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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50,001 | State space model with regression effects | The way this is done, is to first establish the relationship between $\alpha_{t}$ and $\alpha_{t}^{\ast}$ and proceed from there. We take the initial state equations above and take
$$\alpha_{t}^{\ast} = \mathsf{T}_{t}^{-1}\mathsf{W}_{t}\beta + \alpha_{t},$$
we see that we can write
$$\alpha_{t + 1}^{\ast} = \mathsf{T}... | State space model with regression effects | The way this is done, is to first establish the relationship between $\alpha_{t}$ and $\alpha_{t}^{\ast}$ and proceed from there. We take the initial state equations above and take
$$\alpha_{t}^{\ast} | State space model with regression effects
The way this is done, is to first establish the relationship between $\alpha_{t}$ and $\alpha_{t}^{\ast}$ and proceed from there. We take the initial state equations above and take
$$\alpha_{t}^{\ast} = \mathsf{T}_{t}^{-1}\mathsf{W}_{t}\beta + \alpha_{t},$$
we see that we can w... | State space model with regression effects
The way this is done, is to first establish the relationship between $\alpha_{t}$ and $\alpha_{t}^{\ast}$ and proceed from there. We take the initial state equations above and take
$$\alpha_{t}^{\ast} |
50,002 | multi stage binomial "process" | From $$\mathbb{E}[s^{X_1}]=(sp+q)^K$$
(where $q=1-p$), it is rather straightforward to show that
$$\mathbb{E}[s^{X_1+\ldots+X_\ell}]=\left\{s(1-q^\ell)+q^\ell\right\}^K$$ Indeed, if we assume it holds for a given $\ell$ (and it does for $\ell=1$), then
\begin{align*}\mathbb{E}[s^{X_1+\ldots+X_{\ell+1}}]&=\mathbb{E}[\m... | multi stage binomial "process" | From $$\mathbb{E}[s^{X_1}]=(sp+q)^K$$
(where $q=1-p$), it is rather straightforward to show that
$$\mathbb{E}[s^{X_1+\ldots+X_\ell}]=\left\{s(1-q^\ell)+q^\ell\right\}^K$$ Indeed, if we assume it holds | multi stage binomial "process"
From $$\mathbb{E}[s^{X_1}]=(sp+q)^K$$
(where $q=1-p$), it is rather straightforward to show that
$$\mathbb{E}[s^{X_1+\ldots+X_\ell}]=\left\{s(1-q^\ell)+q^\ell\right\}^K$$ Indeed, if we assume it holds for a given $\ell$ (and it does for $\ell=1$), then
\begin{align*}\mathbb{E}[s^{X_1+\ld... | multi stage binomial "process"
From $$\mathbb{E}[s^{X_1}]=(sp+q)^K$$
(where $q=1-p$), it is rather straightforward to show that
$$\mathbb{E}[s^{X_1+\ldots+X_\ell}]=\left\{s(1-q^\ell)+q^\ell\right\}^K$$ Indeed, if we assume it holds |
50,003 | Linear regression VS linear modeling | Comment made into an answer per suggestion of gung.
Linear modeling can have meanings, outside Statistics, well beyond the Wikipedia entry Linear Model in whuber's comment above. For instance, Linear Programming https://en.wikipedia.org/wiki/Linear_programming is the minimization or maximization of a linear function of... | Linear regression VS linear modeling | Comment made into an answer per suggestion of gung.
Linear modeling can have meanings, outside Statistics, well beyond the Wikipedia entry Linear Model in whuber's comment above. For instance, Linear | Linear regression VS linear modeling
Comment made into an answer per suggestion of gung.
Linear modeling can have meanings, outside Statistics, well beyond the Wikipedia entry Linear Model in whuber's comment above. For instance, Linear Programming https://en.wikipedia.org/wiki/Linear_programming is the minimization or... | Linear regression VS linear modeling
Comment made into an answer per suggestion of gung.
Linear modeling can have meanings, outside Statistics, well beyond the Wikipedia entry Linear Model in whuber's comment above. For instance, Linear |
50,004 | Linear regression VS linear modeling | From my point of view, linear regression is one kind of linear modeling. Thus, this modeling can refer to a full rank model (regression) or to a model not of full rank (experimental designs, for example). Modeling is a more general term, with several applications. | Linear regression VS linear modeling | From my point of view, linear regression is one kind of linear modeling. Thus, this modeling can refer to a full rank model (regression) or to a model not of full rank (experimental designs, for examp | Linear regression VS linear modeling
From my point of view, linear regression is one kind of linear modeling. Thus, this modeling can refer to a full rank model (regression) or to a model not of full rank (experimental designs, for example). Modeling is a more general term, with several applications. | Linear regression VS linear modeling
From my point of view, linear regression is one kind of linear modeling. Thus, this modeling can refer to a full rank model (regression) or to a model not of full rank (experimental designs, for examp |
50,005 | Linear regression VS linear modeling | My impression is that the term linear regression (especially linear regression 'analysis') is used more often to explain relations while modeling is used more often in context of predictions and predictive models. | Linear regression VS linear modeling | My impression is that the term linear regression (especially linear regression 'analysis') is used more often to explain relations while modeling is used more often in context of predictions and predi | Linear regression VS linear modeling
My impression is that the term linear regression (especially linear regression 'analysis') is used more often to explain relations while modeling is used more often in context of predictions and predictive models. | Linear regression VS linear modeling
My impression is that the term linear regression (especially linear regression 'analysis') is used more often to explain relations while modeling is used more often in context of predictions and predi |
50,006 | What are some good references on how probability theory got mathematically rigorous? | I don't know if this counts as an answer, or just a comment (moderators please!), but I believe one should look to the works of Anders Hald.
A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935 2007 Springer
A History of Probability and Statistics and Their Applications before 1750 (2003) ... | What are some good references on how probability theory got mathematically rigorous? | I don't know if this counts as an answer, or just a comment (moderators please!), but I believe one should look to the works of Anders Hald.
A History of Parametric Statistical Inference from Bernoull | What are some good references on how probability theory got mathematically rigorous?
I don't know if this counts as an answer, or just a comment (moderators please!), but I believe one should look to the works of Anders Hald.
A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935 2007 Springe... | What are some good references on how probability theory got mathematically rigorous?
I don't know if this counts as an answer, or just a comment (moderators please!), but I believe one should look to the works of Anders Hald.
A History of Parametric Statistical Inference from Bernoull |
50,007 | Is it possible to have a case where $D'$ is zero but Logistic Regression is still able to classify accurately? | Your intuition is correct: such an example is impossible.
To see why not, consider both $M_1$ and $M_2$ as collections of $p$-vectors. Because the predicted value of any vector in a logistic regression is a linear function, perfect prediction means there exists a codimension-$1$ affine hyperspace that separates all th... | Is it possible to have a case where $D'$ is zero but Logistic Regression is still able to classify a | Your intuition is correct: such an example is impossible.
To see why not, consider both $M_1$ and $M_2$ as collections of $p$-vectors. Because the predicted value of any vector in a logistic regressi | Is it possible to have a case where $D'$ is zero but Logistic Regression is still able to classify accurately?
Your intuition is correct: such an example is impossible.
To see why not, consider both $M_1$ and $M_2$ as collections of $p$-vectors. Because the predicted value of any vector in a logistic regression is a l... | Is it possible to have a case where $D'$ is zero but Logistic Regression is still able to classify a
Your intuition is correct: such an example is impossible.
To see why not, consider both $M_1$ and $M_2$ as collections of $p$-vectors. Because the predicted value of any vector in a logistic regressi |
50,008 | group fixed-effects, not individual-fixed effects using plm in R | I have worked on similar projects and am confronting one right now. The way that we handle this is to put in a fixed effect for each village and then to cluster the standard errors by village. This is not a perfect solution, but is fairly standard practice.
The plm package in R and xtreg ..., fe command in Stata, and t... | group fixed-effects, not individual-fixed effects using plm in R | I have worked on similar projects and am confronting one right now. The way that we handle this is to put in a fixed effect for each village and then to cluster the standard errors by village. This is | group fixed-effects, not individual-fixed effects using plm in R
I have worked on similar projects and am confronting one right now. The way that we handle this is to put in a fixed effect for each village and then to cluster the standard errors by village. This is not a perfect solution, but is fairly standard practic... | group fixed-effects, not individual-fixed effects using plm in R
I have worked on similar projects and am confronting one right now. The way that we handle this is to put in a fixed effect for each village and then to cluster the standard errors by village. This is |
50,009 | What is the difference between the M5 regression model tree and the Cubist method for regression? | As you mentioned, in the documentation for cubist here, they state that it is an extension to M5 model. The specifications seems to be overlapping with description of M5 model that you have mentioned above. In caret documentation, they specify M5, M5Rules and cubist as M5 (RWeka) Models here.
I guess M5 is RWeka packa... | What is the difference between the M5 regression model tree and the Cubist method for regression? | As you mentioned, in the documentation for cubist here, they state that it is an extension to M5 model. The specifications seems to be overlapping with description of M5 model that you have mentioned | What is the difference between the M5 regression model tree and the Cubist method for regression?
As you mentioned, in the documentation for cubist here, they state that it is an extension to M5 model. The specifications seems to be overlapping with description of M5 model that you have mentioned above. In caret docume... | What is the difference between the M5 regression model tree and the Cubist method for regression?
As you mentioned, in the documentation for cubist here, they state that it is an extension to M5 model. The specifications seems to be overlapping with description of M5 model that you have mentioned |
50,010 | What is the difference between the M5 regression model tree and the Cubist method for regression? | From what I have understood, in the cubist algorithm a linear model is made per decision node, and that model is then extended each node further down the tree. This should result in a more continuous predicted value whereas M5P might suffer from discontinuities when jumping from one leaf node to the other by crossing a... | What is the difference between the M5 regression model tree and the Cubist method for regression? | From what I have understood, in the cubist algorithm a linear model is made per decision node, and that model is then extended each node further down the tree. This should result in a more continuous | What is the difference between the M5 regression model tree and the Cubist method for regression?
From what I have understood, in the cubist algorithm a linear model is made per decision node, and that model is then extended each node further down the tree. This should result in a more continuous predicted value wherea... | What is the difference between the M5 regression model tree and the Cubist method for regression?
From what I have understood, in the cubist algorithm a linear model is made per decision node, and that model is then extended each node further down the tree. This should result in a more continuous |
50,011 | How to determine overlap of two empirical distribution based on quantiles? | Because you will be doing this for $\binom{10}{2}=45$ pairs of distributions, you will want a reasonably efficient method.
The question asks to solve (at least approximately) an equation of the form $G_0(\alpha)-G_1(1-\alpha)=0$ where the $G_i$ are the inverse empirical CDFs. Equivalently, you could solve $F_0(z)+F_1(z... | How to determine overlap of two empirical distribution based on quantiles? | Because you will be doing this for $\binom{10}{2}=45$ pairs of distributions, you will want a reasonably efficient method.
The question asks to solve (at least approximately) an equation of the form $ | How to determine overlap of two empirical distribution based on quantiles?
Because you will be doing this for $\binom{10}{2}=45$ pairs of distributions, you will want a reasonably efficient method.
The question asks to solve (at least approximately) an equation of the form $G_0(\alpha)-G_1(1-\alpha)=0$ where the $G_i$ ... | How to determine overlap of two empirical distribution based on quantiles?
Because you will be doing this for $\binom{10}{2}=45$ pairs of distributions, you will want a reasonably efficient method.
The question asks to solve (at least approximately) an equation of the form $ |
50,012 | How to determine overlap of two empirical distribution based on quantiles? | I hit upon the idea of using the empirical cumulative distribution function. The answer is approximate to any desired degree of significant digits. Here is what I've come up with:
CDF.intersect<-function(a, b){
#a and b are vectors of the same metric, intent is to find cdf
if(median(a) < median(b)){
Fn1<-ecdf(a)
Fn... | How to determine overlap of two empirical distribution based on quantiles? | I hit upon the idea of using the empirical cumulative distribution function. The answer is approximate to any desired degree of significant digits. Here is what I've come up with:
CDF.intersect<-funct | How to determine overlap of two empirical distribution based on quantiles?
I hit upon the idea of using the empirical cumulative distribution function. The answer is approximate to any desired degree of significant digits. Here is what I've come up with:
CDF.intersect<-function(a, b){
#a and b are vectors of the same m... | How to determine overlap of two empirical distribution based on quantiles?
