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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37,301 | Calculating Probability of x1 > x2 | Your problem may sound easy, but it's surprisingly complicated.
In order to assess the probability that Rachel's CPGA (call it $y_1$) is larger than Tobias' ($y_2$), while knowing what their hgpa, sat and ltrs-scores are, is the same as writing $P(y_2 - y_1 > 0 | X)$, where $X$ are their scores. Because we can write $... | Calculating Probability of x1 > x2 | Your problem may sound easy, but it's surprisingly complicated.
In order to assess the probability that Rachel's CPGA (call it $y_1$) is larger than Tobias' ($y_2$), while knowing what their hgpa, sat | Calculating Probability of x1 > x2
Your problem may sound easy, but it's surprisingly complicated.
In order to assess the probability that Rachel's CPGA (call it $y_1$) is larger than Tobias' ($y_2$), while knowing what their hgpa, sat and ltrs-scores are, is the same as writing $P(y_2 - y_1 > 0 | X)$, where $X$ are t... | Calculating Probability of x1 > x2
Your problem may sound easy, but it's surprisingly complicated.
In order to assess the probability that Rachel's CPGA (call it $y_1$) is larger than Tobias' ($y_2$), while knowing what their hgpa, sat |
37,302 | KL divergence bounds square of L1 norm | I also bumped into this passage recently! I'm not very familiar with probability/information theory, so I hope this makes sense and my notation is understandable; I tried for precision at the expense of brevity, but there's some notation in the book that I just don't know how to use precisely.
As far as I can tell, the... | KL divergence bounds square of L1 norm | I also bumped into this passage recently! I'm not very familiar with probability/information theory, so I hope this makes sense and my notation is understandable; I tried for precision at the expense | KL divergence bounds square of L1 norm
I also bumped into this passage recently! I'm not very familiar with probability/information theory, so I hope this makes sense and my notation is understandable; I tried for precision at the expense of brevity, but there's some notation in the book that I just don't know how to u... | KL divergence bounds square of L1 norm
I also bumped into this passage recently! I'm not very familiar with probability/information theory, so I hope this makes sense and my notation is understandable; I tried for precision at the expense |
37,303 | Multi categorical Dice loss? | Dice Loss (DL) for Multi-class:
Dice loss is a popular loss function for medical image segmentation which is a measure of overlap between the predicted sample and real sample. This measure ranges from 0 to 1 where a Dice score of 1 denotes the complete overlap as defined as follows
$Loss_{DL}\hspace{0.25em}=\hspace{0.... | Multi categorical Dice loss? | Dice Loss (DL) for Multi-class:
Dice loss is a popular loss function for medical image segmentation which is a measure of overlap between the predicted sample and real sample. This measure ranges fro | Multi categorical Dice loss?
Dice Loss (DL) for Multi-class:
Dice loss is a popular loss function for medical image segmentation which is a measure of overlap between the predicted sample and real sample. This measure ranges from 0 to 1 where a Dice score of 1 denotes the complete overlap as defined as follows
$Loss_{... | Multi categorical Dice loss?
Dice Loss (DL) for Multi-class:
Dice loss is a popular loss function for medical image segmentation which is a measure of overlap between the predicted sample and real sample. This measure ranges fro |
37,304 | Rao-Blackwell unbiased estimator binomial distribution | Update based on whuber's comment.
First some notation. Let $T_{-1} = \sum_{i=2}^nX_i$ and note that $T \sim Binom(nm, \theta)$ and $T_{-1} \sim Binom((n-1)m, \theta)$. Moreover, note that $X_1$ and $T_{-1}$ are independent.
\begin{align*}
\phi(T) &= E(X_1/m |T =t) \\
&= \frac{1}{m}E(X_1|T=t) \\
&= \frac{1}{m}\sum_{x=0}... | Rao-Blackwell unbiased estimator binomial distribution | Update based on whuber's comment.
First some notation. Let $T_{-1} = \sum_{i=2}^nX_i$ and note that $T \sim Binom(nm, \theta)$ and $T_{-1} \sim Binom((n-1)m, \theta)$. Moreover, note that $X_1$ and $T | Rao-Blackwell unbiased estimator binomial distribution
Update based on whuber's comment.
First some notation. Let $T_{-1} = \sum_{i=2}^nX_i$ and note that $T \sim Binom(nm, \theta)$ and $T_{-1} \sim Binom((n-1)m, \theta)$. Moreover, note that $X_1$ and $T_{-1}$ are independent.
\begin{align*}
\phi(T) &= E(X_1/m |T =t) ... | Rao-Blackwell unbiased estimator binomial distribution
Update based on whuber's comment.
First some notation. Let $T_{-1} = \sum_{i=2}^nX_i$ and note that $T \sim Binom(nm, \theta)$ and $T_{-1} \sim Binom((n-1)m, \theta)$. Moreover, note that $X_1$ and $T |
37,305 | Score function of bivariate/multivariate normal distribution | The problem is in the matrix differentiation. As the covariance matrix is symmetric, we have
$$
\frac{\partial l}{\partial \Sigma}=-\Sigma^{-1}+\frac{\operatorname{diag}(\Sigma^{-1})}{2}+\Sigma^{-1}(x-\mu)(x-\mu)'\Sigma^{-1}-\frac{\operatorname{diag}(\Sigma^{-1}(x-\mu)(x-\mu)'\Sigma^{-1})}{2}
$$
where $l$ is the log-li... | Score function of bivariate/multivariate normal distribution | The problem is in the matrix differentiation. As the covariance matrix is symmetric, we have
$$
\frac{\partial l}{\partial \Sigma}=-\Sigma^{-1}+\frac{\operatorname{diag}(\Sigma^{-1})}{2}+\Sigma^{-1}(x | Score function of bivariate/multivariate normal distribution
The problem is in the matrix differentiation. As the covariance matrix is symmetric, we have
$$
\frac{\partial l}{\partial \Sigma}=-\Sigma^{-1}+\frac{\operatorname{diag}(\Sigma^{-1})}{2}+\Sigma^{-1}(x-\mu)(x-\mu)'\Sigma^{-1}-\frac{\operatorname{diag}(\Sigma^{... | Score function of bivariate/multivariate normal distribution
The problem is in the matrix differentiation. As the covariance matrix is symmetric, we have
$$
\frac{\partial l}{\partial \Sigma}=-\Sigma^{-1}+\frac{\operatorname{diag}(\Sigma^{-1})}{2}+\Sigma^{-1}(x |
37,306 | How to dissuade laypeople from drawing inaccurate conclusions about their data? | I wish you had provided more details in your question, but I'm just going to answer it with whatever information you have provided.
I think it's unlikely that they will go back and actually peruse the "resources" you suggest, so you might be better off with reading about these yourself and trying to explain it them wi... | How to dissuade laypeople from drawing inaccurate conclusions about their data? | I wish you had provided more details in your question, but I'm just going to answer it with whatever information you have provided.
I think it's unlikely that they will go back and actually peruse th | How to dissuade laypeople from drawing inaccurate conclusions about their data?
I wish you had provided more details in your question, but I'm just going to answer it with whatever information you have provided.
I think it's unlikely that they will go back and actually peruse the "resources" you suggest, so you might ... | How to dissuade laypeople from drawing inaccurate conclusions about their data?
I wish you had provided more details in your question, but I'm just going to answer it with whatever information you have provided.
I think it's unlikely that they will go back and actually peruse th |
37,307 | Application of Machine Learning to the Automated Theorem Proving | Recent papers I know of are Deep Network Guided Proof Search and Deep Math. Both of these reduce the search-space of current non-ML based theorem-provers by suggesting the next premise or tactic to use, pruning the search tree. (Quite similar to how Alpha Zero still relies on traditional game-tree search, but heavily p... | Application of Machine Learning to the Automated Theorem Proving | Recent papers I know of are Deep Network Guided Proof Search and Deep Math. Both of these reduce the search-space of current non-ML based theorem-provers by suggesting the next premise or tactic to us | Application of Machine Learning to the Automated Theorem Proving
Recent papers I know of are Deep Network Guided Proof Search and Deep Math. Both of these reduce the search-space of current non-ML based theorem-provers by suggesting the next premise or tactic to use, pruning the search tree. (Quite similar to how Alpha... | Application of Machine Learning to the Automated Theorem Proving
Recent papers I know of are Deep Network Guided Proof Search and Deep Math. Both of these reduce the search-space of current non-ML based theorem-provers by suggesting the next premise or tactic to us |
37,308 | Application of Machine Learning to the Automated Theorem Proving | I'm sorry because of adding another answer, but I can't undelete my message, and I do not arrive to talk to admins.
This domain is related to automated theorem proving. But as far as I know there is no automated theorem prover powerfull enough to create such a proof.
The actual automated theorem provers use proposition... | Application of Machine Learning to the Automated Theorem Proving | I'm sorry because of adding another answer, but I can't undelete my message, and I do not arrive to talk to admins.
This domain is related to automated theorem proving. But as far as I know there is n | Application of Machine Learning to the Automated Theorem Proving
I'm sorry because of adding another answer, but I can't undelete my message, and I do not arrive to talk to admins.
This domain is related to automated theorem proving. But as far as I know there is no automated theorem prover powerfull enough to create s... | Application of Machine Learning to the Automated Theorem Proving
I'm sorry because of adding another answer, but I can't undelete my message, and I do not arrive to talk to admins.
This domain is related to automated theorem proving. But as far as I know there is n |
37,309 | Paradox of Poisson process with at least one event in the interval | I finally figured it out!
According to @combo's advice, I am going to use term "occurrence".
Surprisingly, the first part of the rationale for my intuition was almost correct.
If the observed occurrence was at time $t$ from the beginning of the interval, then it is enough to calculate probability that no occurrence occ... | Paradox of Poisson process with at least one event in the interval | I finally figured it out!
According to @combo's advice, I am going to use term "occurrence".
