral B.dB
rephrase exercise 3.9.10 as follows:
delete line 5 and onward until line 8 sentence that starts with Repeat
also delete sentence starting with Compare
set.seed(123) # optional; positive integer
sims <- 1000 # number of simulations
BdB.sim <- function(n) {
B.steps <- 2*n ... | Simulating a stochastic integral | 3.9.10 BdB.R
integral B.dB
rephrase exercise 3.9.10 as follows:
delete line 5 and onward until line 8 sentence that starts with Repeat
also delete sentence starting with Compare
set.seed(123) # o | Simulating a stochastic integral
3.9.10 BdB.R
integral B.dB
rephrase exercise 3.9.10 as follows:
delete line 5 and onward until line 8 sentence that starts with Repeat
also delete sentence starting with Compare
set.seed(123) # optional; positive integer
sims <- 1000 # number of simulations
BdB.sim <- functio... | Simulating a stochastic integral
3.9.10 BdB.R
integral B.dB
rephrase exercise 3.9.10 as follows:
delete line 5 and onward until line 8 sentence that starts with Repeat
also delete sentence starting with Compare
set.seed(123) # o |
41,569 | How to know if a statistic prediction is right? | "This question can be extended ..." -- that's absolutely right. But of course, if you want to step all the way back -- that's the case for every phenomenon. Every time you flip a coin, it gets a little dented, and changes the likelihood of coming up heads. Every time you shoot a basket, your arms are a little more tire... | How to know if a statistic prediction is right? | "This question can be extended ..." -- that's absolutely right. But of course, if you want to step all the way back -- that's the case for every phenomenon. Every time you flip a coin, it gets a littl | How to know if a statistic prediction is right?
"This question can be extended ..." -- that's absolutely right. But of course, if you want to step all the way back -- that's the case for every phenomenon. Every time you flip a coin, it gets a little dented, and changes the likelihood of coming up heads. Every time you ... | How to know if a statistic prediction is right?
"This question can be extended ..." -- that's absolutely right. But of course, if you want to step all the way back -- that's the case for every phenomenon. Every time you flip a coin, it gets a littl |
41,570 | How to know if a statistic prediction is right? | This is a great question and a common one as well. The property you seem to be interested in is ergodicity. If a stochastic process you're interested in is ergodic, then (roughly) these "different day" observations that you see can be combined to assess how successful the weather predictions are; can be combined to der... | How to know if a statistic prediction is right? | This is a great question and a common one as well. The property you seem to be interested in is ergodicity. If a stochastic process you're interested in is ergodic, then (roughly) these "different day | How to know if a statistic prediction is right?
This is a great question and a common one as well. The property you seem to be interested in is ergodicity. If a stochastic process you're interested in is ergodic, then (roughly) these "different day" observations that you see can be combined to assess how successful the... | How to know if a statistic prediction is right?
This is a great question and a common one as well. The property you seem to be interested in is ergodicity. If a stochastic process you're interested in is ergodic, then (roughly) these "different day |
41,571 | How to know if a statistic prediction is right? | Time series econometrics deals with a similar question: If $y_t$ and $x_t$ are time series variables, should you trust a linear regression with the two variables? The answer is "it depends".
It depends on whether the observed relationship between the two variables would continue to be true in the future. If $y_t$ and $... | How to know if a statistic prediction is right? | Time series econometrics deals with a similar question: If $y_t$ and $x_t$ are time series variables, should you trust a linear regression with the two variables? The answer is "it depends".
It depend | How to know if a statistic prediction is right?
Time series econometrics deals with a similar question: If $y_t$ and $x_t$ are time series variables, should you trust a linear regression with the two variables? The answer is "it depends".
It depends on whether the observed relationship between the two variables would c... | How to know if a statistic prediction is right?
Time series econometrics deals with a similar question: If $y_t$ and $x_t$ are time series variables, should you trust a linear regression with the two variables? The answer is "it depends".