I hit upon the idea of using the empirical cumulative distribution function. The answer is approximate to any desired degree of significant digits. Here is what I've come up with:
CDF.intersect<-funct |
50,013 | Maximizing likelihood versus MCMC sampling: Comparing Parameters and Deviance | Imagine that your posterior is somewhat Gaussian. The expectation of the squared euclidean norm of the best of $N$ draw depends on the dimension $d$ and is asymptotically $O(1/N^{2/d})$, but the average remains $O(1/N)$. As soon as you have more than 2 dimensions, the average converges faster. You have $d=4$ so the ave... | Maximizing likelihood versus MCMC sampling: Comparing Parameters and Deviance | Imagine that your posterior is somewhat Gaussian. The expectation of the squared euclidean norm of the best of $N$ draw depends on the dimension $d$ and is asymptotically $O(1/N^{2/d})$, but the avera | Maximizing likelihood versus MCMC sampling: Comparing Parameters and Deviance
Imagine that your posterior is somewhat Gaussian. The expectation of the squared euclidean norm of the best of $N$ draw depends on the dimension $d$ and is asymptotically $O(1/N^{2/d})$, but the average remains $O(1/N)$. As soon as you have m... | Maximizing likelihood versus MCMC sampling: Comparing Parameters and Deviance
Imagine that your posterior is somewhat Gaussian. The expectation of the squared euclidean norm of the best of $N$ draw depends on the dimension $d$ and is asymptotically $O(1/N^{2/d})$, but the avera |
50,014 | Assuming a probability density for MLE to do model selection | Motivation: I am trying to use Akaike Information Criterion to assess model ranking and over-fitting risk for a set of nonlinear models.
As I understand it, I must compute the maximum likelihood estimator for each model.
If you want an AIC, yes, you would need MLE. But the AIC is not automatically ideal. [One thing yo... | Assuming a probability density for MLE to do model selection | Motivation: I am trying to use Akaike Information Criterion to assess model ranking and over-fitting risk for a set of nonlinear models.
As I understand it, I must compute the maximum likelihood estim | Assuming a probability density for MLE to do model selection
Motivation: I am trying to use Akaike Information Criterion to assess model ranking and over-fitting risk for a set of nonlinear models.
As I understand it, I must compute the maximum likelihood estimator for each model.
If you want an AIC, yes, you would ne... | Assuming a probability density for MLE to do model selection
Motivation: I am trying to use Akaike Information Criterion to assess model ranking and over-fitting risk for a set of nonlinear models.
As I understand it, I must compute the maximum likelihood estim |
50,015 | On the Autocorrelation Matrix of an ARMA(2,2) to derive the Yule Walker Equations | Let's define a general ARMA model of orders $(p,q)$ as follows:
$$
\psi_t \equiv \sum_{i=0}^p \alpha_i\, y_{t-i} = \sum_{i=0}^q \theta_i\, \epsilon_{t-i} \,,
\mbox{ with } \epsilon_t \sim NID\,(0, \sigma^2_\epsilon) \,.
$$
where $\alpha_0$ and $\theta_0$ are normalised to $1$.
You can check that multiplying $\psi_t$ by... | On the Autocorrelation Matrix of an ARMA(2,2) to derive the Yule Walker Equations | Let's define a general ARMA model of orders $(p,q)$ as follows:
$$
\psi_t \equiv \sum_{i=0}^p \alpha_i\, y_{t-i} = \sum_{i=0}^q \theta_i\, \epsilon_{t-i} \,,
\mbox{ with } \epsilon_t \sim NID\,(0, \si | On the Autocorrelation Matrix of an ARMA(2,2) to derive the Yule Walker Equations
Let's define a general ARMA model of orders $(p,q)$ as follows:
$$
\psi_t \equiv \sum_{i=0}^p \alpha_i\, y_{t-i} = \sum_{i=0}^q \theta_i\, \epsilon_{t-i} \,,
\mbox{ with } \epsilon_t \sim NID\,(0, \sigma^2_\epsilon) \,.
$$
where $\alpha_0... | On the Autocorrelation Matrix of an ARMA(2,2) to derive the Yule Walker Equations
Let's define a general ARMA model of orders $(p,q)$ as follows:
$$
\psi_t \equiv \sum_{i=0}^p \alpha_i\, y_{t-i} = \sum_{i=0}^q \theta_i\, \epsilon_{t-i} \,,
\mbox{ with } \epsilon_t \sim NID\,(0, \si |
50,016 | Fitting two different mixture distributions [closed] | I would recommend using the flexmix package. You can see in the page 9 of the vignette here: https://cran.r-project.org/web/packages/flexmix/vignettes/flexmix-intro.pdf.
If you wanted, for example, a mixture of a poisson and a normal distribution, you'd want something like:
example <- flexmix(y~1, data=dat, k=2,
... | Fitting two different mixture distributions [closed] | I would recommend using the flexmix package. You can see in the page 9 of the vignette here: https://cran.r-project.org/web/packages/flexmix/vignettes/flexmix-intro.pdf.
If you wanted, for example, a | Fitting two different mixture distributions [closed]
I would recommend using the flexmix package. You can see in the page 9 of the vignette here: https://cran.r-project.org/web/packages/flexmix/vignettes/flexmix-intro.pdf.
If you wanted, for example, a mixture of a poisson and a normal distribution, you'd want somethin... | Fitting two different mixture distributions [closed]
I would recommend using the flexmix package. You can see in the page 9 of the vignette here: https://cran.r-project.org/web/packages/flexmix/vignettes/flexmix-intro.pdf.
If you wanted, for example, a |
50,017 | Estimating standard error of parameters of linear model fitted using gradient descent | I found that bootstrap gives estimates that are pretty close to those from OLS, but works with literally any training algorithm.
Bootstrap is a kind of Monte Carlo method and roughly boils down to repeated sampling with replacement from original dataset and collecting values of a target statistic. Having a set of stat... | Estimating standard error of parameters of linear model fitted using gradient descent | I found that bootstrap gives estimates that are pretty close to those from OLS, but works with literally any training algorithm.
Bootstrap is a kind of Monte Carlo method and roughly boils down to re | Estimating standard error of parameters of linear model fitted using gradient descent
I found that bootstrap gives estimates that are pretty close to those from OLS, but works with literally any training algorithm.
Bootstrap is a kind of Monte Carlo method and roughly boils down to repeated sampling with replacement f... | Estimating standard error of parameters of linear model fitted using gradient descent
I found that bootstrap gives estimates that are pretty close to those from OLS, but works with literally any training algorithm.
Bootstrap is a kind of Monte Carlo method and roughly boils down to re |
50,018 | Regression with t-distributed errors and MASS::rlm | It looks to me like you can supply your own psi function.
The already-supplied psi-functions are just simple functions (try MASS:::psi.huber and MASS:::psi.hampel for example). They're rather neatly set up in that the same function supplies both the psi function and its derivative, depending on whether they're called ... | Regression with t-distributed errors and MASS::rlm | It looks to me like you can supply your own psi function.
The already-supplied psi-functions are just simple functions (try MASS:::psi.huber and MASS:::psi.hampel for example). They're rather neatly | Regression with t-distributed errors and MASS::rlm
It looks to me like you can supply your own psi function.
The already-supplied psi-functions are just simple functions (try MASS:::psi.huber and MASS:::psi.hampel for example). They're rather neatly set up in that the same function supplies both the psi function and i... | Regression with t-distributed errors and MASS::rlm
It looks to me like you can supply your own psi function.
The already-supplied psi-functions are just simple functions (try MASS:::psi.huber and MASS:::psi.hampel for example). They're rather neatly |
50,019 | Log-rank / Cox analysis with very unequal sized groups: alternative calculations of p-value? | In these kinds of comparisons, you'll find that what happens is a two-sample test becomes very approximately a one sample test where all the power comes from the smaller group (they are being "calibrated" to the larger group), and so the assumptions behind sample sizes in 1 sample tests apply for that group. 3 deaths d... | Log-rank / Cox analysis with very unequal sized groups: alternative calculations of p-value? | In these kinds of comparisons, you'll find that what happens is a two-sample test becomes very approximately a one sample test where all the power comes from the smaller group (they are being "calibra | Log-rank / Cox analysis with very unequal sized groups: alternative calculations of p-value?
In these kinds of comparisons, you'll find that what happens is a two-sample test becomes very approximately a one sample test where all the power comes from the smaller group (they are being "calibrated" to the larger group), ... | Log-rank / Cox analysis with very unequal sized groups: alternative calculations of p-value?
In these kinds of comparisons, you'll find that what happens is a two-sample test becomes very approximately a one sample test where all the power comes from the smaller group (they are being "calibra |
50,020 | Log-rank / Cox analysis with very unequal sized groups: alternative calculations of p-value? | Do not pay too much attention to the p-values. They just provide a probability that you might accidentally have found a survival difference in your particular study sample when there really isn't a difference in the population as a whole.
You evidently want to use predictor variables for each new patient to classify re... | Log-rank / Cox analysis with very unequal sized groups: alternative calculations of p-value? | Do not pay too much attention to the p-values. They just provide a probability that you might accidentally have found a survival difference in your particular study sample when there really isn't a di | Log-rank / Cox analysis with very unequal sized groups: alternative calculations of p-value?
Do not pay too much attention to the p-values. They just provide a probability that you might accidentally have found a survival difference in your particular study sample when there really isn't a difference in the population ... | Log-rank / Cox analysis with very unequal sized groups: alternative calculations of p-value?
Do not pay too much attention to the p-values. They just provide a probability that you might accidentally have found a survival difference in your particular study sample when there really isn't a di |
50,021 | Difference-in-differences with no pre-treatment? | The issue I see with your approach is that you will not be able to see anything about the pre-treatment differences unless you have very precise information about the experiment or policy. It will be hard or even impossible to say something about the common trend assumption between the treatment and control groups whic... | Difference-in-differences with no pre-treatment? | The issue I see with your approach is that you will not be able to see anything about the pre-treatment differences unless you have very precise information about the experiment or policy. It will be | Difference-in-differences with no pre-treatment?
The issue I see with your approach is that you will not be able to see anything about the pre-treatment differences unless you have very precise information about the experiment or policy. It will be hard or even impossible to say something about the common trend assumpt... | Difference-in-differences with no pre-treatment?
The issue I see with your approach is that you will not be able to see anything about the pre-treatment differences unless you have very precise information about the experiment or policy. It will be |
50,022 | Gaussian Mixture Model parameters from density | You can use minimum squared errors in order to estimate/fit a mixture density to your data (Note that this method also inherits problems of uniqueness of the estimators, as any other approach in the context of finite mixtures).
Basically, the idea is to minimize the distances between a mixture density (with fixed numbe... | Gaussian Mixture Model parameters from density | You can use minimum squared errors in order to estimate/fit a mixture density to your data (Note that this method also inherits problems of uniqueness of the estimators, as any other approach in the c | Gaussian Mixture Model parameters from density
You can use minimum squared errors in order to estimate/fit a mixture density to your data (Note that this method also inherits problems of uniqueness of the estimators, as any other approach in the context of finite mixtures).
Basically, the idea is to minimize the distan... | Gaussian Mixture Model parameters from density
You can use minimum squared errors in order to estimate/fit a mixture density to your data (Note that this method also inherits problems of uniqueness of the estimators, as any other approach in the c |
50,023 | Gaussian Mixture Model parameters from density | If you are willing to code a bit, you can implement your own version of the EM algorithm that takes into account the density value of a grid point. So instead of using the usual likelihood function:
$$
\log L(\Theta) = \sum_{t=1}^L\left [{\sum_{i=1}^N \phi(\boldsymbol r_t|\boldsymbol \mu_i,\boldsymbol \Sigma_i)} \right... | Gaussian Mixture Model parameters from density | If you are willing to code a bit, you can implement your own version of the EM algorithm that takes into account the density value of a grid point. So instead of using the usual likelihood function:
$ | Gaussian Mixture Model parameters from density
If you are willing to code a bit, you can implement your own version of the EM algorithm that takes into account the density value of a grid point. So instead of using the usual likelihood function:
$$
\log L(\Theta) = \sum_{t=1}^L\left [{\sum_{i=1}^N \phi(\boldsymbol r_t|... | Gaussian Mixture Model parameters from density
If you are willing to code a bit, you can implement your own version of the EM algorithm that takes into account the density value of a grid point. So instead of using the usual likelihood function:
$ |
50,024 | Sample Mean of AR(1) model | FIRST STEP
Sometimes, patience and algebra are still required to obtain what we need to obtain. In your case, by repeated substitution as already suggested we get
$$X_t = \sum_{j=0}^t\phi^j\epsilon_{t-j}$$
and we note that, although not clearly stated in the question, here we have $E(\epsilon_t) = \mu$, not necessarily... | Sample Mean of AR(1) model | FIRST STEP
Sometimes, patience and algebra are still required to obtain what we need to obtain. In your case, by repeated substitution as already suggested we get
$$X_t = \sum_{j=0}^t\phi^j\epsilon_{t | Sample Mean of AR(1) model
FIRST STEP
Sometimes, patience and algebra are still required to obtain what we need to obtain. In your case, by repeated substitution as already suggested we get
$$X_t = \sum_{j=0}^t\phi^j\epsilon_{t-j}$$
and we note that, although not clearly stated in the question, here we have $E(\epsilon... | Sample Mean of AR(1) model
FIRST STEP
Sometimes, patience and algebra are still required to obtain what we need to obtain. In your case, by repeated substitution as already suggested we get
$$X_t = \sum_{j=0}^t\phi^j\epsilon_{t |
50,025 | How to select kernel for Gaussian Process? | One possibility you might try is simulating Gaussian Processes with different kernels. In that way, you can get a feel for what the different kernels will produce. This can most easily be done by selecting a grid of values and simulating from the multivariate normal implied by that grid. To make things easier, just use... | How to select kernel for Gaussian Process? | One possibility you might try is simulating Gaussian Processes with different kernels. In that way, you can get a feel for what the different kernels will produce. This can most easily be done by sele | How to select kernel for Gaussian Process?