Surprisingly, the first part of the rationale for my intuition was almost correct.
If the observed occurren | Paradox of Poisson process with at least one event in the interval
I finally figured it out!
According to @combo's advice, I am going to use term "occurrence".
Surprisingly, the first part of the rationale for my intuition was almost correct.
If the observed occurrence was at time $t$ from the beginning of the interval... | Paradox of Poisson process with at least one event in the interval
I finally figured it out!
According to @combo's advice, I am going to use term "occurrence".
Surprisingly, the first part of the rationale for my intuition was almost correct.
If the observed occurren |
37,310 | Paradox of Poisson process with at least one event in the interval | A quick note on terminology to avoid confusing ourselves: I will refer to something happening at a particular time as an "occurence" rather than an "event" in order to avoid confusion with the more rigorous definition of an event as an element of the sample space.
Let's start from the definition of the Poisson countin... | Paradox of Poisson process with at least one event in the interval | A quick note on terminology to avoid confusing ourselves: I will refer to something happening at a particular time as an "occurence" rather than an "event" in order to avoid confusion with the more r | Paradox of Poisson process with at least one event in the interval
A quick note on terminology to avoid confusing ourselves: I will refer to something happening at a particular time as an "occurence" rather than an "event" in order to avoid confusion with the more rigorous definition of an event as an element of the s... | Paradox of Poisson process with at least one event in the interval
A quick note on terminology to avoid confusing ourselves: I will refer to something happening at a particular time as an "occurence" rather than an "event" in order to avoid confusion with the more r |
37,311 | Paradox of Poisson process with at least one event in the interval | Of your two ways of approaching the problem, the second one seems to be spot on. It is much more rigorous and makes complete sense to me.
However, I had a little more difficulty in understanding the first approach, which gave reason to believe that this is the source of your mistake.
First of all, out of curiosity,wh... | Paradox of Poisson process with at least one event in the interval | Of your two ways of approaching the problem, the second one seems to be spot on. It is much more rigorous and makes complete sense to me.
However, I had a little more difficulty in understanding the | Paradox of Poisson process with at least one event in the interval
Of your two ways of approaching the problem, the second one seems to be spot on. It is much more rigorous and makes complete sense to me.
However, I had a little more difficulty in understanding the first approach, which gave reason to believe that thi... | Paradox of Poisson process with at least one event in the interval
Of your two ways of approaching the problem, the second one seems to be spot on. It is much more rigorous and makes complete sense to me.
However, I had a little more difficulty in understanding the |
37,312 | Why logarithmic scale for hyper-parameter optimization? | ... because logarithmic scale enables us to search a bigger space quickly. In your SVM example, we do not know the range for the hyper-parameter. So, a quicker way is trying dramatically different values, say, 1, 10, 100, 1000, which come from a logarithmic scale.
In addition, I think log scale search is the first step... | Why logarithmic scale for hyper-parameter optimization? | ... because logarithmic scale enables us to search a bigger space quickly. In your SVM example, we do not know the range for the hyper-parameter. So, a quicker way is trying dramatically different val | Why logarithmic scale for hyper-parameter optimization?
... because logarithmic scale enables us to search a bigger space quickly. In your SVM example, we do not know the range for the hyper-parameter. So, a quicker way is trying dramatically different values, say, 1, 10, 100, 1000, which come from a logarithmic scale.... | Why logarithmic scale for hyper-parameter optimization?
... because logarithmic scale enables us to search a bigger space quickly. In your SVM example, we do not know the range for the hyper-parameter. So, a quicker way is trying dramatically different val |
37,313 | Can something be "very statistically significant"? [duplicate] | Significance testing has two different interpretations. The Neyman-Pearson interpretation is that a result is significant, or it is not significant, that is all that can be said. That is all you can say. The Fisher tradition is that a p-value is a representation of the strength of evidence against the null hypothesis -... | Can something be "very statistically significant"? [duplicate] | Significance testing has two different interpretations. The Neyman-Pearson interpretation is that a result is significant, or it is not significant, that is all that can be said. That is all you can s | Can something be "very statistically significant"? [duplicate]
Significance testing has two different interpretations. The Neyman-Pearson interpretation is that a result is significant, or it is not significant, that is all that can be said. That is all you can say. The Fisher tradition is that a p-value is a represent... | Can something be "very statistically significant"? [duplicate]
Significance testing has two different interpretations. The Neyman-Pearson interpretation is that a result is significant, or it is not significant, that is all that can be said. That is all you can s |
37,314 | Can something be "very statistically significant"? [duplicate] | if the p-value is around 0.05, we can say it is marginally significant, but p-value is very small (ex: 0.0006), then we can say it is statistically significant. I am not sure, you can use the term "very significant". | Can something be "very statistically significant"? [duplicate] | if the p-value is around 0.05, we can say it is marginally significant, but p-value is very small (ex: 0.0006), then we can say it is statistically significant. I am not sure, you can use the term "ve | Can something be "very statistically significant"? [duplicate]
if the p-value is around 0.05, we can say it is marginally significant, but p-value is very small (ex: 0.0006), then we can say it is statistically significant. I am not sure, you can use the term "very significant". | Can something be "very statistically significant"? [duplicate]
if the p-value is around 0.05, we can say it is marginally significant, but p-value is very small (ex: 0.0006), then we can say it is statistically significant. I am not sure, you can use the term "ve |
37,315 | What is the confidence interval of a p-value? | The problem is that a p value is not an estimate of a parameter so the idea of a confidence interval does not apply. It also does not make sense to talk about the uncertainty surrounding a p value. The p value is certain; the conclusion you draw from it is not. | What is the confidence interval of a p-value? | The problem is that a p value is not an estimate of a parameter so the idea of a confidence interval does not apply. It also does not make sense to talk about the uncertainty surrounding a p value. Th | What is the confidence interval of a p-value?
The problem is that a p value is not an estimate of a parameter so the idea of a confidence interval does not apply. It also does not make sense to talk about the uncertainty surrounding a p value. The p value is certain; the conclusion you draw from it is not. | What is the confidence interval of a p-value?
The problem is that a p value is not an estimate of a parameter so the idea of a confidence interval does not apply. It also does not make sense to talk about the uncertainty surrounding a p value. Th |
37,316 | Which variance estimate to use for a Wald test? | Either approach is legitimate, with both leading to the same asymptotic null distribution of the statistic.
$\sqrt{n}(\hat{\theta}_n - \theta_0) \rightarrow_d N(0, i(\theta_0)^{-1})$ implies that $\hat{\theta}_n \to_p \theta_0$ so that the continuous mapping theorem (CMT) yields that $i(\hat{\theta}_n) \to_p i(\theta_0... | Which variance estimate to use for a Wald test? | Either approach is legitimate, with both leading to the same asymptotic null distribution of the statistic.
$\sqrt{n}(\hat{\theta}_n - \theta_0) \rightarrow_d N(0, i(\theta_0)^{-1})$ implies that $\ha | Which variance estimate to use for a Wald test?
Either approach is legitimate, with both leading to the same asymptotic null distribution of the statistic.
$\sqrt{n}(\hat{\theta}_n - \theta_0) \rightarrow_d N(0, i(\theta_0)^{-1})$ implies that $\hat{\theta}_n \to_p \theta_0$ so that the continuous mapping theorem (CMT)... | Which variance estimate to use for a Wald test?
Either approach is legitimate, with both leading to the same asymptotic null distribution of the statistic.
$\sqrt{n}(\hat{\theta}_n - \theta_0) \rightarrow_d N(0, i(\theta_0)^{-1})$ implies that $\ha |
37,317 | Regression methods for predicting rank | From what I can tell, the rank-based estimation this paper is referring to is slightly different than what you're interested in. Note that least-squares estimation is based on the idea that $\boldsymbol \beta$ should be chosen to minimize $||\boldsymbol y - \boldsymbol X \boldsymbol \beta||^2$. This isn't suitable in y... | Regression methods for predicting rank | From what I can tell, the rank-based estimation this paper is referring to is slightly different than what you're interested in. Note that least-squares estimation is based on the idea that $\boldsymb | Regression methods for predicting rank
From what I can tell, the rank-based estimation this paper is referring to is slightly different than what you're interested in. Note that least-squares estimation is based on the idea that $\boldsymbol \beta$ should be chosen to minimize $||\boldsymbol y - \boldsymbol X \boldsymb... | Regression methods for predicting rank
From what I can tell, the rank-based estimation this paper is referring to is slightly different than what you're interested in. Note that least-squares estimation is based on the idea that $\boldsymb |
37,318 | Mathematical justification for using recurrent neural networks over feed-forward networks | I don't think this will be a very satisfying answer, because it's somewhat of a proof by definition, but I believe it is correct nonetheless (albeit not very mathematical).
Can anyone provide an example of families of functions which can't be
captured by Feed-forward but can be well approximated by RNNs?
No. At lea... | Mathematical justification for using recurrent neural networks over feed-forward networks | I don't think this will be a very satisfying answer, because it's somewhat of a proof by definition, but I believe it is correct nonetheless (albeit not very mathematical).
Can anyone provide an exam | Mathematical justification for using recurrent neural networks over feed-forward networks
I don't think this will be a very satisfying answer, because it's somewhat of a proof by definition, but I believe it is correct nonetheless (albeit not very mathematical).
Can anyone provide an example of families of functions w... | Mathematical justification for using recurrent neural networks over feed-forward networks
I don't think this will be a very satisfying answer, because it's somewhat of a proof by definition, but I believe it is correct nonetheless (albeit not very mathematical).