It depend |
41,572 | Interpreting glm model output, assessing quality of fit | First, as you have little prior experience with regression models, I would suggest that you obtain two freely available references. An Introduction to Statistical Learning covers linear regression and some examples of generalized linear models in a usefully broad context. Practical Regression and Anova using R, by Fara... | Interpreting glm model output, assessing quality of fit | First, as you have little prior experience with regression models, I would suggest that you obtain two freely available references. An Introduction to Statistical Learning covers linear regression and | Interpreting glm model output, assessing quality of fit
First, as you have little prior experience with regression models, I would suggest that you obtain two freely available references. An Introduction to Statistical Learning covers linear regression and some examples of generalized linear models in a usefully broad ... | Interpreting glm model output, assessing quality of fit
First, as you have little prior experience with regression models, I would suggest that you obtain two freely available references. An Introduction to Statistical Learning covers linear regression and |
41,573 | Interpreting glm model output, assessing quality of fit | Let me add some messages about the lm output and glm output.
About lm output, this page may help you a lot. It interprets the lm() function output in summary().
About glm, info in this page may help.
Additionally, AIC is an estimate of a constant plus the relative distance between the unknown true likelihood funct... | Interpreting glm model output, assessing quality of fit | Let me add some messages about the lm output and glm output.
About lm output, this page may help you a lot. It interprets the lm() function output in summary().
About glm, info in this page may hel | Interpreting glm model output, assessing quality of fit
Let me add some messages about the lm output and glm output.
About lm output, this page may help you a lot. It interprets the lm() function output in summary().
About glm, info in this page may help.
Additionally, AIC is an estimate of a constant plus the rel... | Interpreting glm model output, assessing quality of fit
Let me add some messages about the lm output and glm output.
About lm output, this page may help you a lot. It interprets the lm() function output in summary().
About glm, info in this page may hel |
41,574 | Estimation derived from ignorance | The problem you are describing is related to doomsday argument and sunrise problem.
Estimating something from ignorance in this case relates to Bayesian estimation with uniform prior. In basically any inference problem you have some data $D$ and some parameter $\theta$ that you want to learn about using your data. Ther... | Estimation derived from ignorance | The problem you are describing is related to doomsday argument and sunrise problem.
Estimating something from ignorance in this case relates to Bayesian estimation with uniform prior. In basically any | Estimation derived from ignorance
The problem you are describing is related to doomsday argument and sunrise problem.
Estimating something from ignorance in this case relates to Bayesian estimation with uniform prior. In basically any inference problem you have some data $D$ and some parameter $\theta$ that you want to... | Estimation derived from ignorance
The problem you are describing is related to doomsday argument and sunrise problem.
Estimating something from ignorance in this case relates to Bayesian estimation with uniform prior. In basically any |
41,575 | Estimation derived from ignorance | As a addition to Tim answer, I would note that Gelman and Robert wrote in the paper "The perceived absurdity of Bayesian inference" (http://arxiv.org/pdf/1006.5366v2.pdf) in Section 4 called "The doomsday argument and confusion between frequentist and Bayesian ideas" that the doomsday argument (and Gotts one) is essent... | Estimation derived from ignorance | As a addition to Tim answer, I would note that Gelman and Robert wrote in the paper "The perceived absurdity of Bayesian inference" (http://arxiv.org/pdf/1006.5366v2.pdf) in Section 4 called "The doom | Estimation derived from ignorance
As a addition to Tim answer, I would note that Gelman and Robert wrote in the paper "The perceived absurdity of Bayesian inference" (http://arxiv.org/pdf/1006.5366v2.pdf) in Section 4 called "The doomsday argument and confusion between frequentist and Bayesian ideas" that the doomsday ... | Estimation derived from ignorance
As a addition to Tim answer, I would note that Gelman and Robert wrote in the paper "The perceived absurdity of Bayesian inference" (http://arxiv.org/pdf/1006.5366v2.pdf) in Section 4 called "The doom |
41,576 | Two-sample Kolmogorov-Smirnov test with errors on data points | This is a great question, and it blows my mind that there is not an obvious answer, given that this is essentially the most fundamental statistical comparison scientists make. I came here to ask the exact same question. I don't have a full answer, but I can tell you the inelegant way I'm approaching this problem.