One possibility you might try is simulating Gaussian Processes with different kernels. In that way, you can get a feel for what the different kernels will produce. This can most easily be done by selecting a grid of values and simulating from the multivariate normal implied by... | How to select kernel for Gaussian Process?
One possibility you might try is simulating Gaussian Processes with different kernels. In that way, you can get a feel for what the different kernels will produce. This can most easily be done by sele |
50,026 | How to select kernel for Gaussian Process? | Set aside a second set of training data, and "train" your model architecture using that.
i.e.
1) select an arbitrary kernel
2) train it using training set 1
3) evaluate it on training set 2 (using accuracy, precision, recall, whatever)
4) if !tired: goto 1)
5) else: return kernel with highest evaluation score... | How to select kernel for Gaussian Process? | Set aside a second set of training data, and "train" your model architecture using that.
i.e.
1) select an arbitrary kernel
2) train it using training set 1
3) evaluate it on training set 2 (usi | How to select kernel for Gaussian Process?
Set aside a second set of training data, and "train" your model architecture using that.
i.e.
1) select an arbitrary kernel
2) train it using training set 1
3) evaluate it on training set 2 (using accuracy, precision, recall, whatever)
4) if !tired: goto 1)
5) else: ... | How to select kernel for Gaussian Process?
Set aside a second set of training data, and "train" your model architecture using that.
i.e.
1) select an arbitrary kernel
2) train it using training set 1
3) evaluate it on training set 2 (usi |
50,027 | MCMC: examples of when direct sampling is difficult (but Metropolis Hastings is easy) | I don't have a great example off the top of my head, but MH is easy compared to direct sampling whenever the parameter's prior is not conjugate with that parameter's likelihood. In fact this is the only reason I have ever seen MH preferred. A toy example is that $p \sim \text{Beta}(\alpha, \beta)$, and you wanted to ha... | MCMC: examples of when direct sampling is difficult (but Metropolis Hastings is easy) | I don't have a great example off the top of my head, but MH is easy compared to direct sampling whenever the parameter's prior is not conjugate with that parameter's likelihood. In fact this is the on | MCMC: examples of when direct sampling is difficult (but Metropolis Hastings is easy)
I don't have a great example off the top of my head, but MH is easy compared to direct sampling whenever the parameter's prior is not conjugate with that parameter's likelihood. In fact this is the only reason I have ever seen MH pref... | MCMC: examples of when direct sampling is difficult (but Metropolis Hastings is easy)
I don't have a great example off the top of my head, but MH is easy compared to direct sampling whenever the parameter's prior is not conjugate with that parameter's likelihood. In fact this is the on |
50,028 | Mixed effects modelling; what to do when model is over-specified? | The Keep it maximal proposal is not to be taken as a dogma. Be more pragmatic, and try to determine what level of model complexity your data will support (or at least a maximal level that will be supported).
Computationally speaking: The IWRLS estimation procedure used might not converge to the optimal parameter values... | Mixed effects modelling; what to do when model is over-specified? | The Keep it maximal proposal is not to be taken as a dogma. Be more pragmatic, and try to determine what level of model complexity your data will support (or at least a maximal level that will be supp | Mixed effects modelling; what to do when model is over-specified?
The Keep it maximal proposal is not to be taken as a dogma. Be more pragmatic, and try to determine what level of model complexity your data will support (or at least a maximal level that will be supported).
Computationally speaking: The IWRLS estimation... | Mixed effects modelling; what to do when model is over-specified?
The Keep it maximal proposal is not to be taken as a dogma. Be more pragmatic, and try to determine what level of model complexity your data will support (or at least a maximal level that will be supp |
50,029 | demonstration of benefits of ridge regression over ordinary regression | I try for an answer, but a rather general one.
(1) It depends on what you mean by "performing better". Often, performance is measured in terms of the capability to generalize and forecast. For this cross-validation is an often used tool, where you repeatedly divide the data into a training and test set, fit the model u... | demonstration of benefits of ridge regression over ordinary regression | I try for an answer, but a rather general one.
(1) It depends on what you mean by "performing better". Often, performance is measured in terms of the capability to generalize and forecast. For this cr | demonstration of benefits of ridge regression over ordinary regression
I try for an answer, but a rather general one.
(1) It depends on what you mean by "performing better". Often, performance is measured in terms of the capability to generalize and forecast. For this cross-validation is an often used tool, where you r... | demonstration of benefits of ridge regression over ordinary regression
I try for an answer, but a rather general one.
(1) It depends on what you mean by "performing better". Often, performance is measured in terms of the capability to generalize and forecast. For this cr |
50,030 | Probability generating function for negative values of random variables? | As whuber stated above, there is really no problem here as long as the resultant sum is well-defined in some neighborhood of a finite point in $\mathbb{C}$ (we can always shift things around to find the moments, if they exist, or probabilities, no matter what the number is). There are a few things you can think about. ... | Probability generating function for negative values of random variables? | As whuber stated above, there is really no problem here as long as the resultant sum is well-defined in some neighborhood of a finite point in $\mathbb{C}$ (we can always shift things around to find t | Probability generating function for negative values of random variables?
As whuber stated above, there is really no problem here as long as the resultant sum is well-defined in some neighborhood of a finite point in $\mathbb{C}$ (we can always shift things around to find the moments, if they exist, or probabilities, no... | Probability generating function for negative values of random variables?
As whuber stated above, there is really no problem here as long as the resultant sum is well-defined in some neighborhood of a finite point in $\mathbb{C}$ (we can always shift things around to find t |
50,031 | Probability generating function for negative values of random variables? | I believe it's basically because usually the treatment relies on results that apply to sums of non-negative powers.
An example of the sort of thing that's relied on would be Abel's theorem. With r.v.s that take negative values, you'd have to try to establish the radius of convergence without it.
So there are some issu... | Probability generating function for negative values of random variables? | I believe it's basically because usually the treatment relies on results that apply to sums of non-negative powers.
An example of the sort of thing that's relied on would be Abel's theorem. With r.v. | Probability generating function for negative values of random variables?
I believe it's basically because usually the treatment relies on results that apply to sums of non-negative powers.
An example of the sort of thing that's relied on would be Abel's theorem. With r.v.s that take negative values, you'd have to try ... | Probability generating function for negative values of random variables?
I believe it's basically because usually the treatment relies on results that apply to sums of non-negative powers.
An example of the sort of thing that's relied on would be Abel's theorem. With r.v. |
50,032 | Probability generating function for negative values of random variables? | The (probability) generating function (a/k/a the factorial moment generatring function) is defined as $$h_X(t) = E\{t^X\}.$$ The garden-variety moment generating function is defined as $$M_X(t) = E\{e^{tX}\}.$$ For either to be useful it must exist in a neighborhood of 0 (to pull moments off) or in the case of $h_X(t)... | Probability generating function for negative values of random variables? | The (probability) generating function (a/k/a the factorial moment generatring function) is defined as $$h_X(t) = E\{t^X\}.$$ The garden-variety moment generating function is defined as $$M_X(t) = E\{e | Probability generating function for negative values of random variables?
The (probability) generating function (a/k/a the factorial moment generatring function) is defined as $$h_X(t) = E\{t^X\}.$$ The garden-variety moment generating function is defined as $$M_X(t) = E\{e^{tX}\}.$$ For either to be useful it must exi... | Probability generating function for negative values of random variables?
The (probability) generating function (a/k/a the factorial moment generatring function) is defined as $$h_X(t) = E\{t^X\}.$$ The garden-variety moment generating function is defined as $$M_X(t) = E\{e |
50,033 | Cointegration - same thing as stationary residuals? | No, this is not true. In order to consider a cointegrating relationship your variables need to be at least integrated of order one, $I\left(1\right)
$. In order to carry out a cointegration analysis you would first have to conduct a unit root test to see if your time series are in fact $I\left(1\right)
$. Then you co... | Cointegration - same thing as stationary residuals? | No, this is not true. In order to consider a cointegrating relationship your variables need to be at least integrated of order one, $I\left(1\right)
$. In order to carry out a cointegration analysis | Cointegration - same thing as stationary residuals?
No, this is not true. In order to consider a cointegrating relationship your variables need to be at least integrated of order one, $I\left(1\right)
$. In order to carry out a cointegration analysis you would first have to conduct a unit root test to see if your time... | Cointegration - same thing as stationary residuals?
No, this is not true. In order to consider a cointegrating relationship your variables need to be at least integrated of order one, $I\left(1\right)
$. In order to carry out a cointegration analysis |
50,034 | Smoothing dirty data? | There are methods which use the knowledge of the point in time of the unusual event which leads to a window of response before and after the known event. These methods are called different things but one name is Dynamic Regression or Transfer Functions or armaX models. | Smoothing dirty data? | There are methods which use the knowledge of the point in time of the unusual event which leads to a window of response before and after the known event. These methods are called different things but | Smoothing dirty data?
There are methods which use the knowledge of the point in time of the unusual event which leads to a window of response before and after the known event. These methods are called different things but one name is Dynamic Regression or Transfer Functions or armaX models. | Smoothing dirty data?
There are methods which use the knowledge of the point in time of the unusual event which leads to a window of response before and after the known event. These methods are called different things but |
50,035 | Is $H=\min(t_1,...,t_n)$ a Copula? | One way to prove a function $H$ on the $n$ cube $[0,1]^n$ is a copula is to exhibit a random variable whose distribution function restricted to the cube is $H.$
To that end, let $X$ be a univariate random variable with a uniform distribution on $[0,1],$ which means that for all $t\in[0,1],$ $\Pr(X\le t)=t.$ Define the... | Is $H=\min(t_1,...,t_n)$ a Copula? | One way to prove a function $H$ on the $n$ cube $[0,1]^n$ is a copula is to exhibit a random variable whose distribution function restricted to the cube is $H.$
To that end, let $X$ be a univariate ra | Is $H=\min(t_1,...,t_n)$ a Copula?
One way to prove a function $H$ on the $n$ cube $[0,1]^n$ is a copula is to exhibit a random variable whose distribution function restricted to the cube is $H.$
To that end, let $X$ be a univariate random variable with a uniform distribution on $[0,1],$ which means that for all $t\in[... | Is $H=\min(t_1,...,t_n)$ a Copula?
One way to prove a function $H$ on the $n$ cube $[0,1]^n$ is a copula is to exhibit a random variable whose distribution function restricted to the cube is $H.$
To that end, let $X$ be a univariate ra |
50,036 | Confidence interval for a proportion estimated through stratified sampling | I have no real answer for you, only some thoughts. You are unlucky in that illness is so rare.
I'll first note that this design would have caused trouble even if illness was common. For example, the SE formula for the weighted prevalence requires $n_h$>1 observation per stratum (Cochran, 1977, Chapter 5).
You ask if i... | Confidence interval for a proportion estimated through stratified sampling | I have no real answer for you, only some thoughts. You are unlucky in that illness is so rare.
I'll first note that this design would have caused trouble even if illness was common. For example, the S | Confidence interval for a proportion estimated through stratified sampling
I have no real answer for you, only some thoughts. You are unlucky in that illness is so rare.
I'll first note that this design would have caused trouble even if illness was common. For example, the SE formula for the weighted prevalence require... | Confidence interval for a proportion estimated through stratified sampling
I have no real answer for you, only some thoughts. You are unlucky in that illness is so rare.
I'll first note that this design would have caused trouble even if illness was common. For example, the S |
50,037 | Expectation of conditional normal distribution | To summarize the comments:
Since we assume that $s_1$ and $s_2$ jointly follow a standard bivariate normal distribution, with correlation coefficient $\rho$, then the joint density is
$$f(s_1,s_2) = \frac{1}{2 \pi \sqrt{1-\rho^2}}
\exp\left\{-\frac{s_1^2 +s_2^2 -2\rho s_1s_2}{2(1-\rho^2)}\right\} $$
We also hav... | Expectation of conditional normal distribution | To summarize the comments:
Since we assume that $s_1$ and $s_2$ jointly follow a standard bivariate normal distribution, with correlation coefficient $\rho$, then the joint density is
$$f(s_1,s_2) = \ | Expectation of conditional normal distribution
To summarize the comments:
Since we assume that $s_1$ and $s_2$ jointly follow a standard bivariate normal distribution, with correlation coefficient $\rho$, then the joint density is
$$f(s_1,s_2) = \frac{1}{2 \pi \sqrt{1-\rho^2}}
\exp\left\{-\frac{s_1^2 +s_2^2 -2\... | Expectation of conditional normal distribution
To summarize the comments:
Since we assume that $s_1$ and $s_2$ jointly follow a standard bivariate normal distribution, with correlation coefficient $\rho$, then the joint density is
$$f(s_1,s_2) = \ |
50,038 | I would like help calculating the probability of a simple problem | How would you keep track of the person's walk? All you need to do is (1) remember whether their previous step was a fall or not and (2) note when two falls occur in a row. That is a data structure with three states:
Previous step was not a fall.
