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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49,701 | Formula of the Chebyshev's inequality for an asymmetric interval | The reference for the formula for Chebyshev's inequality for the asymmetric two-sided case,
$$
\mathrm{Pr}( l < X < h ) \ge \frac{ 4 [ ( \mu - l )( h - \mu ) - \sigma^2 ] }{ ( h - l )^2 } ,
$$
points to the paper by Steliga and Szynal (2010).
I've done some further research and Steliga and Szynal cite Ferentinos (1982)... | Formula of the Chebyshev's inequality for an asymmetric interval | The reference for the formula for Chebyshev's inequality for the asymmetric two-sided case,
$$
\mathrm{Pr}( l < X < h ) \ge \frac{ 4 [ ( \mu - l )( h - \mu ) - \sigma^2 ] }{ ( h - l )^2 } ,
$$
points | Formula of the Chebyshev's inequality for an asymmetric interval
The reference for the formula for Chebyshev's inequality for the asymmetric two-sided case,
$$
\mathrm{Pr}( l < X < h ) \ge \frac{ 4 [ ( \mu - l )( h - \mu ) - \sigma^2 ] }{ ( h - l )^2 } ,
$$
points to the paper by Steliga and Szynal (2010).
I've done so... | Formula of the Chebyshev's inequality for an asymmetric interval
The reference for the formula for Chebyshev's inequality for the asymmetric two-sided case,
$$
\mathrm{Pr}( l < X < h ) \ge \frac{ 4 [ ( \mu - l )( h - \mu ) - \sigma^2 ] }{ ( h - l )^2 } ,
$$
points |
49,702 | Bootstrap hypothesis test for median of differences | Bonett & Price (2002) proposed a closed-form solution for this, so not requiring bootstrapping. At the very least, you could compare this to your bootstrapping to see how often that the two methods agree.
Forgive me for the verbose code; I did a lot of comments and did it step-by-step for the purposes of being readable... | Bootstrap hypothesis test for median of differences | Bonett & Price (2002) proposed a closed-form solution for this, so not requiring bootstrapping. At the very least, you could compare this to your bootstrapping to see how often that the two methods ag | Bootstrap hypothesis test for median of differences
Bonett & Price (2002) proposed a closed-form solution for this, so not requiring bootstrapping. At the very least, you could compare this to your bootstrapping to see how often that the two methods agree.
Forgive me for the verbose code; I did a lot of comments and di... | Bootstrap hypothesis test for median of differences
Bonett & Price (2002) proposed a closed-form solution for this, so not requiring bootstrapping. At the very least, you could compare this to your bootstrapping to see how often that the two methods ag |
49,703 | Proper syntax for coding group level variables in mixed effect model using GLMER | There is often confusion about "the level that a variable varies" with mixed effects models, when someone comes more from a multilevel background and/or has used software such as HLM or MLwiN where (from what I remember) it is necessary to specify the level at which a variable varies. This is not the case with mixed ef... | Proper syntax for coding group level variables in mixed effect model using GLMER | There is often confusion about "the level that a variable varies" with mixed effects models, when someone comes more from a multilevel background and/or has used software such as HLM or MLwiN where (f | Proper syntax for coding group level variables in mixed effect model using GLMER
There is often confusion about "the level that a variable varies" with mixed effects models, when someone comes more from a multilevel background and/or has used software such as HLM or MLwiN where (from what I remember) it is necessary to... | Proper syntax for coding group level variables in mixed effect model using GLMER
There is often confusion about "the level that a variable varies" with mixed effects models, when someone comes more from a multilevel background and/or has used software such as HLM or MLwiN where (f |
49,704 | Is there a bootstrap 're-sampling the residuals' equivalent for GLM? | Yes.
The generalization is most clear if you think of linear regression not with an error term, but as a model for the conditional distribution of $Y \mid X$:
$$ Y \mid X \sim Normal(X \beta, \sigma) $$
When using the parametric bootstrap, we can think of our new $y_i$'s as samples from these conditional distributions,... | Is there a bootstrap 're-sampling the residuals' equivalent for GLM? | Yes.
The generalization is most clear if you think of linear regression not with an error term, but as a model for the conditional distribution of $Y \mid X$:
$$ Y \mid X \sim Normal(X \beta, \sigma) | Is there a bootstrap 're-sampling the residuals' equivalent for GLM?
Yes.
The generalization is most clear if you think of linear regression not with an error term, but as a model for the conditional distribution of $Y \mid X$:
$$ Y \mid X \sim Normal(X \beta, \sigma) $$
When using the parametric bootstrap, we can thin... | Is there a bootstrap 're-sampling the residuals' equivalent for GLM?
Yes.
The generalization is most clear if you think of linear regression not with an error term, but as a model for the conditional distribution of $Y \mid X$:
$$ Y \mid X \sim Normal(X \beta, \sigma) |
49,705 | What's the added value of SD line over regression line when examining association between 2 variables? | The SD line is a didactical and visual aid to help seeing the relation for the slope of the regular regression line.
$$\text {slope regression } = r_{xy} \, \frac {\sigma_y}{\sigma_x} = r_{xy} \, \text {slope SD line} $$
The SD line shows how x and y are varying and this can give a more or less steep or flat line depe... | What's the added value of SD line over regression line when examining association between 2 variable | The SD line is a didactical and visual aid to help seeing the relation for the slope of the regular regression line.
$$\text {slope regression } = r_{xy} \, \frac {\sigma_y}{\sigma_x} = r_{xy} \, \te | What's the added value of SD line over regression line when examining association between 2 variables?
The SD line is a didactical and visual aid to help seeing the relation for the slope of the regular regression line.
$$\text {slope regression } = r_{xy} \, \frac {\sigma_y}{\sigma_x} = r_{xy} \, \text {slope SD line... | What's the added value of SD line over regression line when examining association between 2 variable
The SD line is a didactical and visual aid to help seeing the relation for the slope of the regular regression line.
$$\text {slope regression } = r_{xy} \, \frac {\sigma_y}{\sigma_x} = r_{xy} \, \te |
49,706 | Increasing multicollinearity in multilevel/hierarchical modeling? | Since you say :
However, the relationship between $\textbf{y}$ and $\textbf{X}$ is not strictly linear over the entire domain, but could be better modeled as such within several subgroups $g$ (and coefficients are more meaningful if defined for each subgroup):
it sounds to me very much like a mixed effects model (of ... | Increasing multicollinearity in multilevel/hierarchical modeling? | Since you say :
However, the relationship between $\textbf{y}$ and $\textbf{X}$ is not strictly linear over the entire domain, but could be better modeled as such within several subgroups $g$ (and co | Increasing multicollinearity in multilevel/hierarchical modeling?
Since you say :
However, the relationship between $\textbf{y}$ and $\textbf{X}$ is not strictly linear over the entire domain, but could be better modeled as such within several subgroups $g$ (and coefficients are more meaningful if defined for each sub... | Increasing multicollinearity in multilevel/hierarchical modeling?
Since you say :
However, the relationship between $\textbf{y}$ and $\textbf{X}$ is not strictly linear over the entire domain, but could be better modeled as such within several subgroups $g$ (and co |
49,707 | How to statistically compare machine learning "regression" models? | Because my last answer was downvoted, I'm going to provide a full example.
You don't want to compare the residuals, you want to compare losses. Let's say that your regression looks like this
Let's compare two models on RMSE: a linear model and a generalized additive model. Clearly, the linear model will have larger ... | How to statistically compare machine learning "regression" models? | Because my last answer was downvoted, I'm going to provide a full example.
You don't want to compare the residuals, you want to compare losses. Let's say that your regression looks like this
Let's c | How to statistically compare machine learning "regression" models?
Because my last answer was downvoted, I'm going to provide a full example.
You don't want to compare the residuals, you want to compare losses. Let's say that your regression looks like this
Let's compare two models on RMSE: a linear model and a gener... | How to statistically compare machine learning "regression" models?
Because my last answer was downvoted, I'm going to provide a full example.
You don't want to compare the residuals, you want to compare losses. Let's say that your regression looks like this
Let's c |
49,708 | How to statistically compare machine learning "regression" models? | The usual for of evaluating a regressor in machine learning is by evaluating the error on a different dataset from the one used in training. I will assume that your sentence "All algorithms are trained and evaluated on the exact same dataset." mean that there are 2 different data sets, one for training and one for test... | How to statistically compare machine learning "regression" models? | The usual for of evaluating a regressor in machine learning is by evaluating the error on a different dataset from the one used in training. I will assume that your sentence "All algorithms are traine | How to statistically compare machine learning "regression" models?
The usual for of evaluating a regressor in machine learning is by evaluating the error on a different dataset from the one used in training. I will assume that your sentence "All algorithms are trained and evaluated on the exact same dataset." mean that... | How to statistically compare machine learning "regression" models?
The usual for of evaluating a regressor in machine learning is by evaluating the error on a different dataset from the one used in training. I will assume that your sentence "All algorithms are traine |
49,709 | Create Spline from Coefficients and Knots in GAMLSS | the pb() function fits P-splines as described by Eilers and Marx (1996): B-splines on equally spaced knots and finite difference penalties. In the same paper there are some code chunks that show how to fit the model (in the appendix if I remember well).
I do not know about the details of the fitted.gamlss method but th... | Create Spline from Coefficients and Knots in GAMLSS | the pb() function fits P-splines as described by Eilers and Marx (1996): B-splines on equally spaced knots and finite difference penalties. In the same paper there are some code chunks that show how t | Create Spline from Coefficients and Knots in GAMLSS
the pb() function fits P-splines as described by Eilers and Marx (1996): B-splines on equally spaced knots and finite difference penalties. In the same paper there are some code chunks that show how to fit the model (in the appendix if I remember well).
I do not know ... | Create Spline from Coefficients and Knots in GAMLSS
the pb() function fits P-splines as described by Eilers and Marx (1996): B-splines on equally spaced knots and finite difference penalties. In the same paper there are some code chunks that show how t |
49,710 | Create Spline from Coefficients and Knots in GAMLSS | Here's a function call to generate new $y$ values for any $x$.
predict(m1, newdata = data.frame(xs = new_x), data = data.frame(xs=xs))
Note that my xs is from the xs in your example. In general, you'll need to modify this to provide the original data to the predict function, with the original names. | Create Spline from Coefficients and Knots in GAMLSS | Here's a function call to generate new $y$ values for any $x$.
predict(m1, newdata = data.frame(xs = new_x), data = data.frame(xs=xs))
Note that my xs is from the xs in your example. In general, you' | Create Spline from Coefficients and Knots in GAMLSS
Here's a function call to generate new $y$ values for any $x$.
predict(m1, newdata = data.frame(xs = new_x), data = data.frame(xs=xs))
Note that my xs is from the xs in your example. In general, you'll need to modify this to provide the original data to the predict f... | Create Spline from Coefficients and Knots in GAMLSS
Here's a function call to generate new $y$ values for any $x$.
predict(m1, newdata = data.frame(xs = new_x), data = data.frame(xs=xs))
Note that my xs is from the xs in your example. In general, you' |
49,711 | L1-regularization enforces sparsity for convex functions | Regarding your question about general convex functions, you will get a sparse solution given that you apply a sparsity-inducing norm (which l1 is one such norm). For further information, read up to section 1.3 (including) here: https://hal.archives-ouvertes.fr/hal-00613125v1/document
In general (taken form the link):
... | L1-regularization enforces sparsity for convex functions | Regarding your question about general convex functions, you will get a sparse solution given that you apply a sparsity-inducing norm (which l1 is one such norm). For further information, read up to se | L1-regularization enforces sparsity for convex functions
Regarding your question about general convex functions, you will get a sparse solution given that you apply a sparsity-inducing norm (which l1 is one such norm). For further information, read up to section 1.3 (including) here: https://hal.archives-ouvertes.fr/ha... | L1-regularization enforces sparsity for convex functions
Regarding your question about general convex functions, you will get a sparse solution given that you apply a sparsity-inducing norm (which l1 is one such norm). For further information, read up to se |
49,712 | L1-regularization enforces sparsity for convex functions | No, f(x) = (|x|-1)**2 is convex, and has an infinite number of zeros. | L1-regularization enforces sparsity for convex functions | No, f(x) = (|x|-1)**2 is convex, and has an infinite number of zeros. | L1-regularization enforces sparsity for convex functions
No, f(x) = (|x|-1)**2 is convex, and has an infinite number of zeros. | L1-regularization enforces sparsity for convex functions
No, f(x) = (|x|-1)**2 is convex, and has an infinite number of zeros. |
49,713 | Can you delete the missing values before the analysis of a time series dataset? | On the one hand, you should not be deleting anything. Information is power. On the other hand, I am highly skeptical about your ability to perform missing data imputation for the missing river-days. It is not clear how different rivers are related, and missing data imputation adds value only if different variables (riv... | Can you delete the missing values before the analysis of a time series dataset? | On the one hand, you should not be deleting anything. Information is power. On the other hand, I am highly skeptical about your ability to perform missing data imputation for the missing river-days. I | Can you delete the missing values before the analysis of a time series dataset?
On the one hand, you should not be deleting anything. Information is power. On the other hand, I am highly skeptical about your ability to perform missing data imputation for the missing river-days. It is not clear how different rivers are ... | Can you delete the missing values before the analysis of a time series dataset?
On the one hand, you should not be deleting anything. Information is power. On the other hand, I am highly skeptical about your ability to perform missing data imputation for the missing river-days. I |
49,714 | Can you delete the missing values before the analysis of a time series dataset? | I would leave all of the data in, but then I would dig through to make sure there were not patterns misleading my data (e.g., that all of the new rivers are smaller because the state has been adding monitoring sites but already had the major rivers covered).