1) Ra... | Two-sample Kolmogorov-Smirnov test with errors on data points | This is a great question, and it blows my mind that there is not an obvious answer, given that this is essentially the most fundamental statistical comparison scientists make. I came here to ask the e | Two-sample Kolmogorov-Smirnov test with errors on data points
This is a great question, and it blows my mind that there is not an obvious answer, given that this is essentially the most fundamental statistical comparison scientists make. I came here to ask the exact same question. I don't have a full answer, but I can ... | Two-sample Kolmogorov-Smirnov test with errors on data points
This is a great question, and it blows my mind that there is not an obvious answer, given that this is essentially the most fundamental statistical comparison scientists make. I came here to ask the e |
41,577 | Two-sample Kolmogorov-Smirnov test with errors on data points | The K-S test compares two probability density functions (see e.g. Wikipedia). To my knowledge, it is not meant to compare measurements with errors.
One way to approach your problem is perhaps to fit an ensemble of PDF models to your data, for instance using a Monte Carlo approach to sample sensible model parameters. Th... | Two-sample Kolmogorov-Smirnov test with errors on data points | The K-S test compares two probability density functions (see e.g. Wikipedia). To my knowledge, it is not meant to compare measurements with errors.
One way to approach your problem is perhaps to fit a | Two-sample Kolmogorov-Smirnov test with errors on data points
The K-S test compares two probability density functions (see e.g. Wikipedia). To my knowledge, it is not meant to compare measurements with errors.
One way to approach your problem is perhaps to fit an ensemble of PDF models to your data, for instance using ... | Two-sample Kolmogorov-Smirnov test with errors on data points
The K-S test compares two probability density functions (see e.g. Wikipedia). To my knowledge, it is not meant to compare measurements with errors.
One way to approach your problem is perhaps to fit a |
41,578 | Calculate sample size based on Conversion Rate, Minimum Detectable Effect, Statistical power and Significance level | I feel your pain. I blew so many hours yesterday looking at sites like:
http://www.evanmiller.org/ab-testing/sample-size.html#!3;80;5;20;1
https://www.stat.ubc.ca/~rollin/stats/ssize/b2.html
https://select-statistics.co.uk/calculators/sample-size-calculator-two-proportions/
And none of them provided a formula, whic... | Calculate sample size based on Conversion Rate, Minimum Detectable Effect, Statistical power and Sig | I feel your pain. I blew so many hours yesterday looking at sites like:
http://www.evanmiller.org/ab-testing/sample-size.html#!3;80;5;20;1
https://www.stat.ubc.ca/~rollin/stats/ssize/b2.html
https:/ | Calculate sample size based on Conversion Rate, Minimum Detectable Effect, Statistical power and Significance level
I feel your pain. I blew so many hours yesterday looking at sites like:
http://www.evanmiller.org/ab-testing/sample-size.html#!3;80;5;20;1
https://www.stat.ubc.ca/~rollin/stats/ssize/b2.html
https://sel... | Calculate sample size based on Conversion Rate, Minimum Detectable Effect, Statistical power and Sig
I feel your pain. I blew so many hours yesterday looking at sites like:
http://www.evanmiller.org/ab-testing/sample-size.html#!3;80;5;20;1
https://www.stat.ubc.ca/~rollin/stats/ssize/b2.html
https:/ |
41,579 | Calculate sample size based on Conversion Rate, Minimum Detectable Effect, Statistical power and Significance level | This calculator has the formulas:
http://powerandsamplesize.com/Calculators/Compare-2-Proportions/2-Sample-Equality
for pB you need to enter pA+MDE, I believe. | Calculate sample size based on Conversion Rate, Minimum Detectable Effect, Statistical power and Sig | This calculator has the formulas:
http://powerandsamplesize.com/Calculators/Compare-2-Proportions/2-Sample-Equality
for pB you need to enter pA+MDE, I believe. | Calculate sample size based on Conversion Rate, Minimum Detectable Effect, Statistical power and Significance level
This calculator has the formulas:
http://powerandsamplesize.com/Calculators/Compare-2-Proportions/2-Sample-Equality
for pB you need to enter pA+MDE, I believe. | Calculate sample size based on Conversion Rate, Minimum Detectable Effect, Statistical power and Sig
This calculator has the formulas:
http://powerandsamplesize.com/Calculators/Compare-2-Proportions/2-Sample-Equality
for pB you need to enter pA+MDE, I believe. |
41,580 | Relative importance of variables in Cox regression | Thanks for trying those functions. I believe that both metrics you mentioned are excellent in this context. This is useful for any model that gives rise to Wald statistics (which is virtually all models) although likelihood ratio $\chi^2$ statistics would be even better (but more tedious to compute).