Previous step was a fall.
At some point in the past, two steps in a ro... | I would like help calculating the probability of a simple problem | How would you keep track of the person's walk? All you need to do is (1) remember whether their previous step was a fall or not and (2) note when two falls occur in a row. That is a data structure w | I would like help calculating the probability of a simple problem
How would you keep track of the person's walk? All you need to do is (1) remember whether their previous step was a fall or not and (2) note when two falls occur in a row. That is a data structure with three states:
Previous step was not a fall.
Prev... | I would like help calculating the probability of a simple problem
How would you keep track of the person's walk? All you need to do is (1) remember whether their previous step was a fall or not and (2) note when two falls occur in a row. That is a data structure w |
50,039 | kozachenko-leonenko entropy estimation | Use the k-th nearest neighbor instead, for k as large as needed to obtain an $\epsilon_i > 0$. To reflect this in the Kozachenko-Leonenko estimator, simply replace $\psi(1)$ with $\psi(k)$. Since it's allowed to vary k from point to point, you could for instance look for the "closest distinct neighbor" each time. (If y... | kozachenko-leonenko entropy estimation | Use the k-th nearest neighbor instead, for k as large as needed to obtain an $\epsilon_i > 0$. To reflect this in the Kozachenko-Leonenko estimator, simply replace $\psi(1)$ with $\psi(k)$. Since it's | kozachenko-leonenko entropy estimation
Use the k-th nearest neighbor instead, for k as large as needed to obtain an $\epsilon_i > 0$. To reflect this in the Kozachenko-Leonenko estimator, simply replace $\psi(1)$ with $\psi(k)$. Since it's allowed to vary k from point to point, you could for instance look for the "clos... | kozachenko-leonenko entropy estimation
Use the k-th nearest neighbor instead, for k as large as needed to obtain an $\epsilon_i > 0$. To reflect this in the Kozachenko-Leonenko estimator, simply replace $\psi(1)$ with $\psi(k)$. Since it's |
50,040 | Neural Network: What if there are multiple right answers for a given set of inputs? | A neural network can in principle deal with this. Actually, I believe they are among the best models for this task. The question is whether it is modeled correctly.
Say you are looking at a regression problem and minimize the sum of squares, i.e.
$$L(\theta) = \sum_i (\hat{y}_i - y_i)^2.$$
Here, $L$ is the loss functio... | Neural Network: What if there are multiple right answers for a given set of inputs? | A neural network can in principle deal with this. Actually, I believe they are among the best models for this task. The question is whether it is modeled correctly.
Say you are looking at a regression | Neural Network: What if there are multiple right answers for a given set of inputs?
A neural network can in principle deal with this. Actually, I believe they are among the best models for this task. The question is whether it is modeled correctly.
Say you are looking at a regression problem and minimize the sum of squ... | Neural Network: What if there are multiple right answers for a given set of inputs?
A neural network can in principle deal with this. Actually, I believe they are among the best models for this task. The question is whether it is modeled correctly.
Say you are looking at a regression |
50,041 | Neural Network: What if there are multiple right answers for a given set of inputs? | Perhaps an RNN can solve this "order doesn't matter" problem.
Consider the task of image captioning which has been successfully implemented by Stanford and Google. Now consider that an image might have multiple equally correct solutions, "dog playing with cat" or "cat playing with dog". I believe using an RNN (recurre... | Neural Network: What if there are multiple right answers for a given set of inputs? | Perhaps an RNN can solve this "order doesn't matter" problem.
Consider the task of image captioning which has been successfully implemented by Stanford and Google. Now consider that an image might ha | Neural Network: What if there are multiple right answers for a given set of inputs?
Perhaps an RNN can solve this "order doesn't matter" problem.
Consider the task of image captioning which has been successfully implemented by Stanford and Google. Now consider that an image might have multiple equally correct solution... | Neural Network: What if there are multiple right answers for a given set of inputs?
Perhaps an RNN can solve this "order doesn't matter" problem.
Consider the task of image captioning which has been successfully implemented by Stanford and Google. Now consider that an image might ha |
50,042 | Neural Network: What if there are multiple right answers for a given set of inputs? | Firstly there is no reason for back propagation to 'fail' in the case of ambiguous data. Here is why.
Neural nets work by producing a truly highly non-linear function by composing linear functions with a non-linear activation function. The model class of neural nets are functions of this class. Roughly speaking a ne... | Neural Network: What if there are multiple right answers for a given set of inputs? | Firstly there is no reason for back propagation to 'fail' in the case of ambiguous data. Here is why.
Neural nets work by producing a truly highly non-linear function by composing linear functions wi | Neural Network: What if there are multiple right answers for a given set of inputs?
Firstly there is no reason for back propagation to 'fail' in the case of ambiguous data. Here is why.
Neural nets work by producing a truly highly non-linear function by composing linear functions with a non-linear activation function.... | Neural Network: What if there are multiple right answers for a given set of inputs?
Firstly there is no reason for back propagation to 'fail' in the case of ambiguous data. Here is why.
Neural nets work by producing a truly highly non-linear function by composing linear functions wi |
50,043 | Neural Network: What if there are multiple right answers for a given set of inputs? | If you have more than one output $o_1, o_2,..,o_n$ for the $n$ possible correct answers. I have found the following error function works for about up to 4 expected answers:
$$E(o) = \tanh|e-o_1| \tanh|e-o_2|...\tanh|e-o_n|$$
Where $e$ is the expected result which is a random one of the correct answers.
Notice that the ... | Neural Network: What if there are multiple right answers for a given set of inputs? | If you have more than one output $o_1, o_2,..,o_n$ for the $n$ possible correct answers. I have found the following error function works for about up to 4 expected answers:
$$E(o) = \tanh|e-o_1| \tanh | Neural Network: What if there are multiple right answers for a given set of inputs?
If you have more than one output $o_1, o_2,..,o_n$ for the $n$ possible correct answers. I have found the following error function works for about up to 4 expected answers:
$$E(o) = \tanh|e-o_1| \tanh|e-o_2|...\tanh|e-o_n|$$
Where $e$ i... | Neural Network: What if there are multiple right answers for a given set of inputs?
If you have more than one output $o_1, o_2,..,o_n$ for the $n$ possible correct answers. I have found the following error function works for about up to 4 expected answers:
$$E(o) = \tanh|e-o_1| \tanh |
50,044 | Univariate priors for the parameters of a Beta distribution | Any prior on $\alpha$ (or $\beta$) is admissible as long as it satisfies the requirements of the beta distribution in your parameterization, usually $\alpha >0$ and $\beta >0$, and as long as it yields a finite posterior. Assuming univariate priors and independence of $\alpha$ and $\beta$, one option might be the expon... | Univariate priors for the parameters of a Beta distribution | Any prior on $\alpha$ (or $\beta$) is admissible as long as it satisfies the requirements of the beta distribution in your parameterization, usually $\alpha >0$ and $\beta >0$, and as long as it yield | Univariate priors for the parameters of a Beta distribution
Any prior on $\alpha$ (or $\beta$) is admissible as long as it satisfies the requirements of the beta distribution in your parameterization, usually $\alpha >0$ and $\beta >0$, and as long as it yields a finite posterior. Assuming univariate priors and indepen... | Univariate priors for the parameters of a Beta distribution
Any prior on $\alpha$ (or $\beta$) is admissible as long as it satisfies the requirements of the beta distribution in your parameterization, usually $\alpha >0$ and $\beta >0$, and as long as it yield |
50,045 | Test the randomness (uniformly distributed) on a 64 bit float random generator | As it stands, this is not a good way to test whether floating point numbers are uniformly distributed. Like Aksakal, I wondered about whether the bits of the exponent part of the floating point representation would be uniformly distributed. The answer to this is that they aren't uniformly distributed, because there are... | Test the randomness (uniformly distributed) on a 64 bit float random generator | As it stands, this is not a good way to test whether floating point numbers are uniformly distributed. Like Aksakal, I wondered about whether the bits of the exponent part of the floating point repres | Test the randomness (uniformly distributed) on a 64 bit float random generator
As it stands, this is not a good way to test whether floating point numbers are uniformly distributed. Like Aksakal, I wondered about whether the bits of the exponent part of the floating point representation would be uniformly distributed. ... | Test the randomness (uniformly distributed) on a 64 bit float random generator
As it stands, this is not a good way to test whether floating point numbers are uniformly distributed. Like Aksakal, I wondered about whether the bits of the exponent part of the floating point repres |
50,046 | Test the randomness (uniformly distributed) on a 64 bit float random generator | have you looked at A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications by NIST?
I think it's a great place to start your analysis. | Test the randomness (uniformly distributed) on a 64 bit float random generator | have you looked at A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications by NIST?
I think it's a great place to start your analysis. | Test the randomness (uniformly distributed) on a 64 bit float random generator
have you looked at A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications by NIST?
I think it's a great place to start your analysis. | Test the randomness (uniformly distributed) on a 64 bit float random generator
have you looked at A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications by NIST?
I think it's a great place to start your analysis. |
50,047 | Interaction effects in non-linear models | The way I solved the issue that the interaction effects in terms of marginal effect differ across observations is that in my article I did not look at interaction effects in terms of marginal effects but in terms of odds ratios.
With marginal effects you try to fit a linear line on top of a non-linear line, and this d... | Interaction effects in non-linear models | The way I solved the issue that the interaction effects in terms of marginal effect differ across observations is that in my article I did not look at interaction effects in terms of marginal effects | Interaction effects in non-linear models
The way I solved the issue that the interaction effects in terms of marginal effect differ across observations is that in my article I did not look at interaction effects in terms of marginal effects but in terms of odds ratios.
With marginal effects you try to fit a linear lin... | Interaction effects in non-linear models
The way I solved the issue that the interaction effects in terms of marginal effect differ across observations is that in my article I did not look at interaction effects in terms of marginal effects |
50,048 | How can I estimate the shape of a curve where the predictor variable is right censored interval variable? | It turns out that the problem of regression with an interval-censored independent variable is much less studied than regression with an interval-censored dependent variable. There are at least a dozen studies on this topic, but as an applied researcher with limited mathematical statistics, I found few of them accessibl... | How can I estimate the shape of a curve where the predictor variable is right censored interval vari | It turns out that the problem of regression with an interval-censored independent variable is much less studied than regression with an interval-censored dependent variable. There are at least a dozen | How can I estimate the shape of a curve where the predictor variable is right censored interval variable?
It turns out that the problem of regression with an interval-censored independent variable is much less studied than regression with an interval-censored dependent variable. There are at least a dozen studies on th... | How can I estimate the shape of a curve where the predictor variable is right censored interval vari
It turns out that the problem of regression with an interval-censored independent variable is much less studied than regression with an interval-censored dependent variable. There are at least a dozen |
50,049 | What are some differences between confirmatory analysis and exploratory analysis? | First EDA will be done on the data set to understand the data & prepare the hypothesis, then confirmatory analysis is done. In EDA, most of the time we do visual analysis. Whereas in Confirmatory analysis we take probability models into consideration.
Comparison from here:
Confirmatory Analysis
Inferential Statistics... | What are some differences between confirmatory analysis and exploratory analysis? | First EDA will be done on the data set to understand the data & prepare the hypothesis, then confirmatory analysis is done. In EDA, most of the time we do visual analysis. Whereas in Confirmatory anal | What are some differences between confirmatory analysis and exploratory analysis?
First EDA will be done on the data set to understand the data & prepare the hypothesis, then confirmatory analysis is done. In EDA, most of the time we do visual analysis. Whereas in Confirmatory analysis we take probability models into c... | What are some differences between confirmatory analysis and exploratory analysis?
First EDA will be done on the data set to understand the data & prepare the hypothesis, then confirmatory analysis is done. In EDA, most of the time we do visual analysis. Whereas in Confirmatory anal |
50,050 | What are some differences between confirmatory analysis and exploratory analysis? | I don't think there is a set recipe for when to perform which. You have to use the tools required for the task, whether they are most useful for an exploratory analysis or testing hypotheses. It is likely you will begin with hypotheses (that's why you collected this data in the first place right?) and then test them.... | What are some differences between confirmatory analysis and exploratory analysis? | I don't think there is a set recipe for when to perform which. You have to use the tools required for the task, whether they are most useful for an exploratory analysis or testing hypotheses. It is | What are some differences between confirmatory analysis and exploratory analysis?