Can anyone provide an exam |
37,319 | RNNs for Sparse Time Series Data | This depends a bit on whether interpolating between points to infill missing data points makes sense, i.e. is there a high correlation between points or are they completely random at each minute reading. If they are correlated then filling them in with even time intervals is probably the way to go. If the values are ra... | RNNs for Sparse Time Series Data | This depends a bit on whether interpolating between points to infill missing data points makes sense, i.e. is there a high correlation between points or are they completely random at each minute readi | RNNs for Sparse Time Series Data
This depends a bit on whether interpolating between points to infill missing data points makes sense, i.e. is there a high correlation between points or are they completely random at each minute reading. If they are correlated then filling them in with even time intervals is probably th... | RNNs for Sparse Time Series Data
This depends a bit on whether interpolating between points to infill missing data points makes sense, i.e. is there a high correlation between points or are they completely random at each minute readi |
37,320 | Do I need to do regularization if I have already used early stopping? | Logically the answer is no: since early stopping is an alternative to L2 regularization, and used mainly to be faster than regularization, it is not meant to be used with a regularized cost function.
L1 regularization is used for a different purpose and I think that early stopping is not meant to be equivalent to L1 re... | Do I need to do regularization if I have already used early stopping? | Logically the answer is no: since early stopping is an alternative to L2 regularization, and used mainly to be faster than regularization, it is not meant to be used with a regularized cost function.
| Do I need to do regularization if I have already used early stopping?
Logically the answer is no: since early stopping is an alternative to L2 regularization, and used mainly to be faster than regularization, it is not meant to be used with a regularized cost function.
L1 regularization is used for a different purpose ... | Do I need to do regularization if I have already used early stopping?
Logically the answer is no: since early stopping is an alternative to L2 regularization, and used mainly to be faster than regularization, it is not meant to be used with a regularized cost function.
|
37,321 | Do I need to do regularization if I have already used early stopping? | You don't specify on what you're considering early stopping vs. regularization, but, in general, I think that early stopping is not necessarily a substitute for l1 regularization.
Consider partial least squares, for example, with early stopping. PLS can be viewed as optimizing the gradient out of a finite set of gradie... | Do I need to do regularization if I have already used early stopping? | You don't specify on what you're considering early stopping vs. regularization, but, in general, I think that early stopping is not necessarily a substitute for l1 regularization.
Consider partial lea | Do I need to do regularization if I have already used early stopping?
You don't specify on what you're considering early stopping vs. regularization, but, in general, I think that early stopping is not necessarily a substitute for l1 regularization.
Consider partial least squares, for example, with early stopping. PLS ... | Do I need to do regularization if I have already used early stopping?
You don't specify on what you're considering early stopping vs. regularization, but, in general, I think that early stopping is not necessarily a substitute for l1 regularization.
Consider partial lea |
37,322 | Reference to learn how to interpret learning curves of deep convolutional neural networks | 2 things:
You should probably switch your 50/50 train/validation repartition to something like 80% training and 20% validation. In most cases it will improve the classifier performance overall (more training data = better performance)
If you have never heard about "early-stopping" you should look it up, it's an import... | Reference to learn how to interpret learning curves of deep convolutional neural networks | 2 things:
You should probably switch your 50/50 train/validation repartition to something like 80% training and 20% validation. In most cases it will improve the classifier performance overall (more | Reference to learn how to interpret learning curves of deep convolutional neural networks
2 things:
You should probably switch your 50/50 train/validation repartition to something like 80% training and 20% validation. In most cases it will improve the classifier performance overall (more training data = better perform... | Reference to learn how to interpret learning curves of deep convolutional neural networks
2 things:
You should probably switch your 50/50 train/validation repartition to something like 80% training and 20% validation. In most cases it will improve the classifier performance overall (more |
37,323 | Reference to learn how to interpret learning curves of deep convolutional neural networks | I know its an ancient question but i guess if anyone else bumps across it looking for something similar...
I would say the barely decreasing loss value suggests using a lower learning rate? But i guess that's been mentioned in the link you included in your question so you probably considered that.
I would also try to ... | Reference to learn how to interpret learning curves of deep convolutional neural networks | I know its an ancient question but i guess if anyone else bumps across it looking for something similar...
I would say the barely decreasing loss value suggests using a lower learning rate? But i gues | Reference to learn how to interpret learning curves of deep convolutional neural networks
I know its an ancient question but i guess if anyone else bumps across it looking for something similar...
I would say the barely decreasing loss value suggests using a lower learning rate? But i guess that's been mentioned in the... | Reference to learn how to interpret learning curves of deep convolutional neural networks
I know its an ancient question but i guess if anyone else bumps across it looking for something similar...
I would say the barely decreasing loss value suggests using a lower learning rate? But i gues |
37,324 | Reference to learn how to interpret learning curves of deep convolutional neural networks | Here are some suggestions:
Training error and test error are too close (your system is unable to overfit on your training data), this means that your model is too simple. Solution: more layers or more neurons per layer.
Decrease gamma, e.g., 0.01. If the curve still reach plateau early, you can try a larger learning r... | Reference to learn how to interpret learning curves of deep convolutional neural networks | Here are some suggestions:
Training error and test error are too close (your system is unable to overfit on your training data), this means that your model is too simple. Solution: more layers or mor | Reference to learn how to interpret learning curves of deep convolutional neural networks
Here are some suggestions:
Training error and test error are too close (your system is unable to overfit on your training data), this means that your model is too simple. Solution: more layers or more neurons per layer.
Decrease ... | Reference to learn how to interpret learning curves of deep convolutional neural networks
Here are some suggestions:
Training error and test error are too close (your system is unable to overfit on your training data), this means that your model is too simple. Solution: more layers or mor |
37,325 | How to implement generalized hypergeometric function to use in beta-binomial cdf, sf, ppf? | This does not answer your question directly, but if you are thinking of estimating the cumulative distribution function of beta-binomial more efficiently, then you can use a recursive algorithm that is a little bit more efficient than the naive implementation.
Notice that probability mass function of beta-binomial dist... | How to implement generalized hypergeometric function to use in beta-binomial cdf, sf, ppf? | This does not answer your question directly, but if you are thinking of estimating the cumulative distribution function of beta-binomial more efficiently, then you can use a recursive algorithm that i | How to implement generalized hypergeometric function to use in beta-binomial cdf, sf, ppf?
This does not answer your question directly, but if you are thinking of estimating the cumulative distribution function of beta-binomial more efficiently, then you can use a recursive algorithm that is a little bit more efficient... | How to implement generalized hypergeometric function to use in beta-binomial cdf, sf, ppf?
This does not answer your question directly, but if you are thinking of estimating the cumulative distribution function of beta-binomial more efficiently, then you can use a recursive algorithm that i |
37,326 | Dealing with imbalanced/zero-inflated training examples for regression | (a) Assess the performance(s) you are interested in. Thus, if you are mainly interested in getting the expectation of the response E(y) right, then MAE or RMSE are useful. Similarly, you could also the conditional expectation E(y | y > 0), i.e., the expected amount of precipitation given that there is precipitation. If... | Dealing with imbalanced/zero-inflated training examples for regression | (a) Assess the performance(s) you are interested in. Thus, if you are mainly interested in getting the expectation of the response E(y) right, then MAE or RMSE are useful. Similarly, you could also th | Dealing with imbalanced/zero-inflated training examples for regression
(a) Assess the performance(s) you are interested in. Thus, if you are mainly interested in getting the expectation of the response E(y) right, then MAE or RMSE are useful. Similarly, you could also the conditional expectation E(y | y > 0), i.e., the... | Dealing with imbalanced/zero-inflated training examples for regression
(a) Assess the performance(s) you are interested in. Thus, if you are mainly interested in getting the expectation of the response E(y) right, then MAE or RMSE are useful. Similarly, you could also th |
37,327 | Reinforcement learning by Sutton, Tic tac toe self play | I am not sure about the first question. Regarding the second, these are my thoughts:
If you think about the state space of tic-tac-toe, it can be partitioned into two mutually exclusive subsets, one consisting of states seen by the agent when playing first, the other consisting of states seen while playing second. If o... | Reinforcement learning by Sutton, Tic tac toe self play | I am not sure about the first question. Regarding the second, these are my thoughts:
If you think about the state space of tic-tac-toe, it can be partitioned into two mutually exclusive subsets, one c | Reinforcement learning by Sutton, Tic tac toe self play
I am not sure about the first question. Regarding the second, these are my thoughts:
If you think about the state space of tic-tac-toe, it can be partitioned into two mutually exclusive subsets, one consisting of states seen by the agent when playing first, the ot... | Reinforcement learning by Sutton, Tic tac toe self play
I am not sure about the first question. Regarding the second, these are my thoughts:
If you think about the state space of tic-tac-toe, it can be partitioned into two mutually exclusive subsets, one c |
37,328 | What is "Descriptive Discriminant Analysis"? | There exists a real difference between Descriptive Discriminant Analysis(DDA) and Predictive Discriminant Analysis (PDA). which is depicted in the diagram given below. I found it here: http://as.wiley.com/WileyCDA/WileyTitle/productCd-0471468150.html | What is "Descriptive Discriminant Analysis"? | There exists a real difference between Descriptive Discriminant Analysis(DDA) and Predictive Discriminant Analysis (PDA). which is depicted in the diagram given below. I found it here: http://as.wiley | What is "Descriptive Discriminant Analysis"?
There exists a real difference between Descriptive Discriminant Analysis(DDA) and Predictive Discriminant Analysis (PDA). which is depicted in the diagram given below. I found it here: http://as.wiley.com/WileyCDA/WileyTitle/productCd-0471468150.html | What is "Descriptive Discriminant Analysis"?
There exists a real difference between Descriptive Discriminant Analysis(DDA) and Predictive Discriminant Analysis (PDA). which is depicted in the diagram given below. I found it here: http://as.wiley |
37,329 | How to interpret daily vs. hourly "% chance of rain" precipitation forecasts? | I was a little bit confused at first when thinking about the matter. However, the two main reason why you won't be able to harmonize forecasts on hourly and daily basis is the following.