You can use th... | Relative importance of variables in Cox regression | Thanks for trying those functions. I believe that both metrics you mentioned are excellent in this context. This is useful for any model that gives rise to Wald statistics (which is virtually all mo | Relative importance of variables in Cox regression
Thanks for trying those functions. I believe that both metrics you mentioned are excellent in this context. This is useful for any model that gives rise to Wald statistics (which is virtually all models) although likelihood ratio $\chi^2$ statistics would be even bet... | Relative importance of variables in Cox regression
Thanks for trying those functions. I believe that both metrics you mentioned are excellent in this context. This is useful for any model that gives rise to Wald statistics (which is virtually all mo |
41,581 | If a decision tree already has very low entropy, do we still need a random forest | The short answer is variance. The long answer is variance and also generalization. Decision trees have high variance: a slight change in the training data can cause a big change in how the splits occur, and therefore the predictions aren't very stable. Before RF, there was a lot of attention paid to pruning decision tr... | If a decision tree already has very low entropy, do we still need a random forest | The short answer is variance. The long answer is variance and also generalization. Decision trees have high variance: a slight change in the training data can cause a big change in how the splits occu | If a decision tree already has very low entropy, do we still need a random forest
The short answer is variance. The long answer is variance and also generalization. Decision trees have high variance: a slight change in the training data can cause a big change in how the splits occur, and therefore the predictions aren'... | If a decision tree already has very low entropy, do we still need a random forest
The short answer is variance. The long answer is variance and also generalization. Decision trees have high variance: a slight change in the training data can cause a big change in how the splits occu |
41,582 | Bootstrap method- downsides | There's two different ways to interpret this question:
1.) Is there any types of data such that bootstrapping standard estimators leads to invalid inference?
2.) Are there any non standard estimators such that bootstrap leads to invalid inference?
The answer to both questions is yes.
In the first case, as you mention... | Bootstrap method- downsides | There's two different ways to interpret this question:
1.) Is there any types of data such that bootstrapping standard estimators leads to invalid inference?
2.) Are there any non standard estimators | Bootstrap method- downsides
There's two different ways to interpret this question:
1.) Is there any types of data such that bootstrapping standard estimators leads to invalid inference?
2.) Are there any non standard estimators such that bootstrap leads to invalid inference?
The answer to both questions is yes.
In th... | Bootstrap method- downsides
There's two different ways to interpret this question:
1.) Is there any types of data such that bootstrapping standard estimators leads to invalid inference?
2.) Are there any non standard estimators |
41,583 | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training set or gradient of the loss function? | I've implemented this here in a way that performs comparably to other implementations at least in my testing.
At each step you have a residual R calculated across the entire data set (before any base learners are fit its the residual from predicting the average).
You subsample without replacement and fit the learner ... | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training | I've implemented this here in a way that performs comparably to other implementations at least in my testing.
At each step you have a residual R calculated across the entire data set (before any bas | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training set or gradient of the loss function?
I've implemented this here in a way that performs comparably to other implementations at least in my testing.
At each step you have a residual R calculated across the entire data ... | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training
I've implemented this here in a way that performs comparably to other implementations at least in my testing.
At each step you have a residual R calculated across the entire data set (before any bas |
41,584 | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training set or gradient of the loss function? | I tried to decipher the steps in the original Friedman 2002 paper. If I am not wrong, it appears that we actually both deal with the current residuals and the original training set. Especially, the algorithm is as follows:
Here is what I have understood, step by step. Please tell me if there is something amiss. See (*... | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training | I tried to decipher the steps in the original Friedman 2002 paper. If I am not wrong, it appears that we actually both deal with the current residuals and the original training set. Especially, the al | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training set or gradient of the loss function?