The other caveat is that you may need to use precipitation in... | Can you delete the missing values before the analysis of a time series dataset? | I would leave all of the data in, but then I would dig through to make sure there were not patterns misleading my data (e.g., that all of the new rivers are smaller because the state has been adding m | Can you delete the missing values before the analysis of a time series dataset?
I would leave all of the data in, but then I would dig through to make sure there were not patterns misleading my data (e.g., that all of the new rivers are smaller because the state has been adding monitoring sites but already had the majo... | Can you delete the missing values before the analysis of a time series dataset?
I would leave all of the data in, but then I would dig through to make sure there were not patterns misleading my data (e.g., that all of the new rivers are smaller because the state has been adding m |
49,715 | Unbiased estimator of the ratio of variances | Assuming the two samples are independent of each other.
Use the fact that $\frac{(m-1)S_1^2}{\sigma_1^2}\sim \chi^2_{m-1}$ and $\frac{(n-1)S_2^2}{\sigma_2^2}\sim \chi^2_{n-1}$, where $S_1^2=\frac1{m-1}\sum\limits_{i=1}^m (X_i-\overline X)^2$ and $S_2^2=\frac1{n-1}\sum\limits_{i=1}^n (Y_i-\overline Y)^2$ are the sample ... | Unbiased estimator of the ratio of variances | Assuming the two samples are independent of each other.
Use the fact that $\frac{(m-1)S_1^2}{\sigma_1^2}\sim \chi^2_{m-1}$ and $\frac{(n-1)S_2^2}{\sigma_2^2}\sim \chi^2_{n-1}$, where $S_1^2=\frac1{m-1 | Unbiased estimator of the ratio of variances
Assuming the two samples are independent of each other.
Use the fact that $\frac{(m-1)S_1^2}{\sigma_1^2}\sim \chi^2_{m-1}$ and $\frac{(n-1)S_2^2}{\sigma_2^2}\sim \chi^2_{n-1}$, where $S_1^2=\frac1{m-1}\sum\limits_{i=1}^m (X_i-\overline X)^2$ and $S_2^2=\frac1{n-1}\sum\limits... | Unbiased estimator of the ratio of variances
Assuming the two samples are independent of each other.
Use the fact that $\frac{(m-1)S_1^2}{\sigma_1^2}\sim \chi^2_{m-1}$ and $\frac{(n-1)S_2^2}{\sigma_2^2}\sim \chi^2_{n-1}$, where $S_1^2=\frac1{m-1 |
49,716 | Unbiased estimator of the ratio of variances | Using Slutsky's theorem of large sample theory you will get an assymptotic unbiased estimator!
Else if you want to get an estimator of it then find out the MLEs and use the invariance property! | Unbiased estimator of the ratio of variances | Using Slutsky's theorem of large sample theory you will get an assymptotic unbiased estimator!
Else if you want to get an estimator of it then find out the MLEs and use the invariance property! | Unbiased estimator of the ratio of variances
Using Slutsky's theorem of large sample theory you will get an assymptotic unbiased estimator!
Else if you want to get an estimator of it then find out the MLEs and use the invariance property! | Unbiased estimator of the ratio of variances
Using Slutsky's theorem of large sample theory you will get an assymptotic unbiased estimator!
Else if you want to get an estimator of it then find out the MLEs and use the invariance property! |
49,717 | Viral topics. How to describe and characterize bumps in time series of tag-activity on Meta Stack Exchange | I have read of your linked meta post, and it is an interesting situation. If I understand the issue correctly, there has been a proposal to create a tag specific to this particular controversy (such that all posts pertaining to the controversy would be easily identifiable together), and that proposal has been rejected... | Viral topics. How to describe and characterize bumps in time series of tag-activity on Meta Stack Ex | I have read of your linked meta post, and it is an interesting situation. If I understand the issue correctly, there has been a proposal to create a tag specific to this particular controversy (such | Viral topics. How to describe and characterize bumps in time series of tag-activity on Meta Stack Exchange
I have read of your linked meta post, and it is an interesting situation. If I understand the issue correctly, there has been a proposal to create a tag specific to this particular controversy (such that all post... | Viral topics. How to describe and characterize bumps in time series of tag-activity on Meta Stack Ex
I have read of your linked meta post, and it is an interesting situation. If I understand the issue correctly, there has been a proposal to create a tag specific to this particular controversy (such |
49,718 | Density estimation as an optimization problem | (I'll answer the second question, about the results of your maximum likelihood with fixed differential entropy procedure; I don't know the answer to the first, about whether KDE can be phrased as optimizing some objective functional.)
Without additional constraints such as bounds on the derivatives, the problem is ill-... | Density estimation as an optimization problem | (I'll answer the second question, about the results of your maximum likelihood with fixed differential entropy procedure; I don't know the answer to the first, about whether KDE can be phrased as opti | Density estimation as an optimization problem
(I'll answer the second question, about the results of your maximum likelihood with fixed differential entropy procedure; I don't know the answer to the first, about whether KDE can be phrased as optimizing some objective functional.)
Without additional constraints such as ... | Density estimation as an optimization problem
(I'll answer the second question, about the results of your maximum likelihood with fixed differential entropy procedure; I don't know the answer to the first, about whether KDE can be phrased as opti |
49,719 | What is really the Scale or Sigma parameter of a tobit regression? | Tobit regression assumes that there is a latent dependent variable that can take any value. It is part of a normal linear regression equation with a normally distributed error tern. The standard deviation of that error term is the scale parameter. However, a tobit model assumes that this latent variable is only observe... | What is really the Scale or Sigma parameter of a tobit regression? | Tobit regression assumes that there is a latent dependent variable that can take any value. It is part of a normal linear regression equation with a normally distributed error tern. The standard devia | What is really the Scale or Sigma parameter of a tobit regression?
Tobit regression assumes that there is a latent dependent variable that can take any value. It is part of a normal linear regression equation with a normally distributed error tern. The standard deviation of that error term is the scale parameter. Howev... | What is really the Scale or Sigma parameter of a tobit regression?
Tobit regression assumes that there is a latent dependent variable that can take any value. It is part of a normal linear regression equation with a normally distributed error tern. The standard devia |
49,720 | Isolation Forest and average/expected depth formula | I’ll answer myself with help from these other questions in the math section:
https://math.stackexchange.com/questions/3333220/expected-average-depth-in-random-binary-tree-constructed-top-to-bottom
https://math.stackexchange.com/questions/52572/do-harmonic-numbers-have-a-closed-form-expression
From the answer above, the... | Isolation Forest and average/expected depth formula | I’ll answer myself with help from these other questions in the math section:
https://math.stackexchange.com/questions/3333220/expected-average-depth-in-random-binary-tree-constructed-top-to-bottom
htt | Isolation Forest and average/expected depth formula
I’ll answer myself with help from these other questions in the math section:
https://math.stackexchange.com/questions/3333220/expected-average-depth-in-random-binary-tree-constructed-top-to-bottom
https://math.stackexchange.com/questions/52572/do-harmonic-numbers-have... | Isolation Forest and average/expected depth formula
I’ll answer myself with help from these other questions in the math section:
https://math.stackexchange.com/questions/3333220/expected-average-depth-in-random-binary-tree-constructed-top-to-bottom
htt |
49,721 | Isolation Forest and average/expected depth formula | UPDATE:
Now, it seems clearly, there are 3 methods to calculate:
$c(3)= 2H(3-1)-2(3-1)/3 =2(H(3)-1)=2(1+1/2+1/3-1)=1.667 $
$c(3) = 2H(3-1)-2(3-1)/3 = 2(\log {(2)}+ 0.57721566)-4/3) = 1.20739$
$c(3) = 2(H(3)-1) = 2(\log 3+ 0.57721566-1) = 2(1.0986+0.57721566-1) = 1.35$
method1 is accurate result.
method2 is approximat... | Isolation Forest and average/expected depth formula | UPDATE:
Now, it seems clearly, there are 3 methods to calculate:
$c(3)= 2H(3-1)-2(3-1)/3 =2(H(3)-1)=2(1+1/2+1/3-1)=1.667 $
$c(3) = 2H(3-1)-2(3-1)/3 = 2(\log {(2)}+ 0.57721566)-4/3) = 1.20739$
$c(3) = | Isolation Forest and average/expected depth formula
UPDATE:
Now, it seems clearly, there are 3 methods to calculate:
$c(3)= 2H(3-1)-2(3-1)/3 =2(H(3)-1)=2(1+1/2+1/3-1)=1.667 $
$c(3) = 2H(3-1)-2(3-1)/3 = 2(\log {(2)}+ 0.57721566)-4/3) = 1.20739$
$c(3) = 2(H(3)-1) = 2(\log 3+ 0.57721566-1) = 2(1.0986+0.57721566-1) = 1.35... | Isolation Forest and average/expected depth formula
UPDATE:
Now, it seems clearly, there are 3 methods to calculate:
$c(3)= 2H(3-1)-2(3-1)/3 =2(H(3)-1)=2(1+1/2+1/3-1)=1.667 $
$c(3) = 2H(3-1)-2(3-1)/3 = 2(\log {(2)}+ 0.57721566)-4/3) = 1.20739$
$c(3) = |
49,722 | Peeking Inside the Black Box, can Feature importance indicate overfit? | I don't think permutation feature importance can identify overfitting per se, it could however hint whether a good amount of noise has been modelled (overfitting) when features that you know for a fact to be significant, aren't deemed significant (pretty much your case). If you go with splitting, significantly smaller ... | Peeking Inside the Black Box, can Feature importance indicate overfit? | I don't think permutation feature importance can identify overfitting per se, it could however hint whether a good amount of noise has been modelled (overfitting) when features that you know for a fac | Peeking Inside the Black Box, can Feature importance indicate overfit?
I don't think permutation feature importance can identify overfitting per se, it could however hint whether a good amount of noise has been modelled (overfitting) when features that you know for a fact to be significant, aren't deemed significant (p... | Peeking Inside the Black Box, can Feature importance indicate overfit?
I don't think permutation feature importance can identify overfitting per se, it could however hint whether a good amount of noise has been modelled (overfitting) when features that you know for a fac |
49,723 | R Multivariate Normal CDF | The first pmvnorm calculates the probability that variable 1 <=13 AND variable 2 <=15 AND variable <=12 all occurs at the same time. The probability that each individual variable fufills that criteria will be 0.5, however the joint probability will not be 0.5
If we use an example where all variables are uncorrelated
m... | R Multivariate Normal CDF | The first pmvnorm calculates the probability that variable 1 <=13 AND variable 2 <=15 AND variable <=12 all occurs at the same time. The probability that each individual variable fufills that criteri | R Multivariate Normal CDF
The first pmvnorm calculates the probability that variable 1 <=13 AND variable 2 <=15 AND variable <=12 all occurs at the same time. The probability that each individual variable fufills that criteria will be 0.5, however the joint probability will not be 0.5
If we use an example where all va... | R Multivariate Normal CDF
The first pmvnorm calculates the probability that variable 1 <=13 AND variable 2 <=15 AND variable <=12 all occurs at the same time. The probability that each individual variable fufills that criteri |
49,724 | Probability that all cards have been drawn [duplicate] | I think the solution would go something like this:
Let $P(m, n, k, x, y)$ be the probability of seeing exactly $x$ cards at least once over $k$ draws, once $y$ cards have already been seen.
Then $P(m, n, k, x, 0) = \sum_{i=0}^{x}P(m, n, k-1, x-i, 0) * P(m, n, 1, i, x-i)$
I think the possibilities under the sum sign are... | Probability that all cards have been drawn [duplicate] | I think the solution would go something like this:
Let $P(m, n, k, x, y)$ be the probability of seeing exactly $x$ cards at least once over $k$ draws, once $y$ cards have already been seen.
Then $P(m, | Probability that all cards have been drawn [duplicate]
I think the solution would go something like this:
Let $P(m, n, k, x, y)$ be the probability of seeing exactly $x$ cards at least once over $k$ draws, once $y$ cards have already been seen.
Then $P(m, n, k, x, 0) = \sum_{i=0}^{x}P(m, n, k-1, x-i, 0) * P(m, n, 1, i,... | Probability that all cards have been drawn [duplicate]
I think the solution would go something like this:
Let $P(m, n, k, x, y)$ be the probability of seeing exactly $x$ cards at least once over $k$ draws, once $y$ cards have already been seen.
Then $P(m, |
49,725 | Probability that all cards have been drawn [duplicate] | This is a simple variant of the coupon collector's problem, which uses the classical occupancy distribution. Let $K$ be the number of distinct cards that have been drawn, distributed according to the classical occupancy distribution. With $m$ distinct cards in the deck, and $n \geqslant m$ random draws with replaceme... | Probability that all cards have been drawn [duplicate] | This is a simple variant of the coupon collector's problem, which uses the classical occupancy distribution. Let $K$ be the number of distinct cards that have been drawn, distributed according to the | Probability that all cards have been drawn [duplicate]
This is a simple variant of the coupon collector's problem, which uses the classical occupancy distribution. Let $K$ be the number of distinct cards that have been drawn, distributed according to the classical occupancy distribution. With $m$ distinct cards in th... | Probability that all cards have been drawn [duplicate]
This is a simple variant of the coupon collector's problem, which uses the classical occupancy distribution. Let $K$ be the number of distinct cards that have been drawn, distributed according to the |
49,726 | What is meant by existence of a (discrete-time) stochastic process? | Could anyone offer a simple example of an existent process?