The events for rain in breakdown perspective are not independent. Aggregating probabilities would require knowledge on how the events... | How to interpret daily vs. hourly "% chance of rain" precipitation forecasts? | I was a little bit confused at first when thinking about the matter. However, the two main reason why you won't be able to harmonize forecasts on hourly and daily basis is the following.
The events fo | How to interpret daily vs. hourly "% chance of rain" precipitation forecasts?
I was a little bit confused at first when thinking about the matter. However, the two main reason why you won't be able to harmonize forecasts on hourly and daily basis is the following.
The events for rain in breakdown perspective are not in... | How to interpret daily vs. hourly "% chance of rain" precipitation forecasts?
I was a little bit confused at first when thinking about the matter. However, the two main reason why you won't be able to harmonize forecasts on hourly and daily basis is the following.
The events fo |
37,330 | A name for operator-dependent cross-product | My understanding of the question is that it asks for a name for any $p\times p$ matrix $\mathbf F$ with elements $F_{ij} = f(\mathbf X_i, \mathbf X_j)$, where $\mathbf X_k$ are columns of a $n\times p$ data matrix $\mathbf X$ and $f(\cdot, \cdot)$ is some arbitrary function.
This can be seen as a generalization of cova... | A name for operator-dependent cross-product | My understanding of the question is that it asks for a name for any $p\times p$ matrix $\mathbf F$ with elements $F_{ij} = f(\mathbf X_i, \mathbf X_j)$, where $\mathbf X_k$ are columns of a $n\times p | A name for operator-dependent cross-product
My understanding of the question is that it asks for a name for any $p\times p$ matrix $\mathbf F$ with elements $F_{ij} = f(\mathbf X_i, \mathbf X_j)$, where $\mathbf X_k$ are columns of a $n\times p$ data matrix $\mathbf X$ and $f(\cdot, \cdot)$ is some arbitrary function.
... | A name for operator-dependent cross-product
My understanding of the question is that it asks for a name for any $p\times p$ matrix $\mathbf F$ with elements $F_{ij} = f(\mathbf X_i, \mathbf X_j)$, where $\mathbf X_k$ are columns of a $n\times p |
37,331 | Autocorrelation of concatenated independent AR(1) processes | Executive summary: It seems that you are mistaking noise for true autocorrelation due to a small sample size.
You can simply confirm this by increasing the k parameter in your code. See these examples below (I have used your same set.seed(987) throughout to maintain replicability):
k=1000 (your original code)
k=2000
... | Autocorrelation of concatenated independent AR(1) processes | Executive summary: It seems that you are mistaking noise for true autocorrelation due to a small sample size.
You can simply confirm this by increasing the k parameter in your code. See these examples | Autocorrelation of concatenated independent AR(1) processes
Executive summary: It seems that you are mistaking noise for true autocorrelation due to a small sample size.
You can simply confirm this by increasing the k parameter in your code. See these examples below (I have used your same set.seed(987) throughout to ma... | Autocorrelation of concatenated independent AR(1) processes
Executive summary: It seems that you are mistaking noise for true autocorrelation due to a small sample size.
You can simply confirm this by increasing the k parameter in your code. See these examples |
37,332 | Decomposition of average squared bias (in Elements of Statistical Learning) | The result is basically due to the property of best linear estimator. Note that we don't assume $f(X)$ is linear here. Nevertheless we can find the linear predictor that approximates $f$ the best.
Recall the definition of $\beta_*$: $\beta_{*} = \arg\min_\beta E{[(f(X) - X^T \beta)^2]}$. We can derive the theoretical ... | Decomposition of average squared bias (in Elements of Statistical Learning) | The result is basically due to the property of best linear estimator. Note that we don't assume $f(X)$ is linear here. Nevertheless we can find the linear predictor that approximates $f$ the best.
Re | Decomposition of average squared bias (in Elements of Statistical Learning)
The result is basically due to the property of best linear estimator. Note that we don't assume $f(X)$ is linear here. Nevertheless we can find the linear predictor that approximates $f$ the best.
Recall the definition of $\beta_*$: $\beta_{*}... | Decomposition of average squared bias (in Elements of Statistical Learning)
The result is basically due to the property of best linear estimator. Note that we don't assume $f(X)$ is linear here. Nevertheless we can find the linear predictor that approximates $f$ the best.
Re |
37,333 | Decomposition of average squared bias (in Elements of Statistical Learning) | Yes, this isn't the usual bias-variance decomposition, rather it's a further decomposition of the bias.
Someone else has already answered this. | Decomposition of average squared bias (in Elements of Statistical Learning) | Yes, this isn't the usual bias-variance decomposition, rather it's a further decomposition of the bias.
Someone else has already answered this. | Decomposition of average squared bias (in Elements of Statistical Learning)
Yes, this isn't the usual bias-variance decomposition, rather it's a further decomposition of the bias.
Someone else has already answered this. | Decomposition of average squared bias (in Elements of Statistical Learning)
Yes, this isn't the usual bias-variance decomposition, rather it's a further decomposition of the bias.
Someone else has already answered this. |
37,334 | Are all balls in the urn the same color (when they can't be seen clearly) | I admit I didn't fully read the other answer, but a crude approach would just be to note that $a$ follows a binomial$(n, p = e_r)$ distribution when all the balls are robin's egg blue, so you can reject when $a$ is "too large" based on the binomial model. If this won't do then maybe a likelihood ratio test would be be... | Are all balls in the urn the same color (when they can't be seen clearly) | I admit I didn't fully read the other answer, but a crude approach would just be to note that $a$ follows a binomial$(n, p = e_r)$ distribution when all the balls are robin's egg blue, so you can reje | Are all balls in the urn the same color (when they can't be seen clearly)
I admit I didn't fully read the other answer, but a crude approach would just be to note that $a$ follows a binomial$(n, p = e_r)$ distribution when all the balls are robin's egg blue, so you can reject when $a$ is "too large" based on the binomi... | Are all balls in the urn the same color (when they can't be seen clearly)
I admit I didn't fully read the other answer, but a crude approach would just be to note that $a$ follows a binomial$(n, p = e_r)$ distribution when all the balls are robin's egg blue, so you can reje |
37,335 | Are all balls in the urn the same color (when they can't be seen clearly) | I think I have the likelihood function (Full discloser, I am not 100% sure). Once you derive a likelihood though the rest of the hypothesis test should be easier.
Suppose you drew a sample of size $n$ denoted as $(X_1,...X_n)$. For simplicity, lets say;
$$
X_i = \begin{cases}
1\;\;\mathrm{if \; classified \; as\; col... | Are all balls in the urn the same color (when they can't be seen clearly) | I think I have the likelihood function (Full discloser, I am not 100% sure). Once you derive a likelihood though the rest of the hypothesis test should be easier.
Suppose you drew a sample of size $n | Are all balls in the urn the same color (when they can't be seen clearly)
I think I have the likelihood function (Full discloser, I am not 100% sure). Once you derive a likelihood though the rest of the hypothesis test should be easier.
Suppose you drew a sample of size $n$ denoted as $(X_1,...X_n)$. For simplicity, ... | Are all balls in the urn the same color (when they can't be seen clearly)
I think I have the likelihood function (Full discloser, I am not 100% sure). Once you derive a likelihood though the rest of the hypothesis test should be easier.
Suppose you drew a sample of size $n |
37,336 | Mathematical foundation of using MCMC in global optimization | Consider the Metropolis Hastings algorithm with a target distribution $\pi(x) = e^{-\beta E(x)}$ where $E$ is a real valued function (historically the energy of the physical system). (note that $\pi(x) = \pi(E(x))$).
Lets see what are the consequences of this choice to the expected relative number of samples with a giv... | Mathematical foundation of using MCMC in global optimization | Consider the Metropolis Hastings algorithm with a target distribution $\pi(x) = e^{-\beta E(x)}$ where $E$ is a real valued function (historically the energy of the physical system). (note that $\pi(x | Mathematical foundation of using MCMC in global optimization
Consider the Metropolis Hastings algorithm with a target distribution $\pi(x) = e^{-\beta E(x)}$ where $E$ is a real valued function (historically the energy of the physical system). (note that $\pi(x) = \pi(E(x))$).
Lets see what are the consequences of this... | Mathematical foundation of using MCMC in global optimization
Consider the Metropolis Hastings algorithm with a target distribution $\pi(x) = e^{-\beta E(x)}$ where $E$ is a real valued function (historically the energy of the physical system). (note that $\pi(x |
37,337 | Expressing conditional covariance matrix in terms of covariance matrix | This rule holds when the random variables are jointly normally distributed, but it does not apply more generally; i.e., for other joint distributions it might not hold. In a related answer here it is shown that the Mahalanobis distance can be decomposed as follows:
$$\begin{equation} \begin{aligned}
D^2 (\boldsymbol{... | Expressing conditional covariance matrix in terms of covariance matrix | This rule holds when the random variables are jointly normally distributed, but it does not apply more generally; i.e., for other joint distributions it might not hold. In a related answer here it i | Expressing conditional covariance matrix in terms of covariance matrix
This rule holds when the random variables are jointly normally distributed, but it does not apply more generally; i.e., for other joint distributions it might not hold. In a related answer here it is shown that the Mahalanobis distance can be deco... | Expressing conditional covariance matrix in terms of covariance matrix
This rule holds when the random variables are jointly normally distributed, but it does not apply more generally; i.e., for other joint distributions it might not hold. In a related answer here it i |
37,338 | ML covariance estimation from Expectation-Maximization with missing data | It turns out the algorithm is rather simple. Starting out with initial estimates of $\mathbf{\mu}$ and $\boldsymbol{\Sigma}$:
Create a bias matrix $\mathbf{B}$ of dimension $nvar\times nvar$, initialized with zeros.