I tried to decipher the steps in the original Friedman 2002 paper. If I am not wrong, it appears that we actually both deal with the current residuals and the original training set.... | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training
I tried to decipher the steps in the original Friedman 2002 paper. If I am not wrong, it appears that we actually both deal with the current residuals and the original training set. Especially, the al |
41,585 | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training set or gradient of the loss function? | The concept of residuals makes sense on any set of data for which:
You can use your model to make predictions and
You have a true response value on each record
So, if you, for example, split your full training data in two halves and then train on the first half, you can still predict on the second half and compute th... | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training | The concept of residuals makes sense on any set of data for which:
You can use your model to make predictions and
You have a true response value on each record
So, if you, for example, split your fu | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training set or gradient of the loss function?
The concept of residuals makes sense on any set of data for which:
You can use your model to make predictions and
You have a true response value on each record
So, if you, for exa... | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training
The concept of residuals makes sense on any set of data for which:
You can use your model to make predictions and
You have a true response value on each record
So, if you, for example, split your fu |
41,586 | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training set or gradient of the loss function? | I think you are confusing the features with the dependent variable. In gradient boosting models you fit the tree on the current gradient (which coincides with residuals for Gaussian models) using already existing features. Features do not change, only the gradient is changing at each step, because of the updating. Grad... | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training | I think you are confusing the features with the dependent variable. In gradient boosting models you fit the tree on the current gradient (which coincides with residuals for Gaussian models) using alre | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training set or gradient of the loss function?
I think you are confusing the features with the dependent variable. In gradient boosting models you fit the tree on the current gradient (which coincides with residuals for Gaussian... | Which data are used at each step of Stochastic Gradient Boosting? Subsample of the original training
I think you are confusing the features with the dependent variable. In gradient boosting models you fit the tree on the current gradient (which coincides with residuals for Gaussian models) using alre |
41,587 | Expected value of product of non independent Bernoulli random variables (correlations are known) | Ordinarily, bivariate relationships do not determine multivariate ones, so we ought to expect that you cannot compute this expectation in terms of just the first two moments. The following describes a method to produce loads of counterexamples and exhibits an explicit one for four correlated Bernoulli variables.
Gene... | Expected value of product of non independent Bernoulli random variables (correlations are known) | Ordinarily, bivariate relationships do not determine multivariate ones, so we ought to expect that you cannot compute this expectation in terms of just the first two moments. The following describes | Expected value of product of non independent Bernoulli random variables (correlations are known)
Ordinarily, bivariate relationships do not determine multivariate ones, so we ought to expect that you cannot compute this expectation in terms of just the first two moments. The following describes a method to produce loa... | Expected value of product of non independent Bernoulli random variables (correlations are known)
Ordinarily, bivariate relationships do not determine multivariate ones, so we ought to expect that you cannot compute this expectation in terms of just the first two moments. The following describes |
41,588 | Testing for Granger Causality | Follow this procedure (Engle-Granger Test for Cointegration):
1) Test to see if your series are stationary using adfuller test (stock prices and GDP levels are usually not)
2) If they are not, difference them and see if the differenced series are now stationary (they usually are).
3) If they are, your ORIGINAL series a... | Testing for Granger Causality | Follow this procedure (Engle-Granger Test for Cointegration):
1) Test to see if your series are stationary using adfuller test (stock prices and GDP levels are usually not)
2) If they are not, differe | Testing for Granger Causality
Follow this procedure (Engle-Granger Test for Cointegration):
1) Test to see if your series are stationary using adfuller test (stock prices and GDP levels are usually not)
2) If they are not, difference them and see if the differenced series are now stationary (they usually are).
3) If th... | Testing for Granger Causality
Follow this procedure (Engle-Granger Test for Cointegration):
1) Test to see if your series are stationary using adfuller test (stock prices and GDP levels are usually not)
2) If they are not, differe |
41,589 | The relationship between cumulative distribution vs cumulative density vs probability density | Looking at the links you provided, and what I'v seen in the past, there seems to be a lot of different names for what is essentially a particular function and its derivative.