I don't think there is a set recipe for when to perform which. You have to use the tools required for the task, whether they are most useful for an exploratory analysis or testing hypotheses. It is likely you will begin with hypotheses ... | What are some differences between confirmatory analysis and exploratory analysis?
I don't think there is a set recipe for when to perform which. You have to use the tools required for the task, whether they are most useful for an exploratory analysis or testing hypotheses. It is |
50,051 | Importance Sampling to evaluate integral in R | When running the code provided for the second function I get
> c(mean(Y),var(Y))
[1] 3.2981238 0.5203621
> integrate(f,0.01,1)
3.19264 with absolute error < 1.1e-06
which means that the true value of the integral is close to 3.2, not to 0.70.
If you want to integrate f from 0.3 to 8, then the importance function must ... | Importance Sampling to evaluate integral in R | When running the code provided for the second function I get
> c(mean(Y),var(Y))
[1] 3.2981238 0.5203621
> integrate(f,0.01,1)
3.19264 with absolute error < 1.1e-06
which means that the true value of | Importance Sampling to evaluate integral in R
When running the code provided for the second function I get
> c(mean(Y),var(Y))
[1] 3.2981238 0.5203621
> integrate(f,0.01,1)
3.19264 with absolute error < 1.1e-06
which means that the true value of the integral is close to 3.2, not to 0.70.
If you want to integrate f fro... | Importance Sampling to evaluate integral in R
When running the code provided for the second function I get
> c(mean(Y),var(Y))
[1] 3.2981238 0.5203621
> integrate(f,0.01,1)
3.19264 with absolute error < 1.1e-06
which means that the true value of |
50,052 | Regression with "unidirectional" noise | This set up is equivalent to the Deterministic (Efficiency/Productivity) Frontier Analysis in Econometrics, where the econometrician is trying to measure how far a firm/unit of production is from full-efficiency in the utilization of production factors. The $f(x)$ function is the full-efficiency production function (i.... | Regression with "unidirectional" noise | This set up is equivalent to the Deterministic (Efficiency/Productivity) Frontier Analysis in Econometrics, where the econometrician is trying to measure how far a firm/unit of production is from full | Regression with "unidirectional" noise
This set up is equivalent to the Deterministic (Efficiency/Productivity) Frontier Analysis in Econometrics, where the econometrician is trying to measure how far a firm/unit of production is from full-efficiency in the utilization of production factors. The $f(x)$ function is the ... | Regression with "unidirectional" noise
This set up is equivalent to the Deterministic (Efficiency/Productivity) Frontier Analysis in Econometrics, where the econometrician is trying to measure how far a firm/unit of production is from full |
50,053 | Are sampling weights necessary in logistic regression? | The sampling weights are designed to account for the non-simple random sample nature of your sample. Therefore, they are just as needed in one form of regression as another. Exactly how to do this may be complicated; e.g. in SAS there is PROC SURVEYLOGISTIC to deal with various sorts of samples. In R there is the surve... | Are sampling weights necessary in logistic regression? | The sampling weights are designed to account for the non-simple random sample nature of your sample. Therefore, they are just as needed in one form of regression as another. Exactly how to do this may | Are sampling weights necessary in logistic regression?
The sampling weights are designed to account for the non-simple random sample nature of your sample. Therefore, they are just as needed in one form of regression as another. Exactly how to do this may be complicated; e.g. in SAS there is PROC SURVEYLOGISTIC to deal... | Are sampling weights necessary in logistic regression?
The sampling weights are designed to account for the non-simple random sample nature of your sample. Therefore, they are just as needed in one form of regression as another. Exactly how to do this may |
50,054 | How to measure uncertainty of a parameter when false positives exist? | In principle this is a classification problem. If you would know which observation is a true positive, you could just take these observations and estimate the mean and the variance for them. Doing so, you implicitly assume that the true value follows a normal (or more accurately T-student) distribution defined by the o... | How to measure uncertainty of a parameter when false positives exist? | In principle this is a classification problem. If you would know which observation is a true positive, you could just take these observations and estimate the mean and the variance for them. Doing so, | How to measure uncertainty of a parameter when false positives exist?
In principle this is a classification problem. If you would know which observation is a true positive, you could just take these observations and estimate the mean and the variance for them. Doing so, you implicitly assume that the true value follows... | How to measure uncertainty of a parameter when false positives exist?
In principle this is a classification problem. If you would know which observation is a true positive, you could just take these observations and estimate the mean and the variance for them. Doing so, |
50,055 | Definition of statistical model in case of hierarchical model | I wonder what is $\Theta$ in the case of a hierarchical model. Is it composed of all the latent variables of the model or only the one at the top level? Does this include the hyper-parameters?
As far as I undestand, the definition you point out from Wikipedia outlines that a parametric model is collection $\mathcal{P... | Definition of statistical model in case of hierarchical model | I wonder what is $\Theta$ in the case of a hierarchical model. Is it composed of all the latent variables of the model or only the one at the top level? Does this include the hyper-parameters?
As fa | Definition of statistical model in case of hierarchical model
I wonder what is $\Theta$ in the case of a hierarchical model. Is it composed of all the latent variables of the model or only the one at the top level? Does this include the hyper-parameters?
As far as I undestand, the definition you point out from Wikipe... | Definition of statistical model in case of hierarchical model
I wonder what is $\Theta$ in the case of a hierarchical model. Is it composed of all the latent variables of the model or only the one at the top level? Does this include the hyper-parameters?
As fa |
50,056 | Definition of statistical model in case of hierarchical model | The parameters have no concept of the hierarchy, nor should they. $\Theta$ is the space of possibilities. Consider the example:
$ Y_{ij} \sim \text{Bernoulli}(p_i),$
$p_i \sim \text{Beta}(\alpha, \beta),$
for $i = 1, \ldots, 10$ subjects and $j=1, \ldots 5$ binary outcomes within each subject.
In this case, $\Theta = ... | Definition of statistical model in case of hierarchical model | The parameters have no concept of the hierarchy, nor should they. $\Theta$ is the space of possibilities. Consider the example:
$ Y_{ij} \sim \text{Bernoulli}(p_i),$
$p_i \sim \text{Beta}(\alpha, \be | Definition of statistical model in case of hierarchical model
The parameters have no concept of the hierarchy, nor should they. $\Theta$ is the space of possibilities. Consider the example:
$ Y_{ij} \sim \text{Bernoulli}(p_i),$
$p_i \sim \text{Beta}(\alpha, \beta),$
for $i = 1, \ldots, 10$ subjects and $j=1, \ldots 5$... | Definition of statistical model in case of hierarchical model
The parameters have no concept of the hierarchy, nor should they. $\Theta$ is the space of possibilities. Consider the example:
$ Y_{ij} \sim \text{Bernoulli}(p_i),$
$p_i \sim \text{Beta}(\alpha, \be |
50,057 | Variance of arrival process with shifted exponential distribution | Assuming that the inter-arrivals say $X_n$ ($n \geqslant 1$) are
independent, you have a renewal process, see e.g. this course, or the
classical references quoted in it: the book by D.R. Cox Renewal
Theory or the one by S. Karlin and H.M. Taylor A First Course in
Stochastic Processes, vol. 1 chap. 5.
The $n$-th arrival... | Variance of arrival process with shifted exponential distribution | Assuming that the inter-arrivals say $X_n$ ($n \geqslant 1$) are
independent, you have a renewal process, see e.g. this course, or the
classical references quoted in it: the book by D.R. Cox Renewal
T | Variance of arrival process with shifted exponential distribution
Assuming that the inter-arrivals say $X_n$ ($n \geqslant 1$) are
independent, you have a renewal process, see e.g. this course, or the
classical references quoted in it: the book by D.R. Cox Renewal
Theory or the one by S. Karlin and H.M. Taylor A First ... | Variance of arrival process with shifted exponential distribution
Assuming that the inter-arrivals say $X_n$ ($n \geqslant 1$) are
independent, you have a renewal process, see e.g. this course, or the
classical references quoted in it: the book by D.R. Cox Renewal
T |
50,058 | What is an "Unpaired Bland-Altman plot"? | I have never heard of this name.
In fact, the plot looks just like any Bland Altman plot I have seen, other than there are two sets of data overlaid on the plot. I guess the "unpaired" indicates that you cannot tell which MLEM and ST-MLEM data are coming from the same patient, because there is no linkage between the bl... | What is an "Unpaired Bland-Altman plot"? | I have never heard of this name.
In fact, the plot looks just like any Bland Altman plot I have seen, other than there are two sets of data overlaid on the plot. I guess the "unpaired" indicates that | What is an "Unpaired Bland-Altman plot"?
I have never heard of this name.
In fact, the plot looks just like any Bland Altman plot I have seen, other than there are two sets of data overlaid on the plot. I guess the "unpaired" indicates that you cannot tell which MLEM and ST-MLEM data are coming from the same patient, b... | What is an "Unpaired Bland-Altman plot"?
I have never heard of this name.
In fact, the plot looks just like any Bland Altman plot I have seen, other than there are two sets of data overlaid on the plot. I guess the "unpaired" indicates that |
50,059 | When using a Neural Network to classify more than two classes, is it better to have multiple output nodes (one for each class) or one output node? | Usually when you design a learning process with neural nets, you have to be aware of any structure you induce. This induced structure might be learned by net, since neural nets are very capable of incorporating patterns. The easiest way to induce a desired or undesired structure (learning bias) in the learning process ... | When using a Neural Network to classify more than two classes, is it better to have multiple output | Usually when you design a learning process with neural nets, you have to be aware of any structure you induce. This induced structure might be learned by net, since neural nets are very capable of inc | When using a Neural Network to classify more than two classes, is it better to have multiple output nodes (one for each class) or one output node?
Usually when you design a learning process with neural nets, you have to be aware of any structure you induce. This induced structure might be learned by net, since neural n... | When using a Neural Network to classify more than two classes, is it better to have multiple output
Usually when you design a learning process with neural nets, you have to be aware of any structure you induce. This induced structure might be learned by net, since neural nets are very capable of inc |
50,060 | Why do we say that the variance of the error terms is constant? | The error term ($\epsilon_i$) is indeed a random variable. The normality assumption holds if it has Normal distribution - $\epsilon_i$ ~ $N(\mu,\sigma)$. You are right when you say:
I always think about the error term in a linear regression model as a random variable, with some distribution and a variance
The assumpt... | Why do we say that the variance of the error terms is constant? | The error term ($\epsilon_i$) is indeed a random variable. The normality assumption holds if it has Normal distribution - $\epsilon_i$ ~ $N(\mu,\sigma)$. You are right when you say:
I always think ab | Why do we say that the variance of the error terms is constant?
The error term ($\epsilon_i$) is indeed a random variable. The normality assumption holds if it has Normal distribution - $\epsilon_i$ ~ $N(\mu,\sigma)$. You are right when you say:
I always think about the error term in a linear regression model as a ran... | Why do we say that the variance of the error terms is constant?
The error term ($\epsilon_i$) is indeed a random variable. The normality assumption holds if it has Normal distribution - $\epsilon_i$ ~ $N(\mu,\sigma)$. You are right when you say:
I always think ab |
50,061 | Averaging LASSO coefficients for repeated random partitioning of data | A similar thing with bootstrap replication is implemented in the "bolasso" function of the R package "mht" (for multiple hypothesis testing), and published here http://www.di.ens.fr/sierra/pdfs/icml_bolasso.pdf but they take the intersection of the sets of predictors with nonzero coefficients from all the replication s... | Averaging LASSO coefficients for repeated random partitioning of data | A similar thing with bootstrap replication is implemented in the "bolasso" function of the R package "mht" (for multiple hypothesis testing), and published here http://www.di.ens.fr/sierra/pdfs/icml_b | Averaging LASSO coefficients for repeated random partitioning of data
A similar thing with bootstrap replication is implemented in the "bolasso" function of the R package "mht" (for multiple hypothesis testing), and published here http://www.di.ens.fr/sierra/pdfs/icml_bolasso.pdf but they take the intersection of the s... | Averaging LASSO coefficients for repeated random partitioning of data
A similar thing with bootstrap replication is implemented in the "bolasso" function of the R package "mht" (for multiple hypothesis testing), and published here http://www.di.ens.fr/sierra/pdfs/icml_b |
50,062 | When estimating population mean, how can one half of the sample mean have lower risk than the sample mean itself? | You don't really need a simulation to see how this can happen: @whuber's comment essentially nails it.
Imagine that the population is described by $\mathcal N(1,10)$, i.e. population mean is $\mu=1$ and standard deviation is $\sigma=10$. Let your sample size be $n=10$. The variance of the sample mean (MSE) will be arou... | When estimating population mean, how can one half of the sample mean have lower risk than the sample | You don't really need a simulation to see how this can happen: @whuber's comment essentially nails it.
Imagine that the population is described by $\mathcal N(1,10)$, i.e. population mean is $\mu=1$ a | When estimating population mean, how can one half of the sample mean have lower risk than the sample mean itself?