For each row (observation) with missing data, denote available indices $a$ and missing indices $m$. Giv... | ML covariance estimation from Expectation-Maximization with missing data | It turns out the algorithm is rather simple. Starting out with initial estimates of $\mathbf{\mu}$ and $\boldsymbol{\Sigma}$:
Create a bias matrix $\mathbf{B}$ of dimension $nvar\times nvar$, initial | ML covariance estimation from Expectation-Maximization with missing data
It turns out the algorithm is rather simple. Starting out with initial estimates of $\mathbf{\mu}$ and $\boldsymbol{\Sigma}$:
Create a bias matrix $\mathbf{B}$ of dimension $nvar\times nvar$, initialized with zeros.
For each row (observation) wit... | ML covariance estimation from Expectation-Maximization with missing data
It turns out the algorithm is rather simple. Starting out with initial estimates of $\mathbf{\mu}$ and $\boldsymbol{\Sigma}$:
Create a bias matrix $\mathbf{B}$ of dimension $nvar\times nvar$, initial |
37,339 | Is a pair of null hypothesis and alternative hypothesis always complementary? | I have been having the same question, too. The part confuses me is that in many places I saw that $H_0$ and $H_a$ are not complementary, e.g., $H_0$: $\mu$ = 0, $H_a$: $\mu$ < 0, rather than $H_0$: $\mu$ >= 0, $H_a$: $\mu$ < 0,
After going through some searches, my current understanding is that $H_0$ and $H_a$ should b... | Is a pair of null hypothesis and alternative hypothesis always complementary? | I have been having the same question, too. The part confuses me is that in many places I saw that $H_0$ and $H_a$ are not complementary, e.g., $H_0$: $\mu$ = 0, $H_a$: $\mu$ < 0, rather than $H_0$: $\ | Is a pair of null hypothesis and alternative hypothesis always complementary?
I have been having the same question, too. The part confuses me is that in many places I saw that $H_0$ and $H_a$ are not complementary, e.g., $H_0$: $\mu$ = 0, $H_a$: $\mu$ < 0, rather than $H_0$: $\mu$ >= 0, $H_a$: $\mu$ < 0,
After going th... | Is a pair of null hypothesis and alternative hypothesis always complementary?
I have been having the same question, too. The part confuses me is that in many places I saw that $H_0$ and $H_a$ are not complementary, e.g., $H_0$: $\mu$ = 0, $H_a$: $\mu$ < 0, rather than $H_0$: $\ |
37,340 | Complexity Parameter in Decision Tree | This is answered in this rpart resource. From p. 25:
For regression models (see next section) the scaled cp has a very direct interpretation: if any split does not increase the overall $R^2$ of the model by at least cp (where $R^2$ is the usual linear-models definition) then that split is decreed to be, a priori, not ... | Complexity Parameter in Decision Tree | This is answered in this rpart resource. From p. 25:
For regression models (see next section) the scaled cp has a very direct interpretation: if any split does not increase the overall $R^2$ of the m | Complexity Parameter in Decision Tree
This is answered in this rpart resource. From p. 25:
For regression models (see next section) the scaled cp has a very direct interpretation: if any split does not increase the overall $R^2$ of the model by at least cp (where $R^2$ is the usual linear-models definition) then that ... | Complexity Parameter in Decision Tree
This is answered in this rpart resource. From p. 25:
For regression models (see next section) the scaled cp has a very direct interpretation: if any split does not increase the overall $R^2$ of the m |
37,341 | Distribution of the exponential of an exponential random variable | \begin{align}
F(y) &= P(Y<y) \\
&= P(e^{aX}<y) \\
&= P(aX<\ln y) \\
&= P(X<\frac{\ln y}{a}) \\
&=\int_0^{\frac{\ln y}{a}}\lambda e^{-\lambda y}dy \\
&= \left.-e^{-\lambda y}\right\vert_{0}^{\frac{\ln y}{a}}\\
&=1-y^{-\lambda/a}
\end{align}
We take derivatives of both side:
$$f(y)=\frac{\lambda}{a}y^{-\lambda/a -1}$$
A... | Distribution of the exponential of an exponential random variable | \begin{align}
F(y) &= P(Y<y) \\
&= P(e^{aX}<y) \\
&= P(aX<\ln y) \\
&= P(X<\frac{\ln y}{a}) \\
&=\int_0^{\frac{\ln y}{a}}\lambda e^{-\lambda y}dy \\
&= \left.-e^{-\lambda y}\right\vert_{0}^{\frac{\ln | Distribution of the exponential of an exponential random variable
\begin{align}
F(y) &= P(Y<y) \\
&= P(e^{aX}<y) \\
&= P(aX<\ln y) \\
&= P(X<\frac{\ln y}{a}) \\
&=\int_0^{\frac{\ln y}{a}}\lambda e^{-\lambda y}dy \\
&= \left.-e^{-\lambda y}\right\vert_{0}^{\frac{\ln y}{a}}\\
&=1-y^{-\lambda/a}
\end{align}
We take deriva... | Distribution of the exponential of an exponential random variable
\begin{align}
F(y) &= P(Y<y) \\
&= P(e^{aX}<y) \\
&= P(aX<\ln y) \\
&= P(X<\frac{\ln y}{a}) \\
&=\int_0^{\frac{\ln y}{a}}\lambda e^{-\lambda y}dy \\
&= \left.-e^{-\lambda y}\right\vert_{0}^{\frac{\ln |
37,342 | Comprehensive list of combination techniques for word-level embeddings with pros/cons | The team around Bengio published an article a few years ago. Maybe this is good enough?
Turian, J., Ratinov, L., & Bengio, Y. (2010). Word representations: a simple and general method for semi-supervised learning (pp. 384–394). Association for Computational Linguistics. | Comprehensive list of combination techniques for word-level embeddings with pros/cons | The team around Bengio published an article a few years ago. Maybe this is good enough?
Turian, J., Ratinov, L., & Bengio, Y. (2010). Word representations: a simple and general method for semi-superv | Comprehensive list of combination techniques for word-level embeddings with pros/cons
The team around Bengio published an article a few years ago. Maybe this is good enough?
Turian, J., Ratinov, L., & Bengio, Y. (2010). Word representations: a simple and general method for semi-supervised learning (pp. 384–394). Assoc... | Comprehensive list of combination techniques for word-level embeddings with pros/cons
The team around Bengio published an article a few years ago. Maybe this is good enough?
Turian, J., Ratinov, L., & Bengio, Y. (2010). Word representations: a simple and general method for semi-superv |
37,343 | Estimating the parameter of a geometric distribution from a single sample | By definition, an estimator is a function $t$ mapping the possible outcomes $\mathbb{N}^{+} = \{1,2,3,\ldots\}$ to the reals. If this is to be unbiased, then--writing $q=1-p$--the expectation must equal $1-q$ for all $q$ in the interval $[0,1]$. Applying the definition of expectation to the formula for the probabiliti... | Estimating the parameter of a geometric distribution from a single sample | By definition, an estimator is a function $t$ mapping the possible outcomes $\mathbb{N}^{+} = \{1,2,3,\ldots\}$ to the reals. If this is to be unbiased, then--writing $q=1-p$--the expectation must equ | Estimating the parameter of a geometric distribution from a single sample
By definition, an estimator is a function $t$ mapping the possible outcomes $\mathbb{N}^{+} = \{1,2,3,\ldots\}$ to the reals. If this is to be unbiased, then--writing $q=1-p$--the expectation must equal $1-q$ for all $q$ in the interval $[0,1]$. ... | Estimating the parameter of a geometric distribution from a single sample
By definition, an estimator is a function $t$ mapping the possible outcomes $\mathbb{N}^{+} = \{1,2,3,\ldots\}$ to the reals. If this is to be unbiased, then--writing $q=1-p$--the expectation must equ |
37,344 | Estimating the parameter of a geometric distribution from a single sample | UPDATE. Re-writing my previous sloppy answer.
There is no unbiased estimator for $p$, here is the proof.
The estimator $p=\frac{1}{k}$ is biased, but it's best you can get in the sense of MLE or method of moments. Here's the derivation in Math SE. | Estimating the parameter of a geometric distribution from a single sample | UPDATE. Re-writing my previous sloppy answer.
There is no unbiased estimator for $p$, here is the proof.
The estimator $p=\frac{1}{k}$ is biased, but it's best you can get in the sense of MLE or meth | Estimating the parameter of a geometric distribution from a single sample
UPDATE. Re-writing my previous sloppy answer.
There is no unbiased estimator for $p$, here is the proof.
The estimator $p=\frac{1}{k}$ is biased, but it's best you can get in the sense of MLE or method of moments. Here's the derivation in Math... | Estimating the parameter of a geometric distribution from a single sample
UPDATE. Re-writing my previous sloppy answer.
There is no unbiased estimator for $p$, here is the proof.
The estimator $p=\frac{1}{k}$ is biased, but it's best you can get in the sense of MLE or meth |
37,345 | Mechanics behind deviation from random distribution | The problem is that you assumed a certain random distribution of IPD and it's not fitting the empirical distribution. So, the formulation of your question is a little confusing given the explanation you given so far. The "deviation" is not from randomness, but of the empirical distribution from the assumed theoretical ... | Mechanics behind deviation from random distribution | The problem is that you assumed a certain random distribution of IPD and it's not fitting the empirical distribution. So, the formulation of your question is a little confusing given the explanation y | Mechanics behind deviation from random distribution
The problem is that you assumed a certain random distribution of IPD and it's not fitting the empirical distribution. So, the formulation of your question is a little confusing given the explanation you given so far. The "deviation" is not from randomness, but of the ... | Mechanics behind deviation from random distribution
The problem is that you assumed a certain random distribution of IPD and it's not fitting the empirical distribution. So, the formulation of your question is a little confusing given the explanation y |
37,346 | Machine learning for pattern recognition in realtime sensor data | I worked on a similar problem a few weeks ago to detect the right peaks in a noisy sensor.