First, let's cross off one of the names you mention in the title: cumulative density function. That just doesn't make sense. A density function ... | The relationship between cumulative distribution vs cumulative density vs probability density | Looking at the links you provided, and what I'v seen in the past, there seems to be a lot of different names for what is essentially a particular function and its derivative.
First, let's cross off o | The relationship between cumulative distribution vs cumulative density vs probability density
Looking at the links you provided, and what I'v seen in the past, there seems to be a lot of different names for what is essentially a particular function and its derivative.
First, let's cross off one of the names you mentio... | The relationship between cumulative distribution vs cumulative density vs probability density
Looking at the links you provided, and what I'v seen in the past, there seems to be a lot of different names for what is essentially a particular function and its derivative.
First, let's cross off o |
41,590 | The relationship between cumulative distribution vs cumulative density vs probability density | I see that the terminology is taking toll here. The basic concept behind those are very simple but takes one to visualize it properly.
First of all, PMF is individual probabilities of each discrete points. PDF is a tool or hack that we use in case of continuous random variable. Among other tasks (as highlighted in comm... | The relationship between cumulative distribution vs cumulative density vs probability density | I see that the terminology is taking toll here. The basic concept behind those are very simple but takes one to visualize it properly.
First of all, PMF is individual probabilities of each discrete po | The relationship between cumulative distribution vs cumulative density vs probability density
I see that the terminology is taking toll here. The basic concept behind those are very simple but takes one to visualize it properly.
First of all, PMF is individual probabilities of each discrete points. PDF is a tool or hac... | The relationship between cumulative distribution vs cumulative density vs probability density
I see that the terminology is taking toll here. The basic concept behind those are very simple but takes one to visualize it properly.
First of all, PMF is individual probabilities of each discrete po |
41,591 | Estimating the best length of n-gram | There could be some statistical criteria for selecting the best $n$, but I believe the best way to select any parameter is to use cross-validation.
Suppose you're building a system for detecting the language of an article and you decided to use n-grams (n-shingles) to represent the documents. Then to select the best $... | Estimating the best length of n-gram | There could be some statistical criteria for selecting the best $n$, but I believe the best way to select any parameter is to use cross-validation.
Suppose you're building a system for detecting the | Estimating the best length of n-gram
There could be some statistical criteria for selecting the best $n$, but I believe the best way to select any parameter is to use cross-validation.
Suppose you're building a system for detecting the language of an article and you decided to use n-grams (n-shingles) to represent the... | Estimating the best length of n-gram
There could be some statistical criteria for selecting the best $n$, but I believe the best way to select any parameter is to use cross-validation.
Suppose you're building a system for detecting the |
41,592 | Where must we use Bagging or Boosting? | Boosting in general has a higher risk of overfitting than bagging.
Mislabeled cases cause much more serious trouble with boosting than with bagging, similar to the outliers you mention.
I'd expect boosting to yield better results than bagging if you can reasonably expect that your submodels don't by themselves put eno... | Where must we use Bagging or Boosting? | Boosting in general has a higher risk of overfitting than bagging.
Mislabeled cases cause much more serious trouble with boosting than with bagging, similar to the outliers you mention.
I'd expect bo | Where must we use Bagging or Boosting?
Boosting in general has a higher risk of overfitting than bagging.
Mislabeled cases cause much more serious trouble with boosting than with bagging, similar to the outliers you mention.
I'd expect boosting to yield better results than bagging if you can reasonably expect that you... | Where must we use Bagging or Boosting?
Boosting in general has a higher risk of overfitting than bagging.
Mislabeled cases cause much more serious trouble with boosting than with bagging, similar to the outliers you mention.
I'd expect bo |
41,593 | Estimation with MLE and returning the score/gradient (QMLE) | The numDeriv package can indeed be used to compute the gradient
and the hessian (if needed). In both cases the argument y of the log-likelihood
is passed through the dots mechanism, using an argument with the suitable name. For a vector-valued function, the jacobian function of the same package can be used
similarly.