You don't really need a simulation to see how this can happen: @whuber's comment essentially nails it.
Imagine that the population is described by $\mathcal N(1,10)$, i.e. population mean is $\mu=1$ and sta... | When estimating population mean, how can one half of the sample mean have lower risk than the sample
You don't really need a simulation to see how this can happen: @whuber's comment essentially nails it.
Imagine that the population is described by $\mathcal N(1,10)$, i.e. population mean is $\mu=1$ a |
50,063 | Ordinal/continuous vs dummy variable for time series regression/data mining | Modeling time continuously introduces the assumption that there is a linear influence of time upon the outcome, conditional upon $x$. However, adjusting for time as a fixed and random effect makes this interpretation a bit untenable.
Yes it does matter, it matters in absolutely all scenarios. You can verify this by sim... | Ordinal/continuous vs dummy variable for time series regression/data mining | Modeling time continuously introduces the assumption that there is a linear influence of time upon the outcome, conditional upon $x$. However, adjusting for time as a fixed and random effect makes thi | Ordinal/continuous vs dummy variable for time series regression/data mining
Modeling time continuously introduces the assumption that there is a linear influence of time upon the outcome, conditional upon $x$. However, adjusting for time as a fixed and random effect makes this interpretation a bit untenable.
Yes it doe... | Ordinal/continuous vs dummy variable for time series regression/data mining
Modeling time continuously introduces the assumption that there is a linear influence of time upon the outcome, conditional upon $x$. However, adjusting for time as a fixed and random effect makes thi |
50,064 | Ordinal/continuous vs dummy variable for time series regression/data mining | What makes you think that time has any effect on the dependent variable?
I'd suggest plotting the dependent variable against time to gauge what sort of model might be useful.
Both approaches - a linear (or non-linear) time trend and seasonal dummy variables might be necessary. (Normally dummy variables are used for se... | Ordinal/continuous vs dummy variable for time series regression/data mining | What makes you think that time has any effect on the dependent variable?
I'd suggest plotting the dependent variable against time to gauge what sort of model might be useful.
Both approaches - a linea | Ordinal/continuous vs dummy variable for time series regression/data mining
What makes you think that time has any effect on the dependent variable?
I'd suggest plotting the dependent variable against time to gauge what sort of model might be useful.
Both approaches - a linear (or non-linear) time trend and seasonal du... | Ordinal/continuous vs dummy variable for time series regression/data mining
What makes you think that time has any effect on the dependent variable?
I'd suggest plotting the dependent variable against time to gauge what sort of model might be useful.
Both approaches - a linea |
50,065 | Sufficiency of order statistics | As mentioned in comments, it's clearly not true for discrete random variables.
The problem is, as the original poster suggested in comments, that we can get ties.
The nonzero probability of ties make the equality
$P(X_1, \ldots, X_n|X_{(1)}, \ldots, X_{(n)}) = \frac{1}{n!}$
- which works in the continuous case - untru... | Sufficiency of order statistics | As mentioned in comments, it's clearly not true for discrete random variables.
The problem is, as the original poster suggested in comments, that we can get ties.
The nonzero probability of ties make | Sufficiency of order statistics
As mentioned in comments, it's clearly not true for discrete random variables.
The problem is, as the original poster suggested in comments, that we can get ties.
The nonzero probability of ties make the equality
$P(X_1, \ldots, X_n|X_{(1)}, \ldots, X_{(n)}) = \frac{1}{n!}$
- which work... | Sufficiency of order statistics
As mentioned in comments, it's clearly not true for discrete random variables.
The problem is, as the original poster suggested in comments, that we can get ties.
The nonzero probability of ties make |
50,066 | conditional sampling of bivariate normals | If you had another bound (such as $\epsilon_2 > T3$), you could sample uniformly and then weights the sample using the bivariate normal density. You would have zero rejection. Maybe in your application it is not too unreasonable to impose such a bound?
Probably better:
You find the intersection between the two linear c... | conditional sampling of bivariate normals | If you had another bound (such as $\epsilon_2 > T3$), you could sample uniformly and then weights the sample using the bivariate normal density. You would have zero rejection. Maybe in your applicatio | conditional sampling of bivariate normals
If you had another bound (such as $\epsilon_2 > T3$), you could sample uniformly and then weights the sample using the bivariate normal density. You would have zero rejection. Maybe in your application it is not too unreasonable to impose such a bound?
Probably better:
You find... | conditional sampling of bivariate normals
If you had another bound (such as $\epsilon_2 > T3$), you could sample uniformly and then weights the sample using the bivariate normal density. You would have zero rejection. Maybe in your applicatio |
50,067 | conditional sampling of bivariate normals | I have used the Gibbs sampling approach. This way only the beginning of the Gibbs sampling is thrown out (stabilization period). Thus number of waisted samples is not increasing with the number of required samples.
Conditional on observing $\varepsilon_1$, $\varepsilon_2$ is sampling from normal distribution with boun... | conditional sampling of bivariate normals | I have used the Gibbs sampling approach. This way only the beginning of the Gibbs sampling is thrown out (stabilization period). Thus number of waisted samples is not increasing with the number of req | conditional sampling of bivariate normals
I have used the Gibbs sampling approach. This way only the beginning of the Gibbs sampling is thrown out (stabilization period). Thus number of waisted samples is not increasing with the number of required samples.
Conditional on observing $\varepsilon_1$, $\varepsilon_2$ is s... | conditional sampling of bivariate normals
I have used the Gibbs sampling approach. This way only the beginning of the Gibbs sampling is thrown out (stabilization period). Thus number of waisted samples is not increasing with the number of req |
50,068 | conditional sampling of bivariate normals | One simple approach that would involve a huge reduction in the rejection rate would be to rotate the coordinates $(\epsilon_1,\epsilon_2)$ to say $(X_1,X_2)$ such that the line $aε_1+bε_2=T_2$ becomes vertical ($cX_1=\tau_2$, say). Then generate from the truncated normal such that $cX_1<\tau_2$. Then generate an indepe... | conditional sampling of bivariate normals | One simple approach that would involve a huge reduction in the rejection rate would be to rotate the coordinates $(\epsilon_1,\epsilon_2)$ to say $(X_1,X_2)$ such that the line $aε_1+bε_2=T_2$ becomes | conditional sampling of bivariate normals
One simple approach that would involve a huge reduction in the rejection rate would be to rotate the coordinates $(\epsilon_1,\epsilon_2)$ to say $(X_1,X_2)$ such that the line $aε_1+bε_2=T_2$ becomes vertical ($cX_1=\tau_2$, say). Then generate from the truncated normal such t... | conditional sampling of bivariate normals
One simple approach that would involve a huge reduction in the rejection rate would be to rotate the coordinates $(\epsilon_1,\epsilon_2)$ to say $(X_1,X_2)$ such that the line $aε_1+bε_2=T_2$ becomes |
50,069 | Chi Square test for survey data | It appears that you are first doing an omnibus test (Chi square test for independence) with 2 df to determine if the "like status" and "gender" are independent or not. And then you are doing post-hoc tests on the individual rows (Chi square goodness of fit tests) to see if the males/females are equally likely under eac... | Chi Square test for survey data | It appears that you are first doing an omnibus test (Chi square test for independence) with 2 df to determine if the "like status" and "gender" are independent or not. And then you are doing post-hoc | Chi Square test for survey data
It appears that you are first doing an omnibus test (Chi square test for independence) with 2 df to determine if the "like status" and "gender" are independent or not. And then you are doing post-hoc tests on the individual rows (Chi square goodness of fit tests) to see if the males/fema... | Chi Square test for survey data
It appears that you are first doing an omnibus test (Chi square test for independence) with 2 df to determine if the "like status" and "gender" are independent or not. And then you are doing post-hoc |
50,070 | Chi Square test for survey data | The portion after "this is what the code does instead" seems off, although it is hard to tell.
The client's request is reasonable. It isn't answered by chi-square, but it still a reasonable request. The proportion of men who liked it is 54/99 = about 54%, of women it is 46/103 = about 46% (you can calculate the exact ... | Chi Square test for survey data | The portion after "this is what the code does instead" seems off, although it is hard to tell.
The client's request is reasonable. It isn't answered by chi-square, but it still a reasonable request. | Chi Square test for survey data
The portion after "this is what the code does instead" seems off, although it is hard to tell.
The client's request is reasonable. It isn't answered by chi-square, but it still a reasonable request. The proportion of men who liked it is 54/99 = about 54%, of women it is 46/103 = about 4... | Chi Square test for survey data
The portion after "this is what the code does instead" seems off, although it is hard to tell.
The client's request is reasonable. It isn't answered by chi-square, but it still a reasonable request. |
50,071 | How do I deal with large data similarity computation? | I have been doing a similar procedure on a regular basis lately. It isn't quick and it takes a decent chunk of HDD space if you process a lot of files. As a note, the data I work with has fewer "features", more "users", and I use perl to process it.
First off, I would not recommend storing the data together as a sing... | How do I deal with large data similarity computation? | I have been doing a similar procedure on a regular basis lately. It isn't quick and it takes a decent chunk of HDD space if you process a lot of files. As a note, the data I work with has fewer "fea | How do I deal with large data similarity computation?
I have been doing a similar procedure on a regular basis lately. It isn't quick and it takes a decent chunk of HDD space if you process a lot of files. As a note, the data I work with has fewer "features", more "users", and I use perl to process it.
First off, I w... | How do I deal with large data similarity computation?
I have been doing a similar procedure on a regular basis lately. It isn't quick and it takes a decent chunk of HDD space if you process a lot of files. As a note, the data I work with has fewer "fea |
50,072 | How do I deal with large data similarity computation? | What you're talking about is a "Vector Space Model" of information retrieval. Wikipedia lists some programs which help with this - the one I'm most familiar with is Lucene.
This page describes their algorithm. The major points are that 1) you can invert your index, 2) you can look through indices in parallel and 3) you... | How do I deal with large data similarity computation? | What you're talking about is a "Vector Space Model" of information retrieval. Wikipedia lists some programs which help with this - the one I'm most familiar with is Lucene.
This page describes their a | How do I deal with large data similarity computation?
What you're talking about is a "Vector Space Model" of information retrieval. Wikipedia lists some programs which help with this - the one I'm most familiar with is Lucene.
This page describes their algorithm. The major points are that 1) you can invert your index, ... | How do I deal with large data similarity computation?
What you're talking about is a "Vector Space Model" of information retrieval. Wikipedia lists some programs which help with this - the one I'm most familiar with is Lucene.
This page describes their a |
50,073 | How do I deal with large data similarity computation? | You could try sorting your data by the total number of "1s" in each row (vector length). This would give you a space to start searching when you're given a new user. For example, if the new user has a length of 1342, you could check all entries with lengths plus or minus 500. You can do this efficiently if the data are... | How do I deal with large data similarity computation? | You could try sorting your data by the total number of "1s" in each row (vector length). This would give you a space to start searching when you're given a new user. For example, if the new user has a | How do I deal with large data similarity computation?
You could try sorting your data by the total number of "1s" in each row (vector length). This would give you a space to start searching when you're given a new user. For example, if the new user has a length of 1342, you could check all entries with lengths plus or ... | How do I deal with large data similarity computation?
You could try sorting your data by the total number of "1s" in each row (vector length). This would give you a space to start searching when you're given a new user. For example, if the new user has a |
50,074 | How do I deal with large data similarity computation? | There are a number of non-euclidean distance measures, some of which are specifically used for binary data. Two distance-measures are:
1) Simple Matching Coefficient;
2) Jaccard Coefficient.
They have some different strengths and weaknesses. In the simple matching coefficient, mutual absences and presences contribute t... | How do I deal with large data similarity computation? | There are a number of non-euclidean distance measures, some of which are specifically used for binary data. Two distance-measures are:
1) Simple Matching Coefficient;
2) Jaccard Coefficient.
They have | How do I deal with large data similarity computation?
There are a number of non-euclidean distance measures, some of which are specifically used for binary data. Two distance-measures are:
1) Simple Matching Coefficient;
2) Jaccard Coefficient.
They have some different strengths and weaknesses. In the simple matching c... | How do I deal with large data similarity computation?
There are a number of non-euclidean distance measures, some of which are specifically used for binary data. Two distance-measures are:
1) Simple Matching Coefficient;
2) Jaccard Coefficient.