A well-known theorem which guarantees the existence of a stochastic process ${(X_n)}_{n \geqslant 1}$, say with $\mathbb{R}$-valued random variables $X_n$, is the Daniell-Kolmogorov extension theorem. A typical application of this theorem gives the existence ... | What is meant by existence of a (discrete-time) stochastic process? | Could anyone offer a simple example of an existent process?
A well-known theorem which guarantees the existence of a stochastic process ${(X_n)}_{n \geqslant 1}$, say with $\mathbb{R}$-valued random | What is meant by existence of a (discrete-time) stochastic process?
Could anyone offer a simple example of an existent process?
A well-known theorem which guarantees the existence of a stochastic process ${(X_n)}_{n \geqslant 1}$, say with $\mathbb{R}$-valued random variables $X_n$, is the Daniell-Kolmogorov extension... | What is meant by existence of a (discrete-time) stochastic process?
Could anyone offer a simple example of an existent process?
A well-known theorem which guarantees the existence of a stochastic process ${(X_n)}_{n \geqslant 1}$, say with $\mathbb{R}$-valued random |
49,727 | What is meant by existence of a (discrete-time) stochastic process? | In this answer I collect and summarize some bits of insight I have received through comments and gathered myself. Considerable credit goes to @IsabellaGhement and @whuber
What is meant by existence of a (discrete-time) stochastic process?
A stochastic process exists if the relevant mathematical objects demanded of th... | What is meant by existence of a (discrete-time) stochastic process? | In this answer I collect and summarize some bits of insight I have received through comments and gathered myself. Considerable credit goes to @IsabellaGhement and @whuber
What is meant by existence o | What is meant by existence of a (discrete-time) stochastic process?
In this answer I collect and summarize some bits of insight I have received through comments and gathered myself. Considerable credit goes to @IsabellaGhement and @whuber
What is meant by existence of a (discrete-time) stochastic process?
A stochasti... | What is meant by existence of a (discrete-time) stochastic process?
In this answer I collect and summarize some bits of insight I have received through comments and gathered myself. Considerable credit goes to @IsabellaGhement and @whuber
What is meant by existence o |
49,728 | Comparing ways to create a composite score | Question 1: You are incorrect that "we don't need any distributional assumption for the biomarkers in logistic regressions." A single-predictor logistic regression specifically assumes that the log-odds of the binary outcome are linearly related to the values of the predictor. So if you are using, say, RNAseq data as p... | Comparing ways to create a composite score | Question 1: You are incorrect that "we don't need any distributional assumption for the biomarkers in logistic regressions." A single-predictor logistic regression specifically assumes that the log-od | Comparing ways to create a composite score
Question 1: You are incorrect that "we don't need any distributional assumption for the biomarkers in logistic regressions." A single-predictor logistic regression specifically assumes that the log-odds of the binary outcome are linearly related to the values of the predictor.... | Comparing ways to create a composite score
Question 1: You are incorrect that "we don't need any distributional assumption for the biomarkers in logistic regressions." A single-predictor logistic regression specifically assumes that the log-od |
49,729 | Hard in calculating predictor‘s Relative Importance for GAM? | The caret package provides one answer. With the default tuneGrid and trainControl,
library(caret)
data("mtcars")
gam1 <- train(
mpg ~ drat + wt + qsec,
data = mtcars,
method = "gam"
)
and you can then apply varImp.
varImp(gam1)
## gam variable importance
## Overall
## wt 100.0
## qsec 26.4
## dra... | Hard in calculating predictor‘s Relative Importance for GAM? | The caret package provides one answer. With the default tuneGrid and trainControl,
library(caret)
data("mtcars")
gam1 <- train(
mpg ~ drat + wt + qsec,
data = mtcars,
method = "gam"
)
and yo | Hard in calculating predictor‘s Relative Importance for GAM?
The caret package provides one answer. With the default tuneGrid and trainControl,
library(caret)
data("mtcars")
gam1 <- train(
mpg ~ drat + wt + qsec,
data = mtcars,
method = "gam"
)
and you can then apply varImp.
varImp(gam1)
## gam variable impo... | Hard in calculating predictor‘s Relative Importance for GAM?
The caret package provides one answer. With the default tuneGrid and trainControl,
library(caret)
data("mtcars")
gam1 <- train(
mpg ~ drat + wt + qsec,
data = mtcars,
method = "gam"
)
and yo |
49,730 | What is *common variance* in factor analysis and how is it estimated? | 1.
According to Mulaik (2009) p. 133-134, given a factor model
\begin{aligned}
Y_1&=\lambda_{11}\xi_1+\dots+\lambda_{1r}\xi_r+\Psi_1\varepsilon_1 \\
Y_2&=\lambda_{21}\xi_1+\dots+\lambda_{2r}\xi_r+\Psi_2\varepsilon_2 \\
&\dots \\
Y_n&=\lambda_{n1}\xi_1+\dots+\lambda_{nr}\xi_r+\Psi_n\varepsilon_n \\
\end{aligned}
where $... | What is *common variance* in factor analysis and how is it estimated? | 1.
According to Mulaik (2009) p. 133-134, given a factor model
\begin{aligned}
Y_1&=\lambda_{11}\xi_1+\dots+\lambda_{1r}\xi_r+\Psi_1\varepsilon_1 \\
Y_2&=\lambda_{21}\xi_1+\dots+\lambda_{2r}\xi_r+\Psi | What is *common variance* in factor analysis and how is it estimated?
1.
According to Mulaik (2009) p. 133-134, given a factor model
\begin{aligned}
Y_1&=\lambda_{11}\xi_1+\dots+\lambda_{1r}\xi_r+\Psi_1\varepsilon_1 \\
Y_2&=\lambda_{21}\xi_1+\dots+\lambda_{2r}\xi_r+\Psi_2\varepsilon_2 \\
&\dots \\
Y_n&=\lambda_{n1}\xi_... | What is *common variance* in factor analysis and how is it estimated?
1.
According to Mulaik (2009) p. 133-134, given a factor model
\begin{aligned}
Y_1&=\lambda_{11}\xi_1+\dots+\lambda_{1r}\xi_r+\Psi_1\varepsilon_1 \\
Y_2&=\lambda_{21}\xi_1+\dots+\lambda_{2r}\xi_r+\Psi |
49,731 | Decomposing $R^2$ into independent variables | I struggled with this same problem--decomposing variance in high-dimensional prediction problems without limiting myself to fitting many, many linear regression models--and came up with the following solution: Shapley Decomposition of R-Squared in Machine Learning Models (with an R implementation).
I would say that th... | Decomposing $R^2$ into independent variables | I struggled with this same problem--decomposing variance in high-dimensional prediction problems without limiting myself to fitting many, many linear regression models--and came up with the following | Decomposing $R^2$ into independent variables
I struggled with this same problem--decomposing variance in high-dimensional prediction problems without limiting myself to fitting many, many linear regression models--and came up with the following solution: Shapley Decomposition of R-Squared in Machine Learning Models (wi... | Decomposing $R^2$ into independent variables
I struggled with this same problem--decomposing variance in high-dimensional prediction problems without limiting myself to fitting many, many linear regression models--and came up with the following |
49,732 | Expectation of inverse of sum of positive iid variables | You cannot bound that expectation in $\sigma, n$. That's because there is the distinct possibility that the expectation do not exist at all (or, is $\infty$.) See I've heard that ratios or inverses of random variables often are problematic, in not having expectations. Why is that?. If the conditions given there is ful... | Expectation of inverse of sum of positive iid variables | You cannot bound that expectation in $\sigma, n$. That's because there is the distinct possibility that the expectation do not exist at all (or, is $\infty$.) See I've heard that ratios or inverses of | Expectation of inverse of sum of positive iid variables
You cannot bound that expectation in $\sigma, n$. That's because there is the distinct possibility that the expectation do not exist at all (or, is $\infty$.) See I've heard that ratios or inverses of random variables often are problematic, in not having expectati... | Expectation of inverse of sum of positive iid variables
You cannot bound that expectation in $\sigma, n$. That's because there is the distinct possibility that the expectation do not exist at all (or, is $\infty$.) See I've heard that ratios or inverses of |
49,733 | Expectation of inverse of sum of positive iid variables | I think I have the gist of it.
Given that $f(x)=1/x$ is infinitely differentiable in 1. Taylor's theorem tells us:
There exists $\varepsilon>0$ such that $f(x) = f(1) + f'(1) (x-1)+ \frac{f''(1)(x-1)^2}{2} + \frac{f'''(\varepsilon) (x-1)^2}{2}$.
In our case, if $X_i$ belongs in the domaine $[v_1;+\infty[$, then $\bar{... | Expectation of inverse of sum of positive iid variables | I think I have the gist of it.
Given that $f(x)=1/x$ is infinitely differentiable in 1. Taylor's theorem tells us:
There exists $\varepsilon>0$ such that $f(x) = f(1) + f'(1) (x-1)+ \frac{f''(1)(x-1)^ | Expectation of inverse of sum of positive iid variables
I think I have the gist of it.
Given that $f(x)=1/x$ is infinitely differentiable in 1. Taylor's theorem tells us:
There exists $\varepsilon>0$ such that $f(x) = f(1) + f'(1) (x-1)+ \frac{f''(1)(x-1)^2}{2} + \frac{f'''(\varepsilon) (x-1)^2}{2}$.
In our case, if $... | Expectation of inverse of sum of positive iid variables
I think I have the gist of it.
Given that $f(x)=1/x$ is infinitely differentiable in 1. Taylor's theorem tells us:
There exists $\varepsilon>0$ such that $f(x) = f(1) + f'(1) (x-1)+ \frac{f''(1)(x-1)^ |
49,734 | What is element-wise max pooling? | In the paper you reference, they do the following:
Assign lidar points to voxels, such that each voxel contains several points.
Augment the point representation by stacking the offset from the voxel centroid to the original representation (denoted $\hat p$ in the text).
Pass each point belonging to a voxel $\hat p_i$ ... | What is element-wise max pooling? | In the paper you reference, they do the following:
Assign lidar points to voxels, such that each voxel contains several points.
Augment the point representation by stacking the offset from the voxel | What is element-wise max pooling?
In the paper you reference, they do the following:
Assign lidar points to voxels, such that each voxel contains several points.
Augment the point representation by stacking the offset from the voxel centroid to the original representation (denoted $\hat p$ in the text).
Pass each poin... | What is element-wise max pooling?
In the paper you reference, they do the following:
Assign lidar points to voxels, such that each voxel contains several points.
Augment the point representation by stacking the offset from the voxel |
49,735 | What is element-wise max pooling? | It's a particular case of 1D max pooling where the pool size and stride are the same as the length of each y_i where 1 <= i <= k.
Unfortunately there doesn't seem to be many implementations or definitions of this to use as reference. At least in here they define it as you are using it. Here how the issuer defined eleme... | What is element-wise max pooling? | It's a particular case of 1D max pooling where the pool size and stride are the same as the length of each y_i where 1 <= i <= k.
Unfortunately there doesn't seem to be many implementations or definit | What is element-wise max pooling?
It's a particular case of 1D max pooling where the pool size and stride are the same as the length of each y_i where 1 <= i <= k.
Unfortunately there doesn't seem to be many implementations or definitions of this to use as reference. At least in here they define it as you are using it.... | What is element-wise max pooling?
It's a particular case of 1D max pooling where the pool size and stride are the same as the length of each y_i where 1 <= i <= k.
Unfortunately there doesn't seem to be many implementations or definit |
49,736 | Can you statistically compare one subset of a population with the whole population? | The data is usually organized by placing each variable value along a column and each individual (student) in a row. I'm assuming that each student was only evaluated once.
The variables could start with student ID (e.g., 1,2,3,...), year, school (that can be coded as 1 for school A, 2 for school B, etc.), Math grade, E... | Can you statistically compare one subset of a population with the whole population? | The data is usually organized by placing each variable value along a column and each individual (student) in a row. I'm assuming that each student was only evaluated once.
The variables could start wi | Can you statistically compare one subset of a population with the whole population?
The data is usually organized by placing each variable value along a column and each individual (student) in a row. I'm assuming that each student was only evaluated once.
The variables could start with student ID (e.g., 1,2,3,...), yea... | Can you statistically compare one subset of a population with the whole population?
The data is usually organized by placing each variable value along a column and each individual (student) in a row. I'm assuming that each student was only evaluated once.
The variables could start wi |
49,737 | Adaptive Parzen Estimator | I was also having some trouble understanding everything when reading the paper. To the specific questions you listed here, I might provide my understanding:
Parzen estimators (or Parzen windows) are indeed kernel density estimators. In the linked wiki page, it is also stated that if the bandwidth is not fixed, the est... | Adaptive Parzen Estimator | I was also having some trouble understanding everything when reading the paper. To the specific questions you listed here, I might provide my understanding:
Parzen estimators (or Parzen windows) are | Adaptive Parzen Estimator
I was also having some trouble understanding everything when reading the paper. To the specific questions you listed here, I might provide my understanding:
Parzen estimators (or Parzen windows) are indeed kernel density estimators. In the linked wiki page, it is also stated that if the bandw... | Adaptive Parzen Estimator
I was also having some trouble understanding everything when reading the paper. To the specific questions you listed here, I might provide my understanding:
Parzen estimators (or Parzen windows) are |
49,738 | Why not normalizing mutual information with harmonic mean of entropies? | The reason the Harmonic Mean is never mentioned as a normalization for MI is that it renders the measure equivalent to another commonly used clustering comparison method, the normalized Variation of Information (VI), where the regular VI is defined as:
\begin{equation}
VI(X,Y) = H(X|Y) + H(Y|X)
\end{equation}
and the n... | Why not normalizing mutual information with harmonic mean of entropies? | The reason the Harmonic Mean is never mentioned as a normalization for MI is that it renders the measure equivalent to another commonly used clustering comparison method, the normalized Variation of I | Why not normalizing mutual information with harmonic mean of entropies?