Y... | Estimation with MLE and returning the score/gradient (QMLE) | The numDeriv package can indeed be used to compute the gradient
and the hessian (if needed). In both cases the argument y of the log-likelihood
is passed through the dots mechanism, using an argument | Estimation with MLE and returning the score/gradient (QMLE)
The numDeriv package can indeed be used to compute the gradient
and the hessian (if needed). In both cases the argument y of the log-likelihood
is passed through the dots mechanism, using an argument with the suitable name. For a vector-valued function, the ja... | Estimation with MLE and returning the score/gradient (QMLE)
The numDeriv package can indeed be used to compute the gradient
and the hessian (if needed). In both cases the argument y of the log-likelihood
is passed through the dots mechanism, using an argument |
41,594 | Regularization in Neural networks | Just a guess, but training using something like SGD (which can be considered a type of online learning, in the sense that it sees only a fraction of the data at a time) looks like this w.r.t. the objective function.
That is, the "trajcetory" of the objective is declining, but it's stochastically bouncing around. Early... | Regularization in Neural networks | Just a guess, but training using something like SGD (which can be considered a type of online learning, in the sense that it sees only a fraction of the data at a time) looks like this w.r.t. the obje | Regularization in Neural networks
Just a guess, but training using something like SGD (which can be considered a type of online learning, in the sense that it sees only a fraction of the data at a time) looks like this w.r.t. the objective function.
That is, the "trajcetory" of the objective is declining, but it's sto... | Regularization in Neural networks
Just a guess, but training using something like SGD (which can be considered a type of online learning, in the sense that it sees only a fraction of the data at a time) looks like this w.r.t. the obje |
41,595 | At what point does cross-validation become overtraining? | Over-optimism with cross validation for stepwise feature selection
As @KarlOveHufthammer already explained, using cross validation for (step-wise) feature selection means that the cross validation is part of the model training. More generally, this applies to all kinds of data-driven feature selection, model comparison... | At what point does cross-validation become overtraining? | Over-optimism with cross validation for stepwise feature selection
As @KarlOveHufthammer already explained, using cross validation for (step-wise) feature selection means that the cross validation is | At what point does cross-validation become overtraining?
Over-optimism with cross validation for stepwise feature selection
As @KarlOveHufthammer already explained, using cross validation for (step-wise) feature selection means that the cross validation is part of the model training. More generally, this applies to all... | At what point does cross-validation become overtraining?
Over-optimism with cross validation for stepwise feature selection
As @KarlOveHufthammer already explained, using cross validation for (step-wise) feature selection means that the cross validation is |
41,596 | How to choose the regularization parameter in ZCA whitening? | If the data was Gaussian distributed with mean $0$ and unknown covariance $\Sigma$ and we put an inverse-Wishart prior on $\Sigma$,
\begin{align}
\Sigma &\sim \mathcal{W^{-1}}(\Psi, \nu), \\
x &\sim \mathcal{N}(0, \Sigma),
\end{align}
the posterior expectation of $\Sigma$ would be
$$\frac{XX^\top + \Psi}{n + \nu - p - ... | How to choose the regularization parameter in ZCA whitening? | If the data was Gaussian distributed with mean $0$ and unknown covariance $\Sigma$ and we put an inverse-Wishart prior on $\Sigma$,
\begin{align}
\Sigma &\sim \mathcal{W^{-1}}(\Psi, \nu), \\
x &\sim \ | How to choose the regularization parameter in ZCA whitening?
If the data was Gaussian distributed with mean $0$ and unknown covariance $\Sigma$ and we put an inverse-Wishart prior on $\Sigma$,
\begin{align}
\Sigma &\sim \mathcal{W^{-1}}(\Psi, \nu), \\
x &\sim \mathcal{N}(0, \Sigma),
\end{align}
the posterior expectatio... | How to choose the regularization parameter in ZCA whitening?