They have |
50,075 | RandomForestClassifier Parameter Optimization | To answer your second question, why accuracy tails off, I put together an example in R that should resemble your problem. I generated ~50 good predictors and ~1000 bad predictors (that are just randomly assigned dummy variables). I start by increasing the number of good predictors, and then after maxing those out I inc... | RandomForestClassifier Parameter Optimization | To answer your second question, why accuracy tails off, I put together an example in R that should resemble your problem. I generated ~50 good predictors and ~1000 bad predictors (that are just random | RandomForestClassifier Parameter Optimization
To answer your second question, why accuracy tails off, I put together an example in R that should resemble your problem. I generated ~50 good predictors and ~1000 bad predictors (that are just randomly assigned dummy variables). I start by increasing the number of good pre... | RandomForestClassifier Parameter Optimization
To answer your second question, why accuracy tails off, I put together an example in R that should resemble your problem. I generated ~50 good predictors and ~1000 bad predictors (that are just random |
50,076 | RandomForestClassifier Parameter Optimization | There is few unorthodox (but not wrong) steps in your approach:
1) Usually, one does not use feature selection in sequence with classification. RF are usually used for one or for the other. It is not clear from the question whether you use the first step to select the "good" words and only use them in the second step,... | RandomForestClassifier Parameter Optimization | There is few unorthodox (but not wrong) steps in your approach:
1) Usually, one does not use feature selection in sequence with classification. RF are usually used for one or for the other. It is not | RandomForestClassifier Parameter Optimization
There is few unorthodox (but not wrong) steps in your approach:
1) Usually, one does not use feature selection in sequence with classification. RF are usually used for one or for the other. It is not clear from the question whether you use the first step to select the "goo... | RandomForestClassifier Parameter Optimization
There is few unorthodox (but not wrong) steps in your approach:
1) Usually, one does not use feature selection in sequence with classification. RF are usually used for one or for the other. It is not |
50,077 | RandomForestClassifier Parameter Optimization | "Number of Features" parameter holds for the amount of randomness in the Random Forest (the fewer features you choose the more random your forest is).
If you have lots of "relevant" features, you can choose small feature set to build each tree. But if only a fraction of your features is relevant, you better choose mor... | RandomForestClassifier Parameter Optimization | "Number of Features" parameter holds for the amount of randomness in the Random Forest (the fewer features you choose the more random your forest is).
If you have lots of "relevant" features, you can | RandomForestClassifier Parameter Optimization
"Number of Features" parameter holds for the amount of randomness in the Random Forest (the fewer features you choose the more random your forest is).
If you have lots of "relevant" features, you can choose small feature set to build each tree. But if only a fraction of yo... | RandomForestClassifier Parameter Optimization
"Number of Features" parameter holds for the amount of randomness in the Random Forest (the fewer features you choose the more random your forest is).
If you have lots of "relevant" features, you can |
50,078 | 1 control group vs. 2 treatments: one ANOVA or two t-tests? | You don't have to run an ANOVA first, but most people do out of habit. (Whether reviewers will give you a hard time about not having done so is a separate issue.) Note that the original Dunnett's test required that the conditions have equal $n$s. The test has since been generalized, so it is fine if you do not have ... | 1 control group vs. 2 treatments: one ANOVA or two t-tests? | You don't have to run an ANOVA first, but most people do out of habit. (Whether reviewers will give you a hard time about not having done so is a separate issue.) Note that the original Dunnett's te | 1 control group vs. 2 treatments: one ANOVA or two t-tests?
You don't have to run an ANOVA first, but most people do out of habit. (Whether reviewers will give you a hard time about not having done so is a separate issue.) Note that the original Dunnett's test required that the conditions have equal $n$s. The test h... | 1 control group vs. 2 treatments: one ANOVA or two t-tests?
You don't have to run an ANOVA first, but most people do out of habit. (Whether reviewers will give you a hard time about not having done so is a separate issue.) Note that the original Dunnett's te |
50,079 | 1 control group vs. 2 treatments: one ANOVA or two t-tests? | If you have three groups you should do an ANOVA (after checking assumptions of normality etc of course) which will test if the three groups differ overall. If that is the case you can then either do contrasts or post-hoc tests to test your hypotheses directly, e.g. does group 1 differ from group 2. How to do contrasts ... | 1 control group vs. 2 treatments: one ANOVA or two t-tests? | If you have three groups you should do an ANOVA (after checking assumptions of normality etc of course) which will test if the three groups differ overall. If that is the case you can then either do c | 1 control group vs. 2 treatments: one ANOVA or two t-tests?
If you have three groups you should do an ANOVA (after checking assumptions of normality etc of course) which will test if the three groups differ overall. If that is the case you can then either do contrasts or post-hoc tests to test your hypotheses directly,... | 1 control group vs. 2 treatments: one ANOVA or two t-tests?
If you have three groups you should do an ANOVA (after checking assumptions of normality etc of course) which will test if the three groups differ overall. If that is the case you can then either do c |
50,080 | Is MLE more efficient than Moment method? | I just wanted to chime in with a story. Last Joint Statistical Meetings, I saw Donald Rubin speak after a few presentations at a causal inference session. He started poking fun at the presenters because their methods were based on inverse probability weighting schemes (resembling the Horvitz-Thompson estimator in sampl... | Is MLE more efficient than Moment method? | I just wanted to chime in with a story. Last Joint Statistical Meetings, I saw Donald Rubin speak after a few presentations at a causal inference session. He started poking fun at the presenters becau | Is MLE more efficient than Moment method?
I just wanted to chime in with a story. Last Joint Statistical Meetings, I saw Donald Rubin speak after a few presentations at a causal inference session. He started poking fun at the presenters because their methods were based on inverse probability weighting schemes (resembli... | Is MLE more efficient than Moment method?
I just wanted to chime in with a story. Last Joint Statistical Meetings, I saw Donald Rubin speak after a few presentations at a causal inference session. He started poking fun at the presenters becau |
50,081 | Is MLE more efficient than Moment method? | Percentile estimates will not have a normal distribution, even asymptotically. Since you know your data are normal, why not consider a tolerance interval. It will not contain the 99.5 and .05 percentiles, per se, but you can set one up to cover 99% of the possible values with X% confidence (adjustible). If your goal is... | Is MLE more efficient than Moment method? | Percentile estimates will not have a normal distribution, even asymptotically. Since you know your data are normal, why not consider a tolerance interval. It will not contain the 99.5 and .05 percenti | Is MLE more efficient than Moment method?
Percentile estimates will not have a normal distribution, even asymptotically. Since you know your data are normal, why not consider a tolerance interval. It will not contain the 99.5 and .05 percentiles, per se, but you can set one up to cover 99% of the possible values with X... | Is MLE more efficient than Moment method?
Percentile estimates will not have a normal distribution, even asymptotically. Since you know your data are normal, why not consider a tolerance interval. It will not contain the 99.5 and .05 percenti |
50,082 | State of the art: Non-parametric density estimation with a boundary and data clumped near zero [duplicate] | If you know the range of your data, you can use
the inverse probit transformation. On a couple
of examples, the fit looked very satisfying visually.
This approach is explained in more detail in a clear paper[1]. I think there
should be an R implementation but I couldn't find it
(perhaps you can contact the author)... | State of the art: Non-parametric density estimation with a boundary and data clumped near zero [dupl | If you know the range of your data, you can use
the inverse probit transformation. On a couple
of examples, the fit looked very satisfying visually.
This approach is explained in more detail in a c | State of the art: Non-parametric density estimation with a boundary and data clumped near zero [duplicate]
If you know the range of your data, you can use
the inverse probit transformation. On a couple
of examples, the fit looked very satisfying visually.
This approach is explained in more detail in a clear paper[1]... | State of the art: Non-parametric density estimation with a boundary and data clumped near zero [dupl
If you know the range of your data, you can use
the inverse probit transformation. On a couple
of examples, the fit looked very satisfying visually.
This approach is explained in more detail in a c |
50,083 | Why describe a sample as i.i.d.? | You have to recall a random variable is just a function that maps an event space into a probability space. For a single realization from a single observation, it may seem redundant to consider that such mappings are defined similarly over $n=1000$ replications. However, the statistical experiment is based on some summa... | Why describe a sample as i.i.d.? | You have to recall a random variable is just a function that maps an event space into a probability space. For a single realization from a single observation, it may seem redundant to consider that su | Why describe a sample as i.i.d.?
You have to recall a random variable is just a function that maps an event space into a probability space. For a single realization from a single observation, it may seem redundant to consider that such mappings are defined similarly over $n=1000$ replications. However, the statistical ... | Why describe a sample as i.i.d.?
You have to recall a random variable is just a function that maps an event space into a probability space. For a single realization from a single observation, it may seem redundant to consider that su |
50,084 | GLM with Temporal Data | I'm still learning a lot in this area, but since you don't have an answer yet, my thoughts are...
The correlation structure you specify in the various functions that allow it (gls, lme, etc) are for within-group correlation, so I don't believe AR1 is correct since the multiple measurements are within the same timeframe... | GLM with Temporal Data | I'm still learning a lot in this area, but since you don't have an answer yet, my thoughts are...
The correlation structure you specify in the various functions that allow it (gls, lme, etc) are for w | GLM with Temporal Data
I'm still learning a lot in this area, but since you don't have an answer yet, my thoughts are...
The correlation structure you specify in the various functions that allow it (gls, lme, etc) are for within-group correlation, so I don't believe AR1 is correct since the multiple measurements are wi... | GLM with Temporal Data
I'm still learning a lot in this area, but since you don't have an answer yet, my thoughts are...
The correlation structure you specify in the various functions that allow it (gls, lme, etc) are for w |
50,085 | How to generate from the copula by inverse conditional cdf function of the copula? | A typical approach (see e.g. Nelsen 2006, p. 41) is to sample two independent uniform distributed random vectors $u$ and $y$ of the desired sample length. The conditional copula $C_u$ (conditioned on $u$) is given through the partial derivative: $$ C_u(v) = \frac{\partial}{\partial u} C(u,v) $$
Hence, one needs to solv... | How to generate from the copula by inverse conditional cdf function of the copula? | A typical approach (see e.g. Nelsen 2006, p. 41) is to sample two independent uniform distributed random vectors $u$ and $y$ of the desired sample length. The conditional copula $C_u$ (conditioned on | How to generate from the copula by inverse conditional cdf function of the copula?
A typical approach (see e.g. Nelsen 2006, p. 41) is to sample two independent uniform distributed random vectors $u$ and $y$ of the desired sample length. The conditional copula $C_u$ (conditioned on $u$) is given through the partial der... | How to generate from the copula by inverse conditional cdf function of the copula?
A typical approach (see e.g. Nelsen 2006, p. 41) is to sample two independent uniform distributed random vectors $u$ and $y$ of the desired sample length. The conditional copula $C_u$ (conditioned on |
50,086 | Joint pdf of a continuous and a discrete rv | Sheldon, Sheldon. How comes that you have to ask a question about math to people like us?
In survival analysis, your setting is called "competing risk". The joint distribution of the earliest failure time and the type of failure is fully described by the so called "cumulative incidence function" (it even allows for cen... | Joint pdf of a continuous and a discrete rv | Sheldon, Sheldon. How comes that you have to ask a question about math to people like us?
In survival analysis, your setting is called "competing risk". The joint distribution of the earliest failure | Joint pdf of a continuous and a discrete rv
Sheldon, Sheldon. How comes that you have to ask a question about math to people like us?
In survival analysis, your setting is called "competing risk". The joint distribution of the earliest failure time and the type of failure is fully described by the so called "cumulative... | Joint pdf of a continuous and a discrete rv
Sheldon, Sheldon. How comes that you have to ask a question about math to people like us?