The reason the Harmonic Mean is never mentioned as a normalization for MI is that it renders the measure equivalent to another commonly used clustering comparison method, the normalized Variation of Information (VI), where the regular VI is defined... | Why not normalizing mutual information with harmonic mean of entropies?
The reason the Harmonic Mean is never mentioned as a normalization for MI is that it renders the measure equivalent to another commonly used clustering comparison method, the normalized Variation of I |
49,739 | How can one interpret a heat map plot | Each square shows the correlation between the variables on each axis. Correlation ranges from -1 to +1. Values closer to zero means there is no linear trend between the two variables. The close to 1 the correlation is the more positively correlated they are; that is as one increases so does the other and the closer to... | How can one interpret a heat map plot | Each square shows the correlation between the variables on each axis. Correlation ranges from -1 to +1. Values closer to zero means there is no linear trend between the two variables. The close to 1 | How can one interpret a heat map plot
Each square shows the correlation between the variables on each axis. Correlation ranges from -1 to +1. Values closer to zero means there is no linear trend between the two variables. The close to 1 the correlation is the more positively correlated they are; that is as one increas... | How can one interpret a heat map plot
Each square shows the correlation between the variables on each axis. Correlation ranges from -1 to +1. Values closer to zero means there is no linear trend between the two variables. The close to 1 |
49,740 | How can one interpret a heat map plot | A heat map is an eye-catcher, nothing more. It gives extreme colors to extreme values so they are easily visible to the naked eye. Apart from that, it's just a matrix of numbers, no special interpretation required. | How can one interpret a heat map plot | A heat map is an eye-catcher, nothing more. It gives extreme colors to extreme values so they are easily visible to the naked eye. Apart from that, it's just a matrix of numbers, no special interpreta | How can one interpret a heat map plot
A heat map is an eye-catcher, nothing more. It gives extreme colors to extreme values so they are easily visible to the naked eye. Apart from that, it's just a matrix of numbers, no special interpretation required. | How can one interpret a heat map plot
A heat map is an eye-catcher, nothing more. It gives extreme colors to extreme values so they are easily visible to the naked eye. Apart from that, it's just a matrix of numbers, no special interpreta |
49,741 | How can one interpret a heat map plot | A heat map is a two-dimensional representation of data in which values are represented by colors. Correlation Heat map is a two dimensional plot of the amount of correlation (measure of dependence) between variables represented by colors. The varying intensity of color represents the measure of correlation.
Correlation... | How can one interpret a heat map plot | A heat map is a two-dimensional representation of data in which values are represented by colors. Correlation Heat map is a two dimensional plot of the amount of correlation (measure of dependence) be | How can one interpret a heat map plot
A heat map is a two-dimensional representation of data in which values are represented by colors. Correlation Heat map is a two dimensional plot of the amount of correlation (measure of dependence) between variables represented by colors. The varying intensity of color represents t... | How can one interpret a heat map plot
A heat map is a two-dimensional representation of data in which values are represented by colors. Correlation Heat map is a two dimensional plot of the amount of correlation (measure of dependence) be |
49,742 | How can I calculate the critical t-values of a linear regression model? | I'm going to construe the question as meaning: What is the t-statistic and what is its probability distribution?
You have
\begin{align}
Y_i = {} & \beta_0 +\beta_1 x_i + \varepsilon_i \quad \text{for } i=1,\ldots,n \\[10pt]
& \varepsilon_1,\ldots,\varepsilon_n \sim \operatorname{iid} \operatorname N(0,\sigma^2). \\[10p... | How can I calculate the critical t-values of a linear regression model? | I'm going to construe the question as meaning: What is the t-statistic and what is its probability distribution?
You have
\begin{align}
Y_i = {} & \beta_0 +\beta_1 x_i + \varepsilon_i \quad \text{for | How can I calculate the critical t-values of a linear regression model?
I'm going to construe the question as meaning: What is the t-statistic and what is its probability distribution?
You have
\begin{align}
Y_i = {} & \beta_0 +\beta_1 x_i + \varepsilon_i \quad \text{for } i=1,\ldots,n \\[10pt]
& \varepsilon_1,\ldots,\... | How can I calculate the critical t-values of a linear regression model?
I'm going to construe the question as meaning: What is the t-statistic and what is its probability distribution?
You have
\begin{align}
Y_i = {} & \beta_0 +\beta_1 x_i + \varepsilon_i \quad \text{for |
49,743 | How can I calculate the critical t-values of a linear regression model? | That answer by Michael Hardy gives you the formulae for manual calculation for simple linear regression. Since you have implemented your model in R the easiest thing would be just to generate the outputs using standard commands in that program:
#Fit a linear regression model
#Substitute the actual names of your data f... | How can I calculate the critical t-values of a linear regression model? | That answer by Michael Hardy gives you the formulae for manual calculation for simple linear regression. Since you have implemented your model in R the easiest thing would be just to generate the out | How can I calculate the critical t-values of a linear regression model?
That answer by Michael Hardy gives you the formulae for manual calculation for simple linear regression. Since you have implemented your model in R the easiest thing would be just to generate the outputs using standard commands in that program:
#F... | How can I calculate the critical t-values of a linear regression model?
That answer by Michael Hardy gives you the formulae for manual calculation for simple linear regression. Since you have implemented your model in R the easiest thing would be just to generate the out |
49,744 | Gauss Original Paper | According to author of several books on history of statistics, Stephen M. Stigler (1981), the method of least squares was first described by Carl Friedrich Gauss in 1809 in his Theoria Modus Corporum Coelestium [Theory of the Motion of Heavenly Bodies] book. In the same work Gauss proposed a form of normal distributio... | Gauss Original Paper | According to author of several books on history of statistics, Stephen M. Stigler (1981), the method of least squares was first described by Carl Friedrich Gauss in 1809 in his Theoria Modus Corporum | Gauss Original Paper
According to author of several books on history of statistics, Stephen M. Stigler (1981), the method of least squares was first described by Carl Friedrich Gauss in 1809 in his Theoria Modus Corporum Coelestium [Theory of the Motion of Heavenly Bodies] book. In the same work Gauss proposed a form ... | Gauss Original Paper
According to author of several books on history of statistics, Stephen M. Stigler (1981), the method of least squares was first described by Carl Friedrich Gauss in 1809 in his Theoria Modus Corporum |
49,745 | Error on mean from measurements made from a distribution with a possible long tail | The behavior that the mean keeps increasing when more samples are added, typically means that the mean time is infinite. You could for example be facing a pareto distribution with $\alpha\le 1$.
You may not be facing this exact distribution, but it is the most standard example of a fairly simple distribution with infi... | Error on mean from measurements made from a distribution with a possible long tail | The behavior that the mean keeps increasing when more samples are added, typically means that the mean time is infinite. You could for example be facing a pareto distribution with $\alpha\le 1$.
You | Error on mean from measurements made from a distribution with a possible long tail
The behavior that the mean keeps increasing when more samples are added, typically means that the mean time is infinite. You could for example be facing a pareto distribution with $\alpha\le 1$.
You may not be facing this exact distribu... | Error on mean from measurements made from a distribution with a possible long tail
The behavior that the mean keeps increasing when more samples are added, typically means that the mean time is infinite. You could for example be facing a pareto distribution with $\alpha\le 1$.
You |
49,746 | Error on mean from measurements made from a distribution with a possible long tail | The difference of the empirical means of two sets of samples might well be larger than the standard error of the mean. Asymptotically, the standard error defines a confidence interval to the level 0.67 or so.
If the distribution has long tails and the sample mean is unstable, the sample standard deviation should be lar... | Error on mean from measurements made from a distribution with a possible long tail | The difference of the empirical means of two sets of samples might well be larger than the standard error of the mean. Asymptotically, the standard error defines a confidence interval to the level 0.6 | Error on mean from measurements made from a distribution with a possible long tail
The difference of the empirical means of two sets of samples might well be larger than the standard error of the mean. Asymptotically, the standard error defines a confidence interval to the level 0.67 or so.
If the distribution has long... | Error on mean from measurements made from a distribution with a possible long tail
The difference of the empirical means of two sets of samples might well be larger than the standard error of the mean. Asymptotically, the standard error defines a confidence interval to the level 0.6 |
49,747 | Error on mean from measurements made from a distribution with a possible long tail | I think the answer to your problem may be more related to your field of study (say, molecular dynamics) than statistics. Statistics deals with probability distribution of random variables and, it does not matter what your distribution is, for applying central limit theorem, for making inferences about population (with ... | Error on mean from measurements made from a distribution with a possible long tail | I think the answer to your problem may be more related to your field of study (say, molecular dynamics) than statistics. Statistics deals with probability distribution of random variables and, it does | Error on mean from measurements made from a distribution with a possible long tail
I think the answer to your problem may be more related to your field of study (say, molecular dynamics) than statistics. Statistics deals with probability distribution of random variables and, it does not matter what your distribution is... | Error on mean from measurements made from a distribution with a possible long tail
I think the answer to your problem may be more related to your field of study (say, molecular dynamics) than statistics. Statistics deals with probability distribution of random variables and, it does |
49,748 | Error on mean from measurements made from a distribution with a possible long tail | EDIT:
If the mean is changing significantly when you add more data then you may not have a finite mean or not unimodal. hist(c(rnorm(100, 0, 1) + rnorm(100, 3, 1)))`. But I'm guessing you've already made a histogram of your data or have been able to visualize it. So Here's what I would do. 1.) Calculate the mean with a... | Error on mean from measurements made from a distribution with a possible long tail | EDIT:
If the mean is changing significantly when you add more data then you may not have a finite mean or not unimodal. hist(c(rnorm(100, 0, 1) + rnorm(100, 3, 1)))`. But I'm guessing you've already m | Error on mean from measurements made from a distribution with a possible long tail
EDIT:
If the mean is changing significantly when you add more data then you may not have a finite mean or not unimodal. hist(c(rnorm(100, 0, 1) + rnorm(100, 3, 1)))`. But I'm guessing you've already made a histogram of your data or have ... | Error on mean from measurements made from a distribution with a possible long tail
EDIT:
If the mean is changing significantly when you add more data then you may not have a finite mean or not unimodal. hist(c(rnorm(100, 0, 1) + rnorm(100, 3, 1)))`. But I'm guessing you've already m |
49,749 | Ratio of Unbiased Estimators | No, it will not be unbiased (unless the estimator of the denominator have zero variance.) And it will not help if the numerator and denominator are independent. In general, if $\hat{\theta}$ is an unbiased estimator of $\theta$ and $g$ is some nonlinear function, it would be a rare case that $g(\hat{\theta})$ is unbia... | Ratio of Unbiased Estimators | No, it will not be unbiased (unless the estimator of the denominator have zero variance.) And it will not help if the numerator and denominator are independent. In general, if $\hat{\theta}$ is an un | Ratio of Unbiased Estimators
No, it will not be unbiased (unless the estimator of the denominator have zero variance.) And it will not help if the numerator and denominator are independent. In general, if $\hat{\theta}$ is an unbiased estimator of $\theta$ and $g$ is some nonlinear function, it would be a rare case th... | Ratio of Unbiased Estimators
No, it will not be unbiased (unless the estimator of the denominator have zero variance.) And it will not help if the numerator and denominator are independent. In general, if $\hat{\theta}$ is an un |
49,750 | Which is the right way to handle imbalanced data in a regression problem? | If I have understood you correctly, the issue here is that you wish to fit your regression in such a way that it performs equally well on both cities, by which you means that you want to minimise the weighted sum-of-squares, with weights that ensure equal total weight to the data from each city. If that is correct, th... | Which is the right way to handle imbalanced data in a regression problem? | If I have understood you correctly, the issue here is that you wish to fit your regression in such a way that it performs equally well on both cities, by which you means that you want to minimise the | Which is the right way to handle imbalanced data in a regression problem?
If I have understood you correctly, the issue here is that you wish to fit your regression in such a way that it performs equally well on both cities, by which you means that you want to minimise the weighted sum-of-squares, with weights that ens... | Which is the right way to handle imbalanced data in a regression problem?
If I have understood you correctly, the issue here is that you wish to fit your regression in such a way that it performs equally well on both cities, by which you means that you want to minimise the |
49,751 | Frequentist vs. Bayesian bias-variance decomposition | Yes, your analysis is correct. For $l_2$, the optimal estimator in the Bayesian setting will always the posterior mean $\left\langle \theta\right\rangle _{p\left(\theta\mid x\right)}$. In the case of absolute loss we would have the posterior median and in the discrete case of constant loss we would have the posterior m... | Frequentist vs. Bayesian bias-variance decomposition | Yes, your analysis is correct. For $l_2$, the optimal estimator in the Bayesian setting will always the posterior mean $\left\langle \theta\right\rangle _{p\left(\theta\mid x\right)}$. In the case of | Frequentist vs. Bayesian bias-variance decomposition
Yes, your analysis is correct. For $l_2$, the optimal estimator in the Bayesian setting will always the posterior mean $\left\langle \theta\right\rangle _{p\left(\theta\mid x\right)}$. In the case of absolute loss we would have the posterior median and in the discret... | Frequentist vs. Bayesian bias-variance decomposition
Yes, your analysis is correct. For $l_2$, the optimal estimator in the Bayesian setting will always the posterior mean $\left\langle \theta\right\rangle _{p\left(\theta\mid x\right)}$. In the case of |
49,752 | Is the Quadratic Approximation of Log-Likelihood Equivalent to the Normal Approximation of the MLE? | How can I show this is the case?