The most important task here is to select the right features. Slope seems like a good idea, maybe not using neighboring points but data points separated by a fixed distance (say 10 or 100, depending on your sample rate).
If it's ... | Machine learning for pattern recognition in realtime sensor data | I worked on a similar problem a few weeks ago to detect the right peaks in a noisy sensor.
The most important task here is to select the right features. Slope seems like a good idea, maybe not using n | Machine learning for pattern recognition in realtime sensor data
I worked on a similar problem a few weeks ago to detect the right peaks in a noisy sensor.
The most important task here is to select the right features. Slope seems like a good idea, maybe not using neighboring points but data points separated by a fixed ... | Machine learning for pattern recognition in realtime sensor data
I worked on a similar problem a few weeks ago to detect the right peaks in a noisy sensor.
The most important task here is to select the right features. Slope seems like a good idea, maybe not using n |
37,347 | How to build separate time series forecasts model for each of 3k customers? | You certainly don't want to build 3,000 separate models! Not only would that be computationally and administratively cumbersome, but it would also mean that each model only has data from one customer, and so you are ignoring data from other customers in each model. This would effectively mean that your predictions fo... | How to build separate time series forecasts model for each of 3k customers? | You certainly don't want to build 3,000 separate models! Not only would that be computationally and administratively cumbersome, but it would also mean that each model only has data from one customer | How to build separate time series forecasts model for each of 3k customers?
You certainly don't want to build 3,000 separate models! Not only would that be computationally and administratively cumbersome, but it would also mean that each model only has data from one customer, and so you are ignoring data from other cu... | How to build separate time series forecasts model for each of 3k customers?
You certainly don't want to build 3,000 separate models! Not only would that be computationally and administratively cumbersome, but it would also mean that each model only has data from one customer |
37,348 | How to build separate time series forecasts model for each of 3k customers? | I faced very similar task at work. First I used an automated ARIMA function applied to each timeseries separately. It worked sufficiently fast for my purposes.
Then I studied the properties of timeseries by doing a big comparative analysis, using both ARIMA, and a number of simpler techniques like linear models with pr... | How to build separate time series forecasts model for each of 3k customers? | I faced very similar task at work. First I used an automated ARIMA function applied to each timeseries separately. It worked sufficiently fast for my purposes.
Then I studied the properties of timeser | How to build separate time series forecasts model for each of 3k customers?
I faced very similar task at work. First I used an automated ARIMA function applied to each timeseries separately. It worked sufficiently fast for my purposes.
Then I studied the properties of timeseries by doing a big comparative analysis, usi... | How to build separate time series forecasts model for each of 3k customers?
I faced very similar task at work. First I used an automated ARIMA function applied to each timeseries separately. It worked sufficiently fast for my purposes.
Then I studied the properties of timeser |
37,349 | How to build separate time series forecasts model for each of 3k customers? | I had a similar project where forecasting was required for 3000 Distributors for one of my clients. I used Automated ARIMA and looped it through clusters of Distributors by their type.
I had to finally formulate a parallel package to handle multiple Distributor types in parallel in order to increase efficiency as model... | How to build separate time series forecasts model for each of 3k customers? | I had a similar project where forecasting was required for 3000 Distributors for one of my clients. I used Automated ARIMA and looped it through clusters of Distributors by their type.
I had to finall | How to build separate time series forecasts model for each of 3k customers?
I had a similar project where forecasting was required for 3000 Distributors for one of my clients. I used Automated ARIMA and looped it through clusters of Distributors by their type.
I had to finally formulate a parallel package to handle mul... | How to build separate time series forecasts model for each of 3k customers?
I had a similar project where forecasting was required for 3000 Distributors for one of my clients. I used Automated ARIMA and looped it through clusters of Distributors by their type.
I had to finall |
37,350 | R lmerTest and Tests of Multiple Random Effects | The documentation on the lmerTest::rand() function is definitely terse.
From what I've been able to gather I think it tests the hypothesis that the random effect variation (i.e., a varying intercept (1 | Consumer) ) is significant versus the null that there is no between group-level variation, $H_0 : \sigma_{\alpha}... | R lmerTest and Tests of Multiple Random Effects | The documentation on the lmerTest::rand() function is definitely terse.
From what I've been able to gather I think it tests the hypothesis that the random effect variation (i.e., a varying intercept | R lmerTest and Tests of Multiple Random Effects
The documentation on the lmerTest::rand() function is definitely terse.
From what I've been able to gather I think it tests the hypothesis that the random effect variation (i.e., a varying intercept (1 | Consumer) ) is significant versus the null that there is no betwe... | R lmerTest and Tests of Multiple Random Effects
The documentation on the lmerTest::rand() function is definitely terse.
From what I've been able to gather I think it tests the hypothesis that the random effect variation (i.e., a varying intercept |
37,351 | R lmerTest and Tests of Multiple Random Effects | The lmerTest documentation describes rand() as yielding
"...a vector of Chi square statistics and corresponding p-values of likelihood ratio tests."
Thus, I believe it is a likelihood ratio test. That is, simply, the comparison of a model with a given random effect to that same model without the random effect.
In r... | R lmerTest and Tests of Multiple Random Effects | The lmerTest documentation describes rand() as yielding
"...a vector of Chi square statistics and corresponding p-values of likelihood ratio tests."
Thus, I believe it is a likelihood ratio test. T | R lmerTest and Tests of Multiple Random Effects
The lmerTest documentation describes rand() as yielding
"...a vector of Chi square statistics and corresponding p-values of likelihood ratio tests."
Thus, I believe it is a likelihood ratio test. That is, simply, the comparison of a model with a given random effect to ... | R lmerTest and Tests of Multiple Random Effects
The lmerTest documentation describes rand() as yielding
"...a vector of Chi square statistics and corresponding p-values of likelihood ratio tests."
Thus, I believe it is a likelihood ratio test. T |
37,352 | Question on how to use EM to estimate parameters of this model | Let me recall the basics of the EM algorithm first. When looking for the maximum likelihood estimate of a likelihood of the form$$\int f(x,z|\beta)\text{d}z,$$ the algorithm proceeds by iteratively maximising (M) expected (E) complete log-likelihoods, which results in maximising (in $\beta$)at iteration $t$ the functio... | Question on how to use EM to estimate parameters of this model | Let me recall the basics of the EM algorithm first. When looking for the maximum likelihood estimate of a likelihood of the form$$\int f(x,z|\beta)\text{d}z,$$ the algorithm proceeds by iteratively ma | Question on how to use EM to estimate parameters of this model
Let me recall the basics of the EM algorithm first. When looking for the maximum likelihood estimate of a likelihood of the form$$\int f(x,z|\beta)\text{d}z,$$ the algorithm proceeds by iteratively maximising (M) expected (E) complete log-likelihoods, which... | Question on how to use EM to estimate parameters of this model
Let me recall the basics of the EM algorithm first. When looking for the maximum likelihood estimate of a likelihood of the form$$\int f(x,z|\beta)\text{d}z,$$ the algorithm proceeds by iteratively ma |
37,353 | How to obtain the quantile function when an analytical form of the distribution is not known | $\DeclareMathOperator*{\med}{med}$The median is the point that minimizes the expected $L^1$ distance:
$$\med_Z f(Z) = \arg\min_m E_z|f(Z) - m|$$
Hence we can simplify your expression:
$$\begin{equation}\med_{z_1 \sim F} \med_{z_2 \sim F} |z_1 - z_2| \\
= \arg\min_{m_1}E_{z_1 \sim F}\left| m_1 - \arg\min_{m_2} E_{z_2 \s... | How to obtain the quantile function when an analytical form of the distribution is not known | $\DeclareMathOperator*{\med}{med}$The median is the point that minimizes the expected $L^1$ distance:
$$\med_Z f(Z) = \arg\min_m E_z|f(Z) - m|$$
Hence we can simplify your expression:
$$\begin{equatio | How to obtain the quantile function when an analytical form of the distribution is not known
$\DeclareMathOperator*{\med}{med}$The median is the point that minimizes the expected $L^1$ distance:
$$\med_Z f(Z) = \arg\min_m E_z|f(Z) - m|$$
Hence we can simplify your expression:
$$\begin{equation}\med_{z_1 \sim F} \med_{z... | How to obtain the quantile function when an analytical form of the distribution is not known
$\DeclareMathOperator*{\med}{med}$The median is the point that minimizes the expected $L^1$ distance:
$$\med_Z f(Z) = \arg\min_m E_z|f(Z) - m|$$
Hence we can simplify your expression:
$$\begin{equatio |
37,354 | How to obtain the quantile function when an analytical form of the distribution is not known | A straightforward data-driven approach to estimating the quantile function consists in:
bootstrapping your observations to generate many more values than are
in your original sample (especially, values beyond the range of the initial limited sample). A good strategy is to use a smoothed bootstrap simulation
scheme to ... | How to obtain the quantile function when an analytical form of the distribution is not known | A straightforward data-driven approach to estimating the quantile function consists in:
bootstrapping your observations to generate many more values than are
in your original sample (especially, valu | How to obtain the quantile function when an analytical form of the distribution is not known
A straightforward data-driven approach to estimating the quantile function consists in:
bootstrapping your observations to generate many more values than are
in your original sample (especially, values beyond the range of the ... | How to obtain the quantile function when an analytical form of the distribution is not known
A straightforward data-driven approach to estimating the quantile function consists in:
bootstrapping your observations to generate many more values than are
in your original sample (especially, valu |
37,355 | How to obtain the quantile function when an analytical form of the distribution is not known | So, I think that the best way to obtain