In survival analysis, your setting is called "competing risk". The joint distribution of the earliest failure |
50,087 | Joint pdf of a continuous and a discrete rv | In simplistic terms, there is no such thing as a joint density of a continuous random variable and a discrete random variable because all the probability mass lies
on two straight lines ($v=0$ and $v=1$) and on these lines, the joint
density, being the probability mass per unit area, is infinite. On the other
hand, th... | Joint pdf of a continuous and a discrete rv | In simplistic terms, there is no such thing as a joint density of a continuous random variable and a discrete random variable because all the probability mass lies
on two straight lines ($v=0$ and $v= | Joint pdf of a continuous and a discrete rv
In simplistic terms, there is no such thing as a joint density of a continuous random variable and a discrete random variable because all the probability mass lies
on two straight lines ($v=0$ and $v=1$) and on these lines, the joint
density, being the probability mass per u... | Joint pdf of a continuous and a discrete rv
In simplistic terms, there is no such thing as a joint density of a continuous random variable and a discrete random variable because all the probability mass lies
on two straight lines ($v=0$ and $v= |
50,088 | Joint pdf of a continuous and a discrete rv | What you have here is a mixture model, specifically a mixture of exponentials. If I understand your problem setup correctly, I believe what you're looking for looks something like this:
$$
u \sim f(x) =
\begin{cases}
f_{Y_1}(x), & V=1 \\
f_{Y_2}(x), & V=0
\end{cases}
$$
or alternatively
$$u \sim f(x) = \theta f_{Y_1}(x... | Joint pdf of a continuous and a discrete rv | What you have here is a mixture model, specifically a mixture of exponentials. If I understand your problem setup correctly, I believe what you're looking for looks something like this:
$$
u \sim f(x) | Joint pdf of a continuous and a discrete rv
What you have here is a mixture model, specifically a mixture of exponentials. If I understand your problem setup correctly, I believe what you're looking for looks something like this:
$$
u \sim f(x) =
\begin{cases}
f_{Y_1}(x), & V=1 \\
f_{Y_2}(x), & V=0
\end{cases}
$$
or al... | Joint pdf of a continuous and a discrete rv
What you have here is a mixture model, specifically a mixture of exponentials. If I understand your problem setup correctly, I believe what you're looking for looks something like this:
$$
u \sim f(x) |
50,089 | Duration analysis of unemployment | First, the incidental parameter problem is pretty easy to solve in a discrete duration model. As long as you are willing to assume a logistic form for your model, you can eliminate the incidental parameters via a clever conditioning argument. The usual cite in economics is Chamberlain (1980, Rev Econ Stud). If you p... | Duration analysis of unemployment | First, the incidental parameter problem is pretty easy to solve in a discrete duration model. As long as you are willing to assume a logistic form for your model, you can eliminate the incidental par | Duration analysis of unemployment
First, the incidental parameter problem is pretty easy to solve in a discrete duration model. As long as you are willing to assume a logistic form for your model, you can eliminate the incidental parameters via a clever conditioning argument. The usual cite in economics is Chamberlai... | Duration analysis of unemployment
First, the incidental parameter problem is pretty easy to solve in a discrete duration model. As long as you are willing to assume a logistic form for your model, you can eliminate the incidental par |
50,090 | Minimum Sample Size Required to Estimate the Probability $P(X \le c)$ for a Constant $c$ (Given a Confidence Level & Confidence Interval) | The Dvoretzky-Kiefer-Wolfowitz inequality can be used here. The required sample size $b$ (I'm using $b$ to distinguish it from $n$ because you already set your population size as $n$ in the problem statement) is determined by $$b \geq \left( {1 \over 2 \epsilon^2 } \right) \mathrm{ln} \left( {2 \over \alpha} \right),$$... | Minimum Sample Size Required to Estimate the Probability $P(X \le c)$ for a Constant $c$ (Given a Co | The Dvoretzky-Kiefer-Wolfowitz inequality can be used here. The required sample size $b$ (I'm using $b$ to distinguish it from $n$ because you already set your population size as $n$ in the problem st | Minimum Sample Size Required to Estimate the Probability $P(X \le c)$ for a Constant $c$ (Given a Confidence Level & Confidence Interval)
The Dvoretzky-Kiefer-Wolfowitz inequality can be used here. The required sample size $b$ (I'm using $b$ to distinguish it from $n$ because you already set your population size as $n$... | Minimum Sample Size Required to Estimate the Probability $P(X \le c)$ for a Constant $c$ (Given a Co
The Dvoretzky-Kiefer-Wolfowitz inequality can be used here. The required sample size $b$ (I'm using $b$ to distinguish it from $n$ because you already set your population size as $n$ in the problem st |
50,091 | Maximum likelihood estimate: Is this possible to solve? | The second problem (d), where the mean is equal to the variance is discussed on pp. 53 of Asymptotic Theory of Statistics and Probability by Anirban DasGupta (2008). The $\mathcal{N}(\theta, \theta)$ distribution, the normal distribution with an equal mean and variance can be seen as a continuous analog of the Poisson ... | Maximum likelihood estimate: Is this possible to solve? | The second problem (d), where the mean is equal to the variance is discussed on pp. 53 of Asymptotic Theory of Statistics and Probability by Anirban DasGupta (2008). The $\mathcal{N}(\theta, \theta)$ | Maximum likelihood estimate: Is this possible to solve?
The second problem (d), where the mean is equal to the variance is discussed on pp. 53 of Asymptotic Theory of Statistics and Probability by Anirban DasGupta (2008). The $\mathcal{N}(\theta, \theta)$ distribution, the normal distribution with an equal mean and var... | Maximum likelihood estimate: Is this possible to solve?
The second problem (d), where the mean is equal to the variance is discussed on pp. 53 of Asymptotic Theory of Statistics and Probability by Anirban DasGupta (2008). The $\mathcal{N}(\theta, \theta)$ |
50,092 | Using KNN for prediction, how should I normalize my data? | I think that depends on the data. If you know your feature is bounded, you could scale it to $[0,1]$. If it's binary I guess $\{0,1\}$ is a good choice, perhaps $\{-1,1\}$. Now, if it's unbounded, the standardization to $\text Z$-scores $\overline x = 0$, $\sigma=1$ is a reasonable choice. | Using KNN for prediction, how should I normalize my data? | I think that depends on the data. If you know your feature is bounded, you could scale it to $[0,1]$. If it's binary I guess $\{0,1\}$ is a good choice, perhaps $\{-1,1\}$. Now, if it's unbounded, the | Using KNN for prediction, how should I normalize my data?
I think that depends on the data. If you know your feature is bounded, you could scale it to $[0,1]$. If it's binary I guess $\{0,1\}$ is a good choice, perhaps $\{-1,1\}$. Now, if it's unbounded, the standardization to $\text Z$-scores $\overline x = 0$, $\sigm... | Using KNN for prediction, how should I normalize my data?
I think that depends on the data. If you know your feature is bounded, you could scale it to $[0,1]$. If it's binary I guess $\{0,1\}$ is a good choice, perhaps $\{-1,1\}$. Now, if it's unbounded, the |
50,093 | Using KNN for prediction, how should I normalize my data? | Similar to K-means, KNN uses distance measure. Therefore
It is better to normalize features. If not, the features with larger values will be dominant.
If you have too many discrete variables and use dummy coding, distance measures would not work well.
Also, I think my answers for K-means would answer your question of... | Using KNN for prediction, how should I normalize my data? | Similar to K-means, KNN uses distance measure. Therefore
It is better to normalize features. If not, the features with larger values will be dominant.
If you have too many discrete variables and use | Using KNN for prediction, how should I normalize my data?
Similar to K-means, KNN uses distance measure. Therefore
It is better to normalize features. If not, the features with larger values will be dominant.
If you have too many discrete variables and use dummy coding, distance measures would not work well.
Also, I ... | Using KNN for prediction, how should I normalize my data?
Similar to K-means, KNN uses distance measure. Therefore
It is better to normalize features. If not, the features with larger values will be dominant.
If you have too many discrete variables and use |
50,094 | What's the probability that as I roll dice I'll see a sum of $7$ on them before I see a sum of $8$? | Question 1
Why does the author say
We could assume that the sample space $S$ contains all sequences of outcomes that terminate as
soon as either the sum $T = 7$ or the sum $T = 8$ is obtained. Then we could find the
sum of the probabilities of all the sequences that terminate when the value $T = 7$ is
obtained... | What's the probability that as I roll dice I'll see a sum of $7$ on them before I see a sum of $8$? | Question 1
Why does the author say
We could assume that the sample space $S$ contains all sequences of outcomes that terminate as
soon as either the sum $T = 7$ or the sum $T = 8$ is obtained. Th | What's the probability that as I roll dice I'll see a sum of $7$ on them before I see a sum of $8$?
Question 1
Why does the author say
We could assume that the sample space $S$ contains all sequences of outcomes that terminate as
soon as either the sum $T = 7$ or the sum $T = 8$ is obtained. Then we could find the... | What's the probability that as I roll dice I'll see a sum of $7$ on them before I see a sum of $8$?
Question 1
Why does the author say
We could assume that the sample space $S$ contains all sequences of outcomes that terminate as
soon as either the sum $T = 7$ or the sum $T = 8$ is obtained. Th |
50,095 | What's the probability that as I roll dice I'll see a sum of $7$ on them before I see a sum of $8$? | Is a definition of what the probability of an event $A$ is e.g.
$$
P(A) = \frac{\text{number of ways $A$ can happen}}{\text{total number of things that can happen}}
$$ Like when you try to figure out what is the probability that you roll a two given that you know you rolled an even number is $1/3$ since there is jus... | What's the probability that as I roll dice I'll see a sum of $7$ on them before I see a sum of $8$? | Is a definition of what the probability of an event $A$ is e.g.
$$
P(A) = \frac{\text{number of ways $A$ can happen}}{\text{total number of things that can happen}}
$$ Like when you try to figure o | What's the probability that as I roll dice I'll see a sum of $7$ on them before I see a sum of $8$?
Is a definition of what the probability of an event $A$ is e.g.
$$
P(A) = \frac{\text{number of ways $A$ can happen}}{\text{total number of things that can happen}}
$$ Like when you try to figure out what is the proba... | What's the probability that as I roll dice I'll see a sum of $7$ on them before I see a sum of $8$?
Is a definition of what the probability of an event $A$ is e.g.
$$
P(A) = \frac{\text{number of ways $A$ can happen}}{\text{total number of things that can happen}}
$$ Like when you try to figure o |
50,096 | How can I combine data from 2 separate experiments? | Effects should be different across experiments, and so should variances. That's the nature of sampling. What you have is just different samples being different. There's no way to know which estimate of variance is closer to true value, or even guess at it with the information you've given and equal N's in the samples. ... | How can I combine data from 2 separate experiments? | Effects should be different across experiments, and so should variances. That's the nature of sampling. What you have is just different samples being different. There's no way to know which estimate o | How can I combine data from 2 separate experiments?
Effects should be different across experiments, and so should variances. That's the nature of sampling. What you have is just different samples being different. There's no way to know which estimate of variance is closer to true value, or even guess at it with the inf... | How can I combine data from 2 separate experiments?
Effects should be different across experiments, and so should variances. That's the nature of sampling. What you have is just different samples being different. There's no way to know which estimate o |
50,097 | How to rate successive predictions of the outcome of an event which are made while it is taking place? | What I am more interested in learning about are approaches that are specifically tailored to my scenario, i.e. which take into account the fact that these predictions are all made on the same outcome and each prediction is made with successively more information.
That's the key: for your predictor to be acceptable, it... | How to rate successive predictions of the outcome of an event which are made while it is taking plac | What I am more interested in learning about are approaches that are specifically tailored to my scenario, i.e. which take into account the fact that these predictions are all made on the same outcome | How to rate successive predictions of the outcome of an event which are made while it is taking place?
What I am more interested in learning about are approaches that are specifically tailored to my scenario, i.e. which take into account the fact that these predictions are all made on the same outcome and each predicti... | How to rate successive predictions of the outcome of an event which are made while it is taking plac
What I am more interested in learning about are approaches that are specifically tailored to my scenario, i.e. which take into account the fact that these predictions are all made on the same outcome |
50,098 | Back-propagation in Neural Nets with >2 hidden layers | This is just a simple computation of the partial derivative and observation, that the derivative on the layer $i$ (from top) can be fully computed using partial derivative for weights in layer $i-1$. This applies to any number of layers, but this leads to so called "vanishing gradient phenomenon" which is a reason for ... | Back-propagation in Neural Nets with >2 hidden layers | This is just a simple computation of the partial derivative and observation, that the derivative on the layer $i$ (from top) can be fully computed using partial derivative for weights in layer $i-1$. | Back-propagation in Neural Nets with >2 hidden layers
This is just a simple computation of the partial derivative and observation, that the derivative on the layer $i$ (from top) can be fully computed using partial derivative for weights in layer $i-1$. This applies to any number of layers, but this leads to so called ... | Back-propagation in Neural Nets with >2 hidden layers
This is just a simple computation of the partial derivative and observation, that the derivative on the layer $i$ (from top) can be fully computed using partial derivative for weights in layer $i-1$. |
50,099 | How do you check the linearity of a multiple regression | Indeed the most common and easy way would be to use scatter plot of residual versus predicted value; a horizontal band of points indicates a linear relationship. | How do you check the linearity of a multiple regression | Indeed the most common and easy way would be to use scatter plot of residual versus predicted value; a horizontal band of points indicates a linear relationship. | How do you check the linearity of a multiple regression
Indeed the most common and easy way would be to use scatter plot of residual versus predicted value; a horizontal band of points indicates a linear relationship. | How do you check the linearity of a multiple regression
Indeed the most common and easy way would be to use scatter plot of residual versus predicted value; a horizontal band of points indicates a linear relationship. |
50,100 | Cross validation for lasso logistic regression | The short answer is, its up to you, depending on your interest. In the past I have used AIC for Lasso.
However it sounds like you are using this model for prediction, and thus using the mis-classification rate is a good idea. However misclassification can be categorized in many ways. Are you interested in the the absol... | Cross validation for lasso logistic regression | The short answer is, its up to you, depending on your interest. In the past I have used AIC for Lasso.
However it sounds like you are using this model for prediction, and thus using the mis-classifica | Cross validation for lasso logistic regression
The short answer is, its up to you, depending on your interest. In the past I have used AIC for Lasso.
However it sounds like you are using this model for prediction, and thus using the mis-classification rate is a good idea. However misclassification can be categorized in... | Cross validation for lasso logistic regression
The short answer is, its up to you, depending on your interest. In the past I have used AIC for Lasso.
However it sounds like you are using this model for prediction, and thus using the mis-classifica |
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