Since you have full specification of the sampling distribution of your observations, you can get the explicit form of the log-likelihood. Treating $\sigma$ as fixed and removing additive constants we have:
$$\ell_\mathbf{x}(\theta) = -\frac{1}{2 \sigma^2} \sum_{i=1}^n (x_i - \theta)^2... | Is the Quadratic Approximation of Log-Likelihood Equivalent to the Normal Approximation of the MLE? | How can I show this is the case?
Since you have full specification of the sampling distribution of your observations, you can get the explicit form of the log-likelihood. Treating $\sigma$ as fixed | Is the Quadratic Approximation of Log-Likelihood Equivalent to the Normal Approximation of the MLE?
How can I show this is the case?
Since you have full specification of the sampling distribution of your observations, you can get the explicit form of the log-likelihood. Treating $\sigma$ as fixed and removing additiv... | Is the Quadratic Approximation of Log-Likelihood Equivalent to the Normal Approximation of the MLE?
How can I show this is the case?
Since you have full specification of the sampling distribution of your observations, you can get the explicit form of the log-likelihood. Treating $\sigma$ as fixed |
49,753 | Calculating confidence intervals of marginal means in linear mixed models | I have just checked your example (using the just released version 0.8.0 of ggeffects), however, instead of using effect() or emmeans() directly, I use the functions from ggeffects, which actually wrap around these functions (ggeffect() and ggemmeans()).
## effect
c4 <- ggeffect(fit, terms = term)
c4 <- c4[,4:5]
## emm... | Calculating confidence intervals of marginal means in linear mixed models | I have just checked your example (using the just released version 0.8.0 of ggeffects), however, instead of using effect() or emmeans() directly, I use the functions from ggeffects, which actually wrap | Calculating confidence intervals of marginal means in linear mixed models
I have just checked your example (using the just released version 0.8.0 of ggeffects), however, instead of using effect() or emmeans() directly, I use the functions from ggeffects, which actually wrap around these functions (ggeffect() and ggemme... | Calculating confidence intervals of marginal means in linear mixed models
I have just checked your example (using the just released version 0.8.0 of ggeffects), however, instead of using effect() or emmeans() directly, I use the functions from ggeffects, which actually wrap |
49,754 | What is Dimension of basis in splines | The easiest way of thinking of a basis is like the building blocks or the set of prototypes used to create something more complex. So when we are setting $k$ to a low number we indirectly force a relatively simple overall shape.
Putting the notion of thing plate regression splines aside for a moment, one of the most tr... | What is Dimension of basis in splines | The easiest way of thinking of a basis is like the building blocks or the set of prototypes used to create something more complex. So when we are setting $k$ to a low number we indirectly force a rela | What is Dimension of basis in splines
The easiest way of thinking of a basis is like the building blocks or the set of prototypes used to create something more complex. So when we are setting $k$ to a low number we indirectly force a relatively simple overall shape.
Putting the notion of thing plate regression splines ... | What is Dimension of basis in splines
The easiest way of thinking of a basis is like the building blocks or the set of prototypes used to create something more complex. So when we are setting $k$ to a low number we indirectly force a rela |
49,755 | What is Dimension of basis in splines | The dimension of the basis is the number of basis function in the basis.
Typically, k reflects how many basis functions are created initially, but identifiability constraints may lower the number of basis functions per smooth that are actually used to fit the model.
k sets some upper limit on the number of basis functi... | What is Dimension of basis in splines | The dimension of the basis is the number of basis function in the basis.
Typically, k reflects how many basis functions are created initially, but identifiability constraints may lower the number of b | What is Dimension of basis in splines
The dimension of the basis is the number of basis function in the basis.
Typically, k reflects how many basis functions are created initially, but identifiability constraints may lower the number of basis functions per smooth that are actually used to fit the model.
k sets some upp... | What is Dimension of basis in splines
The dimension of the basis is the number of basis function in the basis.
Typically, k reflects how many basis functions are created initially, but identifiability constraints may lower the number of b |
49,756 | Does cross validation say anything about parsimony? | First of all, I agree with @HEITZ: if all we have is equal cross validation performance, then that's all we have and it does not allow further distinction. Also, one model may be just as badly underfit as the other is overfit...
As usual, this is where external (independent) knowledge about the situation at hand helps ... | Does cross validation say anything about parsimony? | First of all, I agree with @HEITZ: if all we have is equal cross validation performance, then that's all we have and it does not allow further distinction. Also, one model may be just as badly underfi | Does cross validation say anything about parsimony?
First of all, I agree with @HEITZ: if all we have is equal cross validation performance, then that's all we have and it does not allow further distinction. Also, one model may be just as badly underfit as the other is overfit...
As usual, this is where external (indep... | Does cross validation say anything about parsimony?
First of all, I agree with @HEITZ: if all we have is equal cross validation performance, then that's all we have and it does not allow further distinction. Also, one model may be just as badly underfi |
49,757 | Does cross validation say anything about parsimony? | In the absence of a controlled experiment, it is impossible to favor one of two models with equivalent fit, if parsimony is disregarded. It may be more interesting to interpret the more complex model, but that is story telling. From an agnostic point of view, both yield the same picture of reality. | Does cross validation say anything about parsimony? | In the absence of a controlled experiment, it is impossible to favor one of two models with equivalent fit, if parsimony is disregarded. It may be more interesting to interpret the more complex model, | Does cross validation say anything about parsimony?
In the absence of a controlled experiment, it is impossible to favor one of two models with equivalent fit, if parsimony is disregarded. It may be more interesting to interpret the more complex model, but that is story telling. From an agnostic point of view, both yie... | Does cross validation say anything about parsimony?
In the absence of a controlled experiment, it is impossible to favor one of two models with equivalent fit, if parsimony is disregarded. It may be more interesting to interpret the more complex model, |
49,758 | Two-sample t-test with one the samples having only 1 element? | Here is an example of a two sample t test of $H_0: \mu_1 = \mu_2$ against
$H_1: \mu_1 \ne \mu_2.$ As you specify, the first sample consists of five
observations from a normal distribution and the second sample has only one
observation from a normal distribution with a different mean (and the same
variance). [Simulation... | Two-sample t-test with one the samples having only 1 element? | Here is an example of a two sample t test of $H_0: \mu_1 = \mu_2$ against
$H_1: \mu_1 \ne \mu_2.$ As you specify, the first sample consists of five
observations from a normal distribution and the seco | Two-sample t-test with one the samples having only 1 element?
Here is an example of a two sample t test of $H_0: \mu_1 = \mu_2$ against
$H_1: \mu_1 \ne \mu_2.$ As you specify, the first sample consists of five
observations from a normal distribution and the second sample has only one
observation from a normal distribut... | Two-sample t-test with one the samples having only 1 element?
Here is an example of a two sample t test of $H_0: \mu_1 = \mu_2$ against
$H_1: \mu_1 \ne \mu_2.$ As you specify, the first sample consists of five
observations from a normal distribution and the seco |
49,759 | Finding MLE of $p$ where $X_1\sim\text{Bernoulli}(p)$ and $X_2\sim\text{Bernoulli}(3p)$ | We have
$$\frac{\partial^2\mathscr{L}}{\partial p^2}=-\frac{x_1}{p^2}-\frac{1-x_1}{(1-p)^2}-\frac{x_2}{p^2}-\frac{9(1-x_2)}{(1-3p)^2}$$
which is clearly negative for any $p\in[0,1/3]$ so $\hat{p}$ is a global maximum. | Finding MLE of $p$ where $X_1\sim\text{Bernoulli}(p)$ and $X_2\sim\text{Bernoulli}(3p)$ | We have
$$\frac{\partial^2\mathscr{L}}{\partial p^2}=-\frac{x_1}{p^2}-\frac{1-x_1}{(1-p)^2}-\frac{x_2}{p^2}-\frac{9(1-x_2)}{(1-3p)^2}$$
which is clearly negative for any $p\in[0,1/3]$ so $\hat{p}$ is | Finding MLE of $p$ where $X_1\sim\text{Bernoulli}(p)$ and $X_2\sim\text{Bernoulli}(3p)$
We have
$$\frac{\partial^2\mathscr{L}}{\partial p^2}=-\frac{x_1}{p^2}-\frac{1-x_1}{(1-p)^2}-\frac{x_2}{p^2}-\frac{9(1-x_2)}{(1-3p)^2}$$
which is clearly negative for any $p\in[0,1/3]$ so $\hat{p}$ is a global maximum. | Finding MLE of $p$ where $X_1\sim\text{Bernoulli}(p)$ and $X_2\sim\text{Bernoulli}(3p)$
We have
$$\frac{\partial^2\mathscr{L}}{\partial p^2}=-\frac{x_1}{p^2}-\frac{1-x_1}{(1-p)^2}-\frac{x_2}{p^2}-\frac{9(1-x_2)}{(1-3p)^2}$$
which is clearly negative for any $p\in[0,1/3]$ so $\hat{p}$ is |
49,760 | Finding MLE of $p$ where $X_1\sim\text{Bernoulli}(p)$ and $X_2\sim\text{Bernoulli}(3p)$ | Though your final answer is correct, I think the derivation of the MLE is much more simpler.
Given $x_1,x_2$, the likelihood function is
\begin{align}
L(p\mid x_1,x_2)&=3^{x_2}p^{x_1+x_2}(1-p)^{1-x_1}(1-3p)^{1-x_2}\mathbf1_{x_1,x_2\in\{0,1\}}
\\&=\begin{cases}3p(1-p)&,\text{ if }x_1=0,x_2=1
\\ p(1-3p)&,\text{ if }x_1=1... | Finding MLE of $p$ where $X_1\sim\text{Bernoulli}(p)$ and $X_2\sim\text{Bernoulli}(3p)$ | Though your final answer is correct, I think the derivation of the MLE is much more simpler.
Given $x_1,x_2$, the likelihood function is
\begin{align}
L(p\mid x_1,x_2)&=3^{x_2}p^{x_1+x_2}(1-p)^{1-x_1} | Finding MLE of $p$ where $X_1\sim\text{Bernoulli}(p)$ and $X_2\sim\text{Bernoulli}(3p)$
Though your final answer is correct, I think the derivation of the MLE is much more simpler.
Given $x_1,x_2$, the likelihood function is
\begin{align}
L(p\mid x_1,x_2)&=3^{x_2}p^{x_1+x_2}(1-p)^{1-x_1}(1-3p)^{1-x_2}\mathbf1_{x_1,x_2\... | Finding MLE of $p$ where $X_1\sim\text{Bernoulli}(p)$ and $X_2\sim\text{Bernoulli}(3p)$
Though your final answer is correct, I think the derivation of the MLE is much more simpler.
Given $x_1,x_2$, the likelihood function is
\begin{align}
L(p\mid x_1,x_2)&=3^{x_2}p^{x_1+x_2}(1-p)^{1-x_1} |
49,761 | Difference of notation between cross entropy and joint entropy | Note that this notation for cross-entropy is non-standard. The normal notation is H(p,q). This notation is horrible for two reasons. Firstly, the exact same notation is also used for joint entropy. Secondly, it makes it seem like cross-entropy is symmetric. This is ridiculous, and I’ll be writing Hq(p) instead.
Refere... | Difference of notation between cross entropy and joint entropy | Note that this notation for cross-entropy is non-standard. The normal notation is H(p,q). This notation is horrible for two reasons. Firstly, the exact same notation is also used for joint entropy. Se | Difference of notation between cross entropy and joint entropy
Note that this notation for cross-entropy is non-standard. The normal notation is H(p,q). This notation is horrible for two reasons. Firstly, the exact same notation is also used for joint entropy. Secondly, it makes it seem like cross-entropy is symmetric.... | Difference of notation between cross entropy and joint entropy
Note that this notation for cross-entropy is non-standard. The normal notation is H(p,q). This notation is horrible for two reasons. Firstly, the exact same notation is also used for joint entropy. Se |
49,762 | What to do if time series are non-stationary? [closed] | Take a look at my comments What "more" does differencing (d>0) do in ARIMA than detrend? suggesting alternative approaches ( best suggested by the data ) to evidented non-stationarity symptoms. Classicly differencing is more approptraite for stock market data.
Often times power transforms like logs are attempted to de... | What to do if time series are non-stationary? [closed] | Take a look at my comments What "more" does differencing (d>0) do in ARIMA than detrend? suggesting alternative approaches ( best suggested by the data ) to evidented non-stationarity symptoms. Class | What to do if time series are non-stationary? [closed]
Take a look at my comments What "more" does differencing (d>0) do in ARIMA than detrend? suggesting alternative approaches ( best suggested by the data ) to evidented non-stationarity symptoms. Classicly differencing is more approptraite for stock market data.