If the data was Gaussian distributed with mean $0$ and unknown covariance $\Sigma$ and we put an inverse-Wishart prior on $\Sigma$,
\begin{align}
\Sigma &\sim \mathcal{W^{-1}}(\Psi, \nu), \\
x &\sim \ |
41,597 | Analyzing Ranked Data: Correlation and Factor Analysis? | Yes. However, not very seldom rankings are treated as interval data and are analyzed by parametric procedures (such as ANOVA). For example, this is customarily done in classic conjoint analysis. Conceptually, psychometrically, rankings are ordinal while ratings are potentially interval (albeit often cautiously treated ... | Analyzing Ranked Data: Correlation and Factor Analysis? | Yes. However, not very seldom rankings are treated as interval data and are analyzed by parametric procedures (such as ANOVA). For example, this is customarily done in classic conjoint analysis. Conce | Analyzing Ranked Data: Correlation and Factor Analysis?
Yes. However, not very seldom rankings are treated as interval data and are analyzed by parametric procedures (such as ANOVA). For example, this is customarily done in classic conjoint analysis. Conceptually, psychometrically, rankings are ordinal while ratings ar... | Analyzing Ranked Data: Correlation and Factor Analysis?
Yes. However, not very seldom rankings are treated as interval data and are analyzed by parametric procedures (such as ANOVA). For example, this is customarily done in classic conjoint analysis. Conce |
41,598 | GAM versus GLM: same fit, different significance of predictors | The reason that the significance of the coefficients differs is because, under the modeling assumptions, the calculation of standard errors differs. The correct answer is to choose the model that is most appropriate for--not the data--the scientific question at hand.
For instance, suppose I am interested in measuring ... | GAM versus GLM: same fit, different significance of predictors | The reason that the significance of the coefficients differs is because, under the modeling assumptions, the calculation of standard errors differs. The correct answer is to choose the model that is m | GAM versus GLM: same fit, different significance of predictors
The reason that the significance of the coefficients differs is because, under the modeling assumptions, the calculation of standard errors differs. The correct answer is to choose the model that is most appropriate for--not the data--the scientific questio... | GAM versus GLM: same fit, different significance of predictors
The reason that the significance of the coefficients differs is because, under the modeling assumptions, the calculation of standard errors differs. The correct answer is to choose the model that is m |
41,599 | Model comparison between glm (with Firth correction), random Forest, penalised SVM | Its a very big & open question on which metrics are best to use to access classifier performance. This paper did a great job comparing them:
Caruana, Rich, and Alexandru Niculescu-Mizil. "Data mining in metric space: an empirical analysis of supervised learning performance criteria." Proceedings of the tenth ACM SIGKDD... | Model comparison between glm (with Firth correction), random Forest, penalised SVM | Its a very big & open question on which metrics are best to use to access classifier performance. This paper did a great job comparing them:
Caruana, Rich, and Alexandru Niculescu-Mizil. "Data mining | Model comparison between glm (with Firth correction), random Forest, penalised SVM
Its a very big & open question on which metrics are best to use to access classifier performance. This paper did a great job comparing them:
Caruana, Rich, and Alexandru Niculescu-Mizil. "Data mining in metric space: an empirical analysi... | Model comparison between glm (with Firth correction), random Forest, penalised SVM
Its a very big & open question on which metrics are best to use to access classifier performance. This paper did a great job comparing them:
Caruana, Rich, and Alexandru Niculescu-Mizil. "Data mining |
41,600 | Diebold-Mariano test for predictive accuracy | First, you are supposed to supply raw forecast errors to the Diebold-Mariano test function dm.test. However, you are supplying squared forecast errors (in the text part above the separating line).
Second, the choice of power is entirely due to the loss function, as you noted. It is only you who knows your loss function... | Diebold-Mariano test for predictive accuracy | First, you are supposed to supply raw forecast errors to the Diebold-Mariano test function dm.test. However, you are supplying squared forecast errors (in the text part above the separating line).
Sec | Diebold-Mariano test for predictive accuracy
First, you are supposed to supply raw forecast errors to the Diebold-Mariano test function dm.test. However, you are supplying squared forecast errors (in the text part above the separating line).
Second, the choice of power is entirely due to the loss function, as you noted... | Diebold-Mariano test for predictive accuracy
First, you are supposed to supply raw forecast errors to the Diebold-Mariano test function dm.test. However, you are supplying squared forecast errors (in the text part above the separating line).
Sec |
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