$$\text{med}_{Z\sim F} H(Z)$$
is to:
compute the entries of the $n$ vector $\{H(z_i)\}_{i=1}^n$ of values of $H(z_i)$ corresponding to a grid of $n$ values of $\{z_i\}_{i=1}^n$ placed uniformly on $(F_Z^{-1}(\epsilon),F_Z^{-1}(1-\epsilon))$
Compute the weighted median of $\{H(... | How to obtain the quantile function when an analytical form of the distribution is not known | So, I think that the best way to obtain
$$\text{med}_{Z\sim F} H(Z)$$
is to:
compute the entries of the $n$ vector $\{H(z_i)\}_{i=1}^n$ of values of $H(z_i)$ corresponding to a grid of $n$ values o | How to obtain the quantile function when an analytical form of the distribution is not known
So, I think that the best way to obtain
$$\text{med}_{Z\sim F} H(Z)$$
is to:
compute the entries of the $n$ vector $\{H(z_i)\}_{i=1}^n$ of values of $H(z_i)$ corresponding to a grid of $n$ values of $\{z_i\}_{i=1}^n$ placed ... | How to obtain the quantile function when an analytical form of the distribution is not known
So, I think that the best way to obtain
$$\text{med}_{Z\sim F} H(Z)$$
is to:
compute the entries of the $n$ vector $\{H(z_i)\}_{i=1}^n$ of values of $H(z_i)$ corresponding to a grid of $n$ values o |
37,356 | Resources for the "ah ha" moment when learning Bayes' theorem | I think it's hard to beat Cohen's classic 1994 paper in the American Psychologist, "The earth is round, (p<.05)". You can always find it somewhere on Google, e.g. http://ist-socrates.berkeley.edu/~maccoun/PP279_Cohen1.pdf. He includes a brilliant example based on a medical screening test, and discusses the implication... | Resources for the "ah ha" moment when learning Bayes' theorem | I think it's hard to beat Cohen's classic 1994 paper in the American Psychologist, "The earth is round, (p<.05)". You can always find it somewhere on Google, e.g. http://ist-socrates.berkeley.edu/~mac | Resources for the "ah ha" moment when learning Bayes' theorem
I think it's hard to beat Cohen's classic 1994 paper in the American Psychologist, "The earth is round, (p<.05)". You can always find it somewhere on Google, e.g. http://ist-socrates.berkeley.edu/~maccoun/PP279_Cohen1.pdf. He includes a brilliant example ba... | Resources for the "ah ha" moment when learning Bayes' theorem
I think it's hard to beat Cohen's classic 1994 paper in the American Psychologist, "The earth is round, (p<.05)". You can always find it somewhere on Google, e.g. http://ist-socrates.berkeley.edu/~mac |
37,357 | Review of Box-Jenkins methodology | "Data preparation (identification and Difference data to obtain stationary series)" . Non-stationarity may be the symptom while the cause may be a simple change in the mean or a simple change in trend or a simple change in parameters or a simple change in error variance. Alternatively/conversely an unusual value (pulse... | Review of Box-Jenkins methodology | "Data preparation (identification and Difference data to obtain stationary series)" . Non-stationarity may be the symptom while the cause may be a simple change in the mean or a simple change in trend | Review of Box-Jenkins methodology
"Data preparation (identification and Difference data to obtain stationary series)" . Non-stationarity may be the symptom while the cause may be a simple change in the mean or a simple change in trend or a simple change in parameters or a simple change in error variance. Alternatively/... | Review of Box-Jenkins methodology
"Data preparation (identification and Difference data to obtain stationary series)" . Non-stationarity may be the symptom while the cause may be a simple change in the mean or a simple change in trend |
37,358 | What are hot research topics for PhD dissertation in Biostatistics? | Leah Welty, Emerging Trends, 2013
Davidian, Cutting Edge: Emerging trends in biostatistics, 2012
Modern Issues and Methods in Biostatistics, Springer, 2011 | What are hot research topics for PhD dissertation in Biostatistics? | Leah Welty, Emerging Trends, 2013
Davidian, Cutting Edge: Emerging trends in biostatistics, 2012
Modern Issues and Methods in Biostatistics, Springer, 2011 | What are hot research topics for PhD dissertation in Biostatistics?
Leah Welty, Emerging Trends, 2013
Davidian, Cutting Edge: Emerging trends in biostatistics, 2012
Modern Issues and Methods in Biostatistics, Springer, 2011 | What are hot research topics for PhD dissertation in Biostatistics?
Leah Welty, Emerging Trends, 2013
Davidian, Cutting Edge: Emerging trends in biostatistics, 2012
Modern Issues and Methods in Biostatistics, Springer, 2011 |
37,359 | What are the various basic kernels available? | Neural networks are not a kernel, they are a learning algorithm.
Plenty of kernel functions exist, such as:
sigmoid, popular in the early days of kernel methods due to their influence in neural networks; not really used heavily now
Tanimoto/Jaccard/diffusion, popular for binary features
tree/graph kernels, popular in ... | What are the various basic kernels available? | Neural networks are not a kernel, they are a learning algorithm.
Plenty of kernel functions exist, such as:
sigmoid, popular in the early days of kernel methods due to their influence in neural netwo | What are the various basic kernels available?
Neural networks are not a kernel, they are a learning algorithm.
Plenty of kernel functions exist, such as:
sigmoid, popular in the early days of kernel methods due to their influence in neural networks; not really used heavily now
Tanimoto/Jaccard/diffusion, popular for b... | What are the various basic kernels available?
Neural networks are not a kernel, they are a learning algorithm.
Plenty of kernel functions exist, such as:
sigmoid, popular in the early days of kernel methods due to their influence in neural netwo |
37,360 | Cox discrete time regression model question | The answer lies in the $dt$ terms in Cox's equation 21, which your question omitted.
Cox says that in the continuous case equation 21, $$\frac{\lambda(t; z)\,dt}{1 - \lambda(t; z)\,dt} = e^{-z\beta} \frac{\lambda_0(t)\,dt}{1 - \lambda_0(t)\,dt},$$ reduces to equation 9, $$\lambda(t; z) = e^{z\beta} \lambda_0(t).$$
Cox ... | Cox discrete time regression model question | The answer lies in the $dt$ terms in Cox's equation 21, which your question omitted.
Cox says that in the continuous case equation 21, $$\frac{\lambda(t; z)\,dt}{1 - \lambda(t; z)\,dt} = e^{-z\beta} \ | Cox discrete time regression model question
The answer lies in the $dt$ terms in Cox's equation 21, which your question omitted.
Cox says that in the continuous case equation 21, $$\frac{\lambda(t; z)\,dt}{1 - \lambda(t; z)\,dt} = e^{-z\beta} \frac{\lambda_0(t)\,dt}{1 - \lambda_0(t)\,dt},$$ reduces to equation 9, $$\la... | Cox discrete time regression model question
The answer lies in the $dt$ terms in Cox's equation 21, which your question omitted.
Cox says that in the continuous case equation 21, $$\frac{\lambda(t; z)\,dt}{1 - \lambda(t; z)\,dt} = e^{-z\beta} \ |
37,361 | Using random forest for survival analysis with time varying covariates | Although there is structure to your data, it may be that the variation in baseline risk does not vary substantially enough among your subjects to cause a model without a frailty term to form poor predictions. Of course, it's perfectly possible that a model with a frailty term would perform better than the pooled random... | Using random forest for survival analysis with time varying covariates | Although there is structure to your data, it may be that the variation in baseline risk does not vary substantially enough among your subjects to cause a model without a frailty term to form poor pred | Using random forest for survival analysis with time varying covariates
Although there is structure to your data, it may be that the variation in baseline risk does not vary substantially enough among your subjects to cause a model without a frailty term to form poor predictions. Of course, it's perfectly possible that ... | Using random forest for survival analysis with time varying covariates
Although there is structure to your data, it may be that the variation in baseline risk does not vary substantially enough among your subjects to cause a model without a frailty term to form poor pred |
37,362 | Using random forest for survival analysis with time varying covariates | I am just starting to work with Random Forest but I believe it is mainly the bagging that needs to be iid for each tree and the subset of features selection at each node. I am unaware of any formal constraints on the data itself.
Why it works so well on your data I can not say until I have investigated your data.
But t... | Using random forest for survival analysis with time varying covariates | I am just starting to work with Random Forest but I believe it is mainly the bagging that needs to be iid for each tree and the subset of features selection at each node. I am unaware of any formal co | Using random forest for survival analysis with time varying covariates
I am just starting to work with Random Forest but I believe it is mainly the bagging that needs to be iid for each tree and the subset of features selection at each node. I am unaware of any formal constraints on the data itself.
Why it works so wel... | Using random forest for survival analysis with time varying covariates
I am just starting to work with Random Forest but I believe it is mainly the bagging that needs to be iid for each tree and the subset of features selection at each node. I am unaware of any formal co |
37,363 | High mutual information = (almost) deterministic relationship? | You’re on the right track, but I am hesitant to go that far.
Consider variables forming a perfect “X” scatterplot. In that case, given one one of the variable values, you can narrow it down to two possibilities for the other value. That is, knowing the value of the one variable gives you tremendous information about th... | High mutual information = (almost) deterministic relationship? | You’re on the right track, but I am hesitant to go that far.
Consider variables forming a perfect “X” scatterplot. In that case, given one one of the variable values, you can narrow it down to two pos | High mutual information = (almost) deterministic relationship?
You’re on the right track, but I am hesitant to go that far.
Consider variables forming a perfect “X” scatterplot. In that case, given one one of the variable values, you can narrow it down to two possibilities for the other value. That is, knowing the valu... | High mutual information = (almost) deterministic relationship?
You’re on the right track, but I am hesitant to go that far.
Consider variables forming a perfect “X” scatterplot. In that case, given one one of the variable values, you can narrow it down to two pos |
37,364 | High mutual information = (almost) deterministic relationship? | In addition to the answer by @Dave, I will give an example showing that a deterministic (or one-to-one) relationship is not always possible. I will use a categorical data example, so the joint distribution can be given by a two-way table. But first, one formula for the mutual information is
$$ I(X, Y) = H(X) + H(Y) - H... | High mutual information = (almost) deterministic relationship? | In addition to the answer by @Dave, I will give an example showing that a deterministic (or one-to-one) relationship is not always possible. I will use a categorical data example, so the joint distrib | High mutual information = (almost) deterministic relationship?