Oft... | What to do if time series are non-stationary? [closed]
Take a look at my comments What "more" does differencing (d>0) do in ARIMA than detrend? suggesting alternative approaches ( best suggested by the data ) to evidented non-stationarity symptoms. Class |
49,763 | What to do if time series are non-stationary? [closed] | We actually do not need statistics itself to look at stationarity, and the first test for that is common sense. There is no stationarity because there are external factors that have a major influence on the data. For example, the market crash of Sept. 29, 2008 (in gray in the figure below), and the Dow Jones Industrial... | What to do if time series are non-stationary? [closed] | We actually do not need statistics itself to look at stationarity, and the first test for that is common sense. There is no stationarity because there are external factors that have a major influence | What to do if time series are non-stationary? [closed]
We actually do not need statistics itself to look at stationarity, and the first test for that is common sense. There is no stationarity because there are external factors that have a major influence on the data. For example, the market crash of Sept. 29, 2008 (in ... | What to do if time series are non-stationary? [closed]
We actually do not need statistics itself to look at stationarity, and the first test for that is common sense. There is no stationarity because there are external factors that have a major influence |
49,764 | Why does bagging increase bias? | In principle bagging is performed to reduce variance of fitted values as it increases the stability of the fitted values. In addition, as a rule of thumb I would say that: "the magnitudes of the bias are roughly the same for the bagged and the original procedure" (Bühlmann & Yu, 2002). That is because bagging allows... | Why does bagging increase bias? | In principle bagging is performed to reduce variance of fitted values as it increases the stability of the fitted values. In addition, as a rule of thumb I would say that: "the magnitudes of the bi | Why does bagging increase bias?
In principle bagging is performed to reduce variance of fitted values as it increases the stability of the fitted values. In addition, as a rule of thumb I would say that: "the magnitudes of the bias are roughly the same for the bagged and the original procedure" (Bühlmann & Yu, 2002)... | Why does bagging increase bias?
In principle bagging is performed to reduce variance of fitted values as it increases the stability of the fitted values. In addition, as a rule of thumb I would say that: "the magnitudes of the bi |
49,765 | Is a single neuron in a Neural Network a GLM? | GLM (generalized linear model) are "general" in the sense, that they can use any kind of transformation on the results of the linear combination. So GLMs don't necessary have the form $y=e^{\theta^T*x}$. They just have the form $y=f(\theta^T*x)$ where $f$ is almost any monotonous and differentiable function (link funct... | Is a single neuron in a Neural Network a GLM? | GLM (generalized linear model) are "general" in the sense, that they can use any kind of transformation on the results of the linear combination. So GLMs don't necessary have the form $y=e^{\theta^T*x | Is a single neuron in a Neural Network a GLM?
GLM (generalized linear model) are "general" in the sense, that they can use any kind of transformation on the results of the linear combination. So GLMs don't necessary have the form $y=e^{\theta^T*x}$. They just have the form $y=f(\theta^T*x)$ where $f$ is almost any mono... | Is a single neuron in a Neural Network a GLM?
GLM (generalized linear model) are "general" in the sense, that they can use any kind of transformation on the results of the linear combination. So GLMs don't necessary have the form $y=e^{\theta^T*x |
49,766 | What are models for count data where the variance is not related to the sample size? | One attractive class of models is obtained by discretizing any non-negative random variable $X.$ Let $X$ be in a distribution family $\mathcal{F}.$ Let $\alpha\gt 0$ be a number and set
$$Y = \lfloor X/\alpha \rfloor.$$
This is the process of "binning" by assigning $X$ to one of the intervals $[0,\alpha),$ $[\alpha,... | What are models for count data where the variance is not related to the sample size? | One attractive class of models is obtained by discretizing any non-negative random variable $X.$ Let $X$ be in a distribution family $\mathcal{F}.$ Let $\alpha\gt 0$ be a number and set
$$Y = \lflo | What are models for count data where the variance is not related to the sample size?
One attractive class of models is obtained by discretizing any non-negative random variable $X.$ Let $X$ be in a distribution family $\mathcal{F}.$ Let $\alpha\gt 0$ be a number and set
$$Y = \lfloor X/\alpha \rfloor.$$
This is the ... | What are models for count data where the variance is not related to the sample size?
One attractive class of models is obtained by discretizing any non-negative random variable $X.$ Let $X$ be in a distribution family $\mathcal{F}.$ Let $\alpha\gt 0$ be a number and set
$$Y = \lflo |
49,767 | Train on balanced datasets, used for imbalanced datasets? | You can definitely train a model on an imbalanced dataset, however this often leads to deteriorated performance. Personally, I always do this so that I can measure the effect of applying SMOTE or related techniques.
In many cases, the minority class has too few representative samples to accurately model it leading to p... | Train on balanced datasets, used for imbalanced datasets? | You can definitely train a model on an imbalanced dataset, however this often leads to deteriorated performance. Personally, I always do this so that I can measure the effect of applying SMOTE or rela | Train on balanced datasets, used for imbalanced datasets?
You can definitely train a model on an imbalanced dataset, however this often leads to deteriorated performance. Personally, I always do this so that I can measure the effect of applying SMOTE or related techniques.
In many cases, the minority class has too few ... | Train on balanced datasets, used for imbalanced datasets?
You can definitely train a model on an imbalanced dataset, however this often leads to deteriorated performance. Personally, I always do this so that I can measure the effect of applying SMOTE or rela |
49,768 | Applications of ARCH models | At least, we have the original paper of Engle (1982, Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation), which includes an application that looks at the variance of UK inflation.
The ARCH(p) model, but more often a GARCH(1,1) model, is used as a benchmark in many ... | Applications of ARCH models | At least, we have the original paper of Engle (1982, Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation), which includes an application that looks | Applications of ARCH models
At least, we have the original paper of Engle (1982, Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation), which includes an application that looks at the variance of UK inflation.
The ARCH(p) model, but more often a GARCH(1,1) model, is ... | Applications of ARCH models
At least, we have the original paper of Engle (1982, Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation), which includes an application that looks |
49,769 | Applications of ARCH models | Introduction to (Generalized) Autoregressive
Conditional Heteroskedasticity Models in Time Series
Econometrics (Wong, 2014) is a good introduction to ARCH/GARCH models. | Applications of ARCH models | Introduction to (Generalized) Autoregressive
Conditional Heteroskedasticity Models in Time Series
Econometrics (Wong, 2014) is a good introduction to ARCH/GARCH models. | Applications of ARCH models
Introduction to (Generalized) Autoregressive
Conditional Heteroskedasticity Models in Time Series
Econometrics (Wong, 2014) is a good introduction to ARCH/GARCH models. | Applications of ARCH models
Introduction to (Generalized) Autoregressive
Conditional Heteroskedasticity Models in Time Series
Econometrics (Wong, 2014) is a good introduction to ARCH/GARCH models. |
49,770 | How many natural parameters are really in the exponential family conjugate prior? | It is a correct remark that a conjugate family of priors for an exponential family of distributions with a two-dimensional parameter $(\theta_1,\theta_2)$ can be defined by three parameters and hence that for a Normal family of distributions
$$f(x|\theta_1,\theta_2)\propto
\exp\left\{\frac{-x^2}{2\theta_2}+\frac{x\thet... | How many natural parameters are really in the exponential family conjugate prior? | It is a correct remark that a conjugate family of priors for an exponential family of distributions with a two-dimensional parameter $(\theta_1,\theta_2)$ can be defined by three parameters and hence | How many natural parameters are really in the exponential family conjugate prior?
It is a correct remark that a conjugate family of priors for an exponential family of distributions with a two-dimensional parameter $(\theta_1,\theta_2)$ can be defined by three parameters and hence that for a Normal family of distributi... | How many natural parameters are really in the exponential family conjugate prior?
It is a correct remark that a conjugate family of priors for an exponential family of distributions with a two-dimensional parameter $(\theta_1,\theta_2)$ can be defined by three parameters and hence |
49,771 | Reinforcement Learning split in training and test set necessary? | The split in training, including all optimization of models might be helpful and it is worth to use best practices in general supervised machine learning.
On the other hand, the ultimate measure of quality in Reinforcement Learning is the discounted reward. To quantify the quality, you shall run several episodes after ... | Reinforcement Learning split in training and test set necessary? | The split in training, including all optimization of models might be helpful and it is worth to use best practices in general supervised machine learning.
On the other hand, the ultimate measure of qu | Reinforcement Learning split in training and test set necessary?
The split in training, including all optimization of models might be helpful and it is worth to use best practices in general supervised machine learning.
On the other hand, the ultimate measure of quality in Reinforcement Learning is the discounted rewar... | Reinforcement Learning split in training and test set necessary?
The split in training, including all optimization of models might be helpful and it is worth to use best practices in general supervised machine learning.
On the other hand, the ultimate measure of qu |
49,772 | How to constrain gradient boosting predictions to be non-negative? | One way is to transform your data in such a way that negative values of your "real" variable are impossible. For instance, suppose you have a response variable Y. Define W(Y) = log(Y), then do a regression with W as your response variable. The take your predicted values, and exponentiate them to get back to Y. It's pos... | How to constrain gradient boosting predictions to be non-negative? | One way is to transform your data in such a way that negative values of your "real" variable are impossible. For instance, suppose you have a response variable Y. Define W(Y) = log(Y), then do a regre | How to constrain gradient boosting predictions to be non-negative?
One way is to transform your data in such a way that negative values of your "real" variable are impossible. For instance, suppose you have a response variable Y. Define W(Y) = log(Y), then do a regression with W as your response variable. The take your... | How to constrain gradient boosting predictions to be non-negative?
One way is to transform your data in such a way that negative values of your "real" variable are impossible. For instance, suppose you have a response variable Y. Define W(Y) = log(Y), then do a regre |
49,773 | What is the distribution of min{0,X} when X follows some general normal distribution? | Suppose $X\sim N(\mu, \sigma^2)$ with CDF $\Phi(\cdot; \mu, \sigma^2)$. Then you can calculate the probability $p$ that $X>0$, by taking
$$ p = 1- \Phi(0; \mu, \sigma^2) $$
Then $Y:=\min\{0,X\}$ is a mixture between
a point mass at $0$ with weight $p$
and a truncated normal distribution with parameters $\mu$ and $\si... | What is the distribution of min{0,X} when X follows some general normal distribution? | Suppose $X\sim N(\mu, \sigma^2)$ with CDF $\Phi(\cdot; \mu, \sigma^2)$. Then you can calculate the probability $p$ that $X>0$, by taking
$$ p = 1- \Phi(0; \mu, \sigma^2) $$
Then $Y:=\min\{0,X\}$ is a | What is the distribution of min{0,X} when X follows some general normal distribution?
Suppose $X\sim N(\mu, \sigma^2)$ with CDF $\Phi(\cdot; \mu, \sigma^2)$. Then you can calculate the probability $p$ that $X>0$, by taking
$$ p = 1- \Phi(0; \mu, \sigma^2) $$
Then $Y:=\min\{0,X\}$ is a mixture between
a point mass at ... | What is the distribution of min{0,X} when X follows some general normal distribution?
Suppose $X\sim N(\mu, \sigma^2)$ with CDF $\Phi(\cdot; \mu, \sigma^2)$. Then you can calculate the probability $p$ that $X>0$, by taking
$$ p = 1- \Phi(0; \mu, \sigma^2) $$
Then $Y:=\min\{0,X\}$ is a |
49,774 | What is the distribution of min{0,X} when X follows some general normal distribution? | We have a simple answer for the distribution of $\min(0,X)$ for any random variable $X$ in terms of its distribution function.
Suppose $Y=\min(0,X)$. That is, $$Y=\begin{cases}X&,\text{ if }X\le 0\\0&,\text{ if }X>0\end{cases}$$
Trivially, a plot of $y=\min(0,x)$ for real $x$ would look like
Then distribution function... | What is the distribution of min{0,X} when X follows some general normal distribution? | We have a simple answer for the distribution of $\min(0,X)$ for any random variable $X$ in terms of its distribution function.
Suppose $Y=\min(0,X)$. That is, $$Y=\begin{cases}X&,\text{ if }X\le 0\\0& | What is the distribution of min{0,X} when X follows some general normal distribution?
We have a simple answer for the distribution of $\min(0,X)$ for any random variable $X$ in terms of its distribution function.
Suppose $Y=\min(0,X)$. That is, $$Y=\begin{cases}X&,\text{ if }X\le 0\\0&,\text{ if }X>0\end{cases}$$
Trivi... | What is the distribution of min{0,X} when X follows some general normal distribution?
We have a simple answer for the distribution of $\min(0,X)$ for any random variable $X$ in terms of its distribution function.
Suppose $Y=\min(0,X)$. That is, $$Y=\begin{cases}X&,\text{ if }X\le 0\\0& |
49,775 | Suitable distance metric for time-series clustering with respect to location of shapes | Minor point, DTW is not a metric, just a measure.
The measure you need is constrained DTW (or cDTW),
With enough data you can learn the constraint, but here is it clear it should be about 1/3 the length of the time series.
This tutorial will tell you all you need to know
http://www.cs.unm.edu/~mueen/DTW.pdf
eamonn | Suitable distance metric for time-series clustering with respect to location of shapes | Minor point, DTW is not a metric, just a measure.
The measure you need is constrained DTW (or cDTW),
With enough data you can learn the constraint, but here is it clear it should be about 1/3 the leng | Suitable distance metric for time-series clustering with respect to location of shapes
Minor point, DTW is not a metric, just a measure.
The measure you need is constrained DTW (or cDTW),
With enough data you can learn the constraint, but here is it clear it should be about 1/3 the length of the time series.
This tutor... | Suitable distance metric for time-series clustering with respect to location of shapes
Minor point, DTW is not a metric, just a measure.
The measure you need is constrained DTW (or cDTW),
With enough data you can learn the constraint, but here is it clear it should be about 1/3 the leng |
49,776 | Difference between NA and None in biological dataset | You are dealing with a situation where you have variables (distance to log, diameter of nearest log) that only have meaning in the presence of a previous variable condition (log is present). You can deal with this by coding your variables so that the conditional variables are set to zero if there is no log present, so... | Difference between NA and None in biological dataset | You are dealing with a situation where you have variables (distance to log, diameter of nearest log) that only have meaning in the presence of a previous variable condition (log is present). You can | Difference between NA and None in biological dataset
You are dealing with a situation where you have variables (distance to log, diameter of nearest log) that only have meaning in the presence of a previous variable condition (log is present). You can deal with this by coding your variables so that the conditional var... | Difference between NA and None in biological dataset
You are dealing with a situation where you have variables (distance to log, diameter of nearest log) that only have meaning in the presence of a previous variable condition (log is present). You can |
49,777 | Joint raw moments of multivariate normal | To close this one, as whuber's comment pointed out, let a multivariate distribution be symmetric in the sense
$$(X_1, \ldots, X_m) \sim_d (-X_1, \ldots, -X_m)$$
Suppose also that moments exist. Then
$$E[X_1^{r_1}\cdot ... \cdot X^{r_m}_m] = E[(-X_1)^{r_1}\cdot ... \cdot (-X_m)^{r_m}]$$
$$\implies E[X_1^{r_1}\cdot ... ... | Joint raw moments of multivariate normal | To close this one, as whuber's comment pointed out, let a multivariate distribution be symmetric in the sense
$$(X_1, \ldots, X_m) \sim_d (-X_1, \ldots, -X_m)$$
Suppose also that moments exist. Then
| Joint raw moments of multivariate normal
To close this one, as whuber's comment pointed out, let a multivariate distribution be symmetric in the sense
$$(X_1, \ldots, X_m) \sim_d (-X_1, \ldots, -X_m)$$
Suppose also that moments exist. Then
$$E[X_1^{r_1}\cdot ... \cdot X^{r_m}_m] = E[(-X_1)^{r_1}\cdot ... \cdot (-X_m)^... | Joint raw moments of multivariate normal
To close this one, as whuber's comment pointed out, let a multivariate distribution be symmetric in the sense
$$(X_1, \ldots, X_m) \sim_d (-X_1, \ldots, -X_m)$$
Suppose also that moments exist. Then
|
49,778 | How to find out if two time series correlated? they are of not equal length and with unknown delay between cause and effect, irregular log time? | Before tackling correlation of measurement values, it may be worthwhile to explore the correlation of measurement presence. In other words, there may be information to extract from measurement co-occurence. For instance, it is possible that you measure temperature more often when you eat sweets. If you discover it is t... | How to find out if two time series correlated? they are of not equal length and with unknown delay b | Before tackling correlation of measurement values, it may be worthwhile to explore the correlation of measurement presence. In other words, there may be information to extract from measurement co-occu | How to find out if two time series correlated? they are of not equal length and with unknown delay between cause and effect, irregular log time?
Before tackling correlation of measurement values, it may be worthwhile to explore the correlation of measurement presence. In other words, there may be information to extract... | How to find out if two time series correlated? they are of not equal length and with unknown delay b
Before tackling correlation of measurement values, it may be worthwhile to explore the correlation of measurement presence. In other words, there may be information to extract from measurement co-occu |
49,779 | How to find out if two time series correlated? they are of not equal length and with unknown delay between cause and effect, irregular log time? | You're interested in Granger causality. As for missing data, this will prove costly if you try to use Granger causality, as it uses linear regression (which is quite sensitive to missing data).
You can try inputting the mean temperature to replace the missing values, but this comes with its own issues -- for more on th... | How to find out if two time series correlated? they are of not equal length and with unknown delay b | You're interested in Granger causality. As for missing data, this will prove costly if you try to use Granger causality, as it uses linear regression (which is quite sensitive to missing data).
You ca | How to find out if two time series correlated? they are of not equal length and with unknown delay between cause and effect, irregular log time?
You're interested in Granger causality. As for missing data, this will prove costly if you try to use Granger causality, as it uses linear regression (which is quite sensitive... | How to find out if two time series correlated? they are of not equal length and with unknown delay b
You're interested in Granger causality. As for missing data, this will prove costly if you try to use Granger causality, as it uses linear regression (which is quite sensitive to missing data).
You ca |
49,780 | Bootstrap yielding counterintuitive results (Update: but not anymore) | I think the bootstrap is not wrong. What's wrong is the test statistic you're using. The residual sum of squares is calculated using internal validation. The GAM is overfitting the curve. Polynomials approximations obtained from least squares are known to fit relatively badly in the tails, which is actually where a rea... | Bootstrap yielding counterintuitive results (Update: but not anymore) | I think the bootstrap is not wrong. What's wrong is the test statistic you're using. The residual sum of squares is calculated using internal validation. The GAM is overfitting the curve. Polynomials | Bootstrap yielding counterintuitive results (Update: but not anymore)
I think the bootstrap is not wrong. What's wrong is the test statistic you're using. The residual sum of squares is calculated using internal validation. The GAM is overfitting the curve. Polynomials approximations obtained from least squares are kno... | Bootstrap yielding counterintuitive results (Update: but not anymore)
I think the bootstrap is not wrong. What's wrong is the test statistic you're using. The residual sum of squares is calculated using internal validation. The GAM is overfitting the curve. Polynomials |
49,781 | Coefficient of determination invariant to centering and rescaling of variables | Denote
$$\tilde{y}=\frac{y-\bar{y}}{\sigma_y}=\frac{Hy}{\sigma_y}$$ and
$$\tilde{X}=HX\Sigma_x$$
the scaled variables (other than the scaled constant, which is evidently zero and drops out), where $H=I-\iota\iota'/n$ denotes the demeaning matrix and $\Sigma_x$ is a diagonal matrix with $1/\sigma_{x_j}$ on the main diag... | Coefficient of determination invariant to centering and rescaling of variables | Denote
$$\tilde{y}=\frac{y-\bar{y}}{\sigma_y}=\frac{Hy}{\sigma_y}$$ and
$$\tilde{X}=HX\Sigma_x$$
the scaled variables (other than the scaled constant, which is evidently zero and drops out), where $H= | Coefficient of determination invariant to centering and rescaling of variables
Denote
$$\tilde{y}=\frac{y-\bar{y}}{\sigma_y}=\frac{Hy}{\sigma_y}$$ and
$$\tilde{X}=HX\Sigma_x$$
the scaled variables (other than the scaled constant, which is evidently zero and drops out), where $H=I-\iota\iota'/n$ denotes the demeaning ma... | Coefficient of determination invariant to centering and rescaling of variables
Denote
$$\tilde{y}=\frac{y-\bar{y}}{\sigma_y}=\frac{Hy}{\sigma_y}$$ and
$$\tilde{X}=HX\Sigma_x$$
the scaled variables (other than the scaled constant, which is evidently zero and drops out), where $H= |
49,782 | Cohen's d from a linear regression model | In your regression model, $c_1$ (an unstandardized regression coefficient for a 0/1 indicator variable) is an adjusted mean difference, adjusting for the other variables in the model. As such, you can use $c_1$ as the numerator in the Cohen's $d$ computation, such as:
$$ d = \frac{B}{s_{pooled}} ~, $$
where $B$ is the... | Cohen's d from a linear regression model | In your regression model, $c_1$ (an unstandardized regression coefficient for a 0/1 indicator variable) is an adjusted mean difference, adjusting for the other variables in the model. As such, you can | Cohen's d from a linear regression model
In your regression model, $c_1$ (an unstandardized regression coefficient for a 0/1 indicator variable) is an adjusted mean difference, adjusting for the other variables in the model. As such, you can use $c_1$ as the numerator in the Cohen's $d$ computation, such as:
$$ d = \f... | Cohen's d from a linear regression model
In your regression model, $c_1$ (an unstandardized regression coefficient for a 0/1 indicator variable) is an adjusted mean difference, adjusting for the other variables in the model. As such, you can |
49,783 | Cohen's d from a linear regression model | So if you aren't making an statistical arguments, what needs to "hold"? Are you asking if it accurately measures the effect of $c_1$ when controlling for other variables? Probably not, since in its standard formulation Cohen's $d$ is the mean difference normalized by an estimate of the pooled variance. On the other han... | Cohen's d from a linear regression model | So if you aren't making an statistical arguments, what needs to "hold"? Are you asking if it accurately measures the effect of $c_1$ when controlling for other variables? Probably not, since in its st | Cohen's d from a linear regression model
So if you aren't making an statistical arguments, what needs to "hold"? Are you asking if it accurately measures the effect of $c_1$ when controlling for other variables? Probably not, since in its standard formulation Cohen's $d$ is the mean difference normalized by an estimate... | Cohen's d from a linear regression model
So if you aren't making an statistical arguments, what needs to "hold"? Are you asking if it accurately measures the effect of $c_1$ when controlling for other variables? Probably not, since in its st |
49,784 | Rupees from Bushes in Majora's Mask, what distribution to use? | So I contacted an old Statistics professor I had in college about this problem, and he pointed me to the Multinomial distribution, the exact solution to solving for the odds of getting any specific count of each drop type.
I used the Multinomial function in the form of
N! / (n1! * n2! * n3! *n4!) * (p1^n1 * p2^n2 * p3^... | Rupees from Bushes in Majora's Mask, what distribution to use? | So I contacted an old Statistics professor I had in college about this problem, and he pointed me to the Multinomial distribution, the exact solution to solving for the odds of getting any specific co | Rupees from Bushes in Majora's Mask, what distribution to use?
So I contacted an old Statistics professor I had in college about this problem, and he pointed me to the Multinomial distribution, the exact solution to solving for the odds of getting any specific count of each drop type.
I used the Multinomial function in... | Rupees from Bushes in Majora's Mask, what distribution to use?
So I contacted an old Statistics professor I had in college about this problem, and he pointed me to the Multinomial distribution, the exact solution to solving for the odds of getting any specific co |
49,785 | Rupees from Bushes in Majora's Mask, what distribution to use? | You can compute an exact distribution by using a repeated convolution.
Here is an example with r code:
n = 10
### a vector of probabilities for the number of rupees
p = rep(0,n*5+5+1)
p[1+c(0,1,3,5)] = c(11,3,1,1)/16
### loop some number of times for the number of shrubs
for (i in 2:n) {
p_new = p*0
### go throu... | Rupees from Bushes in Majora's Mask, what distribution to use? | You can compute an exact distribution by using a repeated convolution.
Here is an example with r code:
n = 10
### a vector of probabilities for the number of rupees
p = rep(0,n*5+5+1)
p[1+c(0,1,3,5)] | Rupees from Bushes in Majora's Mask, what distribution to use?
You can compute an exact distribution by using a repeated convolution.
Here is an example with r code:
n = 10
### a vector of probabilities for the number of rupees
p = rep(0,n*5+5+1)
p[1+c(0,1,3,5)] = c(11,3,1,1)/16
### loop some number of times for the... | Rupees from Bushes in Majora's Mask, what distribution to use?
You can compute an exact distribution by using a repeated convolution.
Here is an example with r code:
n = 10
### a vector of probabilities for the number of rupees
p = rep(0,n*5+5+1)
p[1+c(0,1,3,5)] |
49,786 | Stopping rules in group sequential designs | What's the point of having a futility hypothesis?
Government regulations and medical ethics affect the design of medical studies and govern the conduct of clinical trials by describing good clinical practices (GCPs) for studies with both human and non-human animal subjects.
Examples and supporting quotes from the arti... | Stopping rules in group sequential designs | What's the point of having a futility hypothesis?
Government regulations and medical ethics affect the design of medical studies and govern the conduct of clinical trials by describing good clinical | Stopping rules in group sequential designs
What's the point of having a futility hypothesis?
Government regulations and medical ethics affect the design of medical studies and govern the conduct of clinical trials by describing good clinical practices (GCPs) for studies with both human and non-human animal subjects.
E... | Stopping rules in group sequential designs
What's the point of having a futility hypothesis?
Government regulations and medical ethics affect the design of medical studies and govern the conduct of clinical trials by describing good clinical |
49,787 | Trying to implement the Jensen-Shannon Divergence for Multivariate Gaussians | Actually, using the answer in https://stackoverflow.com/questions/26079881/kl-divergence-of-two-gmms (and the fact, that the author factored out the 1/2 from the logarithm, made the montecarlo approximation sample from both distributions to average the result), I would say, that the symmetrized numerical code for jense... | Trying to implement the Jensen-Shannon Divergence for Multivariate Gaussians | Actually, using the answer in https://stackoverflow.com/questions/26079881/kl-divergence-of-two-gmms (and the fact, that the author factored out the 1/2 from the logarithm, made the montecarlo approxi | Trying to implement the Jensen-Shannon Divergence for Multivariate Gaussians
Actually, using the answer in https://stackoverflow.com/questions/26079881/kl-divergence-of-two-gmms (and the fact, that the author factored out the 1/2 from the logarithm, made the montecarlo approximation sample from both distributions to av... | Trying to implement the Jensen-Shannon Divergence for Multivariate Gaussians
Actually, using the answer in https://stackoverflow.com/questions/26079881/kl-divergence-of-two-gmms (and the fact, that the author factored out the 1/2 from the logarithm, made the montecarlo approxi |
49,788 | What is the appropriate zero-correlation parameter model for factors in lmer? | SUMMARY: What is the most appropriate zero-correlation model, depends on the data. There is no universally correct choice.
I will consider the same Machines data set. It has several Workers, each repeatedly tested on all of the three Machines. The maximal mixed model is thus
lmer(score ~ 1 + Machine + (0 + Machine | W... | What is the appropriate zero-correlation parameter model for factors in lmer? | SUMMARY: What is the most appropriate zero-correlation model, depends on the data. There is no universally correct choice.
I will consider the same Machines data set. It has several Workers, each rep | What is the appropriate zero-correlation parameter model for factors in lmer?
SUMMARY: What is the most appropriate zero-correlation model, depends on the data. There is no universally correct choice.
I will consider the same Machines data set. It has several Workers, each repeatedly tested on all of the three Machine... | What is the appropriate zero-correlation parameter model for factors in lmer?
SUMMARY: What is the most appropriate zero-correlation model, depends on the data. There is no universally correct choice.
I will consider the same Machines data set. It has several Workers, each rep |
49,789 | $R^2$ of a regression predicting noise | As per this question, we have
$$R^2 \sim Beta\left (\frac {p-1}{2}, \frac {n-p}{2}\right)$$
in view of your assumption of error normality (the result that the regressors are also multivariate normal would not be necessary).
The answers there also show that the mode of this distribution (you might of course also want to... | $R^2$ of a regression predicting noise | As per this question, we have
$$R^2 \sim Beta\left (\frac {p-1}{2}, \frac {n-p}{2}\right)$$
in view of your assumption of error normality (the result that the regressors are also multivariate normal w | $R^2$ of a regression predicting noise
As per this question, we have
$$R^2 \sim Beta\left (\frac {p-1}{2}, \frac {n-p}{2}\right)$$
in view of your assumption of error normality (the result that the regressors are also multivariate normal would not be necessary).
The answers there also show that the mode of this distrib... | $R^2$ of a regression predicting noise
As per this question, we have
$$R^2 \sim Beta\left (\frac {p-1}{2}, \frac {n-p}{2}\right)$$
in view of your assumption of error normality (the result that the regressors are also multivariate normal w |
49,790 | Questions on Bayesian Softmax Regression [closed] | Logistic regression models probability of success $\mathbb{P}(Y=1 \mid X)$, and uses a Bernoulli likelihood function
$$
Y \sim \mathcal{B}\big(g^{-1}(X\beta)\big)
$$
and, most often, a logistic link function $g^{-1}$. For more then two categories, we use categorical distribution and multinomial regression (recall that ... | Questions on Bayesian Softmax Regression [closed] | Logistic regression models probability of success $\mathbb{P}(Y=1 \mid X)$, and uses a Bernoulli likelihood function
$$
Y \sim \mathcal{B}\big(g^{-1}(X\beta)\big)
$$
and, most often, a logistic link f | Questions on Bayesian Softmax Regression [closed]
Logistic regression models probability of success $\mathbb{P}(Y=1 \mid X)$, and uses a Bernoulli likelihood function
$$
Y \sim \mathcal{B}\big(g^{-1}(X\beta)\big)
$$
and, most often, a logistic link function $g^{-1}$. For more then two categories, we use categorical dis... | Questions on Bayesian Softmax Regression [closed]
Logistic regression models probability of success $\mathbb{P}(Y=1 \mid X)$, and uses a Bernoulli likelihood function
$$
Y \sim \mathcal{B}\big(g^{-1}(X\beta)\big)
$$
and, most often, a logistic link f |
49,791 | Derivatives of features | The first derivative is often referred to as delta MFCC, and second derivative as delta-delta MFCC. The same concepts can also be applied to melspectrograms.
The derivatives of the MFCC models changes, how much variation there is between frames (per filter band). A constant sound would have a high summarized mean MFCC... | Derivatives of features | The first derivative is often referred to as delta MFCC, and second derivative as delta-delta MFCC. The same concepts can also be applied to melspectrograms.
The derivatives of the MFCC models changes | Derivatives of features
The first derivative is often referred to as delta MFCC, and second derivative as delta-delta MFCC. The same concepts can also be applied to melspectrograms.
The derivatives of the MFCC models changes, how much variation there is between frames (per filter band). A constant sound would have a h... | Derivatives of features
The first derivative is often referred to as delta MFCC, and second derivative as delta-delta MFCC. The same concepts can also be applied to melspectrograms.
The derivatives of the MFCC models changes |
49,792 | GANS: Using Discriminator for prediction | The reason why this approach does not work is that at the end of the training, the discriminator converges to a state when both real and generated data are classified with the same probability, i.e. the discriminator is unable to distinguish between them. Consider the opposite: if the discriminator could still distingu... | GANS: Using Discriminator for prediction | The reason why this approach does not work is that at the end of the training, the discriminator converges to a state when both real and generated data are classified with the same probability, i.e. t | GANS: Using Discriminator for prediction
The reason why this approach does not work is that at the end of the training, the discriminator converges to a state when both real and generated data are classified with the same probability, i.e. the discriminator is unable to distinguish between them. Consider the opposite: ... | GANS: Using Discriminator for prediction
The reason why this approach does not work is that at the end of the training, the discriminator converges to a state when both real and generated data are classified with the same probability, i.e. t |
49,793 | GANS: Using Discriminator for prediction | I have a different opinion than above and I think you got misunderstood. I believe it is possible.
Training of GAN is done when the generator fool the discriminator. The Generator is useless at this point and can be used as a generator of synthetic data - there are already papers on this topic https://iopscience.iop.or... | GANS: Using Discriminator for prediction | I have a different opinion than above and I think you got misunderstood. I believe it is possible.
Training of GAN is done when the generator fool the discriminator. The Generator is useless at this p | GANS: Using Discriminator for prediction
I have a different opinion than above and I think you got misunderstood. I believe it is possible.
Training of GAN is done when the generator fool the discriminator. The Generator is useless at this point and can be used as a generator of synthetic data - there are already paper... | GANS: Using Discriminator for prediction
I have a different opinion than above and I think you got misunderstood. I believe it is possible.
Training of GAN is done when the generator fool the discriminator. The Generator is useless at this p |
49,794 | How to calculate the confidence that a trend in a time-series is positive? | The data you describe is what might be considered summary statistics. Whether somebody likes apples can be considered a binary outcome (1 = likes apples, 0 = doesn't like apples). Therefore, if you survey 10,000 people over 6 years then you have 60,000 responses measuring the binary outcome of whether each individual l... | How to calculate the confidence that a trend in a time-series is positive? | The data you describe is what might be considered summary statistics. Whether somebody likes apples can be considered a binary outcome (1 = likes apples, 0 = doesn't like apples). Therefore, if you su | How to calculate the confidence that a trend in a time-series is positive?
The data you describe is what might be considered summary statistics. Whether somebody likes apples can be considered a binary outcome (1 = likes apples, 0 = doesn't like apples). Therefore, if you survey 10,000 people over 6 years then you have... | How to calculate the confidence that a trend in a time-series is positive?
The data you describe is what might be considered summary statistics. Whether somebody likes apples can be considered a binary outcome (1 = likes apples, 0 = doesn't like apples). Therefore, if you su |
49,795 | How to calculate the confidence that a trend in a time-series is positive? | I suggest you take a quick look at hypothesis testing concepts if you already had not done it for understanding what is meant by confidence. In hypothesis testing, you make the distinction that your observed sample is a realization of your data generating process and is susceptible to random deviations from the exact f... | How to calculate the confidence that a trend in a time-series is positive? | I suggest you take a quick look at hypothesis testing concepts if you already had not done it for understanding what is meant by confidence. In hypothesis testing, you make the distinction that your o | How to calculate the confidence that a trend in a time-series is positive?
I suggest you take a quick look at hypothesis testing concepts if you already had not done it for understanding what is meant by confidence. In hypothesis testing, you make the distinction that your observed sample is a realization of your data ... | How to calculate the confidence that a trend in a time-series is positive?
I suggest you take a quick look at hypothesis testing concepts if you already had not done it for understanding what is meant by confidence. In hypothesis testing, you make the distinction that your o |
49,796 | How to calculate the confidence that a trend in a time-series is positive? | A more data-driven analysis i.e. less presumptive of the form of the model... detecting the presence of a level shift and NO TREND ... this uses 3 parameters rather than two which was used in the simple and presumptive trend model in time.
leading to the detection of a pulse at 2016
enter image description here
In... | How to calculate the confidence that a trend in a time-series is positive? | A more data-driven analysis i.e. less presumptive of the form of the model... detecting the presence of a level shift and NO TREND ... this uses 3 parameters rather than two which was used in the simp | How to calculate the confidence that a trend in a time-series is positive?
A more data-driven analysis i.e. less presumptive of the form of the model... detecting the presence of a level shift and NO TREND ... this uses 3 parameters rather than two which was used in the simple and presumptive trend model in time.
lead... | How to calculate the confidence that a trend in a time-series is positive?
A more data-driven analysis i.e. less presumptive of the form of the model... detecting the presence of a level shift and NO TREND ... this uses 3 parameters rather than two which was used in the simp |
49,797 | Levene's test assumptions | Levene's test is just a $t$-test of the absolute values of the deviations of the data from their group means. (If you have more than 2 groups, you use the ANOVA; you can also use Brown-Forsythe version of the test, which takes the absolute values of the deviations from the group medians instead.)
At any rate, it is... | Levene's test assumptions | Levene's test is just a $t$-test of the absolute values of the deviations of the data from their group means. (If you have more than 2 groups, you use the ANOVA; you can also use Brown-Forsythe vers | Levene's test assumptions
Levene's test is just a $t$-test of the absolute values of the deviations of the data from their group means. (If you have more than 2 groups, you use the ANOVA; you can also use Brown-Forsythe version of the test, which takes the absolute values of the deviations from the group medians inst... | Levene's test assumptions
Levene's test is just a $t$-test of the absolute values of the deviations of the data from their group means. (If you have more than 2 groups, you use the ANOVA; you can also use Brown-Forsythe vers |
49,798 | Proof that the Hotelling T$^2$ statistic is invariant under the choice of contrast matrices | To test the null hypothesis $H_{0}\!:\mu_{1}=\mu_{2}=\ldots=\mu_{q}$ via Hotelling's one-sample $T^2$ statistic, $\mathbf{C} \in \mathbb R^{(q-1) \times q}$ can't be an arbitrary matrix with $\mathbf{C}\mathbf1=\mathbf{0}$. It certainly must have $q-1$ linearly independent rows and can be a matrix $\mathbf{C}=\mathbf{A... | Proof that the Hotelling T$^2$ statistic is invariant under the choice of contrast matrices | To test the null hypothesis $H_{0}\!:\mu_{1}=\mu_{2}=\ldots=\mu_{q}$ via Hotelling's one-sample $T^2$ statistic, $\mathbf{C} \in \mathbb R^{(q-1) \times q}$ can't be an arbitrary matrix with $\mathbf{ | Proof that the Hotelling T$^2$ statistic is invariant under the choice of contrast matrices
To test the null hypothesis $H_{0}\!:\mu_{1}=\mu_{2}=\ldots=\mu_{q}$ via Hotelling's one-sample $T^2$ statistic, $\mathbf{C} \in \mathbb R^{(q-1) \times q}$ can't be an arbitrary matrix with $\mathbf{C}\mathbf1=\mathbf{0}$. It c... | Proof that the Hotelling T$^2$ statistic is invariant under the choice of contrast matrices
To test the null hypothesis $H_{0}\!:\mu_{1}=\mu_{2}=\ldots=\mu_{q}$ via Hotelling's one-sample $T^2$ statistic, $\mathbf{C} \in \mathbb R^{(q-1) \times q}$ can't be an arbitrary matrix with $\mathbf{ |
49,799 | How to choose a correlation measure when Pearson is close to 1 and Spearman close to -1? | Your last graph—$y$ vs $x$—provides the insight:
Pearson's correlation coefficient is an inappropriate measure of association here, because your data are not linearly associated, which violates a fundamental assumption of Pearson's measure.
Spearman's correlation coefficient is also inappropriate, because your data a... | How to choose a correlation measure when Pearson is close to 1 and Spearman close to -1? | Your last graph—$y$ vs $x$—provides the insight:
Pearson's correlation coefficient is an inappropriate measure of association here, because your data are not linearly associated, which violates a fun | How to choose a correlation measure when Pearson is close to 1 and Spearman close to -1?
Your last graph—$y$ vs $x$—provides the insight:
Pearson's correlation coefficient is an inappropriate measure of association here, because your data are not linearly associated, which violates a fundamental assumption of Pearson'... | How to choose a correlation measure when Pearson is close to 1 and Spearman close to -1?
Your last graph—$y$ vs $x$—provides the insight:
Pearson's correlation coefficient is an inappropriate measure of association here, because your data are not linearly associated, which violates a fun |
49,800 | Exact details of how word2vec (Skip-gram and CBOW) generate input word pairs | I did more research and found answers:
1. Why is downsampling used in the skip-gram case?
Quote from its paper,
We found that increasing the range improves quality of the resulting word vectors, but it also increases the computational complexity. Since the more distant words are usually less related to the current wo... | Exact details of how word2vec (Skip-gram and CBOW) generate input word pairs | I did more research and found answers:
1. Why is downsampling used in the skip-gram case?
Quote from its paper,
We found that increasing the range improves quality of the resulting word vectors, but | Exact details of how word2vec (Skip-gram and CBOW) generate input word pairs
I did more research and found answers:
1. Why is downsampling used in the skip-gram case?
Quote from its paper,
We found that increasing the range improves quality of the resulting word vectors, but it also increases the computational comple... | Exact details of how word2vec (Skip-gram and CBOW) generate input word pairs
I did more research and found answers:
1. Why is downsampling used in the skip-gram case?
Quote from its paper,
We found that increasing the range improves quality of the resulting word vectors, but |
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