In addition to the answer by @Dave, I will give an example showing that a deterministic (or one-to-one) relationship is not always possible. I will use a categorical data example, so the joint distribution can be given by a two-way table. But first, one for... | High mutual information = (almost) deterministic relationship?
In addition to the answer by @Dave, I will give an example showing that a deterministic (or one-to-one) relationship is not always possible. I will use a categorical data example, so the joint distrib |
37,365 | Joint Models vs the 'usual' time-dependent Cox regression for time-varying predictors | The major breakthrough of the joint models relative to the time-dependent Cox model is that they allow one to deal with the error measurements in the time dependent variables (longitudinal variable in this case). In a Cox model with time dependent covariates we assume that the variables are measured without error.
Some... | Joint Models vs the 'usual' time-dependent Cox regression for time-varying predictors | The major breakthrough of the joint models relative to the time-dependent Cox model is that they allow one to deal with the error measurements in the time dependent variables (longitudinal variable in | Joint Models vs the 'usual' time-dependent Cox regression for time-varying predictors
The major breakthrough of the joint models relative to the time-dependent Cox model is that they allow one to deal with the error measurements in the time dependent variables (longitudinal variable in this case). In a Cox model with t... | Joint Models vs the 'usual' time-dependent Cox regression for time-varying predictors
The major breakthrough of the joint models relative to the time-dependent Cox model is that they allow one to deal with the error measurements in the time dependent variables (longitudinal variable in |
37,366 | Joint Models vs the 'usual' time-dependent Cox regression for time-varying predictors | The major problem is that they are time consuming (computational speaking) and the software is not yet very friendly. There are several approaches and you can let all covariates to be time-dependent, but in this case you should consider to take a multivariate longitudinal model before. In addition for each situation yo... | Joint Models vs the 'usual' time-dependent Cox regression for time-varying predictors | The major problem is that they are time consuming (computational speaking) and the software is not yet very friendly. There are several approaches and you can let all covariates to be time-dependent, | Joint Models vs the 'usual' time-dependent Cox regression for time-varying predictors
The major problem is that they are time consuming (computational speaking) and the software is not yet very friendly. There are several approaches and you can let all covariates to be time-dependent, but in this case you should consid... | Joint Models vs the 'usual' time-dependent Cox regression for time-varying predictors
The major problem is that they are time consuming (computational speaking) and the software is not yet very friendly. There are several approaches and you can let all covariates to be time-dependent, |
37,367 | How does explaining away cause problems for learning? | The only problem I can see from such a "V structure" is that you have two "causes" - this means that there may be difficulty untangling the effect of each "parent". In terms of your example, it could be the case that you observe "earthquake" and "burglary" together (both "on" or both "off"). So you would get a good e... | How does explaining away cause problems for learning? | The only problem I can see from such a "V structure" is that you have two "causes" - this means that there may be difficulty untangling the effect of each "parent". In terms of your example, it could | How does explaining away cause problems for learning?
The only problem I can see from such a "V structure" is that you have two "causes" - this means that there may be difficulty untangling the effect of each "parent". In terms of your example, it could be the case that you observe "earthquake" and "burglary" together... | How does explaining away cause problems for learning?
The only problem I can see from such a "V structure" is that you have two "causes" - this means that there may be difficulty untangling the effect of each "parent". In terms of your example, it could |
37,368 | MLE vs MAP vs conditional MLE with regards to logistic regression | For MLE and MAP you are right. "Conditional MLE" is another way of saying "MLE in a conditional model". Logistic regression is a conditional model in the sense that $\theta$ only controls $P(Y|X)$ (it has no effect on $P(X)$). Therefore the MLE for logistic regression is a conditional MLE. If you have a model in wh... | MLE vs MAP vs conditional MLE with regards to logistic regression | For MLE and MAP you are right. "Conditional MLE" is another way of saying "MLE in a conditional model". Logistic regression is a conditional model in the sense that $\theta$ only controls $P(Y|X)$ ( | MLE vs MAP vs conditional MLE with regards to logistic regression
For MLE and MAP you are right. "Conditional MLE" is another way of saying "MLE in a conditional model". Logistic regression is a conditional model in the sense that $\theta$ only controls $P(Y|X)$ (it has no effect on $P(X)$). Therefore the MLE for lo... | MLE vs MAP vs conditional MLE with regards to logistic regression
For MLE and MAP you are right. "Conditional MLE" is another way of saying "MLE in a conditional model". Logistic regression is a conditional model in the sense that $\theta$ only controls $P(Y|X)$ ( |
37,369 | How exactly is the sum (or mean) centering constraint for splines (also w.r.t. gam from mgcv) done? | Here is a simpler example using the link from Nemo. The question I answer is
How exactly is the sum (or mean) centering constraint for splines (also w.r.t. gam from mgcv) done?
I answer this as this is the title and as
My question is: Even though the fit is very similar, why do my constrained B-Spline-columns diff... | How exactly is the sum (or mean) centering constraint for splines (also w.r.t. gam from mgcv) done? | Here is a simpler example using the link from Nemo. The question I answer is
How exactly is the sum (or mean) centering constraint for splines (also w.r.t. gam from mgcv) done?
I answer this as thi | How exactly is the sum (or mean) centering constraint for splines (also w.r.t. gam from mgcv) done?
Here is a simpler example using the link from Nemo. The question I answer is
How exactly is the sum (or mean) centering constraint for splines (also w.r.t. gam from mgcv) done?
I answer this as this is the title and a... | How exactly is the sum (or mean) centering constraint for splines (also w.r.t. gam from mgcv) done?
Here is a simpler example using the link from Nemo. The question I answer is
How exactly is the sum (or mean) centering constraint for splines (also w.r.t. gam from mgcv) done?
I answer this as thi |
37,370 | The distribution of a sufficient statistic | The functions are identical (same carrier measure, same log-normalizer). | The distribution of a sufficient statistic | The functions are identical (same carrier measure, same log-normalizer). | The distribution of a sufficient statistic
The functions are identical (same carrier measure, same log-normalizer). | The distribution of a sufficient statistic
The functions are identical (same carrier measure, same log-normalizer). |
37,371 | Most efficient way to check answers to exercises when learning from a statistics textbook? | Statistical simulation works nicely, though it can take some time to implement. This skill will pay off in the long run, however.
Solutions manuals can often be found on-line. For instance, H & A have some solutions here. | Most efficient way to check answers to exercises when learning from a statistics textbook? | Statistical simulation works nicely, though it can take some time to implement. This skill will pay off in the long run, however.
Solutions manuals can often be found on-line. For instance, H & A have | Most efficient way to check answers to exercises when learning from a statistics textbook?
Statistical simulation works nicely, though it can take some time to implement. This skill will pay off in the long run, however.
Solutions manuals can often be found on-line. For instance, H & A have some solutions here. | Most efficient way to check answers to exercises when learning from a statistics textbook?
Statistical simulation works nicely, though it can take some time to implement. This skill will pay off in the long run, however.
Solutions manuals can often be found on-line. For instance, H & A have |
37,372 | normalization in max-sum algorithm (loopy belief propagation) | Yes. You need to normalize the messages between each iteration in order to avoid underflow.
You can normalize them so that $\log \sum_i \exp (m(i))$ = 0. | normalization in max-sum algorithm (loopy belief propagation) | Yes. You need to normalize the messages between each iteration in order to avoid underflow.
You can normalize them so that $\log \sum_i \exp (m(i))$ = 0. | normalization in max-sum algorithm (loopy belief propagation)
Yes. You need to normalize the messages between each iteration in order to avoid underflow.
You can normalize them so that $\log \sum_i \exp (m(i))$ = 0. | normalization in max-sum algorithm (loopy belief propagation)
Yes. You need to normalize the messages between each iteration in order to avoid underflow.
You can normalize them so that $\log \sum_i \exp (m(i))$ = 0. |
37,373 | normalization in max-sum algorithm (loopy belief propagation) | I was thinking through @user7814's answer and decided to figure out where his answer came from -- I had a hard time finding information about normalizing in log space so I decided to figure it out myself:
Probability Space vs Log Space Normalization
We can normalize a message $\mathbf{u} = [u_1,\ u_2\, \ldots,\ u_n]$ i... | normalization in max-sum algorithm (loopy belief propagation) | I was thinking through @user7814's answer and decided to figure out where his answer came from -- I had a hard time finding information about normalizing in log space so I decided to figure it out mys | normalization in max-sum algorithm (loopy belief propagation)
I was thinking through @user7814's answer and decided to figure out where his answer came from -- I had a hard time finding information about normalizing in log space so I decided to figure it out myself:
Probability Space vs Log Space Normalization
We can n... | normalization in max-sum algorithm (loopy belief propagation)
I was thinking through @user7814's answer and decided to figure out where his answer came from -- I had a hard time finding information about normalizing in log space so I decided to figure it out mys |
37,374 | Inferring parameters for a regression with features of both multivariate probit and ordinal regression? | Have you looked into the stats literature on reduced-rank vector generalized linear models? It seems you might be trying to identify the model by introducing constraints that in effect make it a hybrid of the probit and ordinal regressions, plus with a multilevel structure on the right-hand side of the equation. This d... | Inferring parameters for a regression with features of both multivariate probit and ordinal regressi | Have you looked into the stats literature on reduced-rank vector generalized linear models? It seems you might be trying to identify the model by introducing constraints that in effect make it a hybri | Inferring parameters for a regression with features of both multivariate probit and ordinal regression?
Have you looked into the stats literature on reduced-rank vector generalized linear models? It seems you might be trying to identify the model by introducing constraints that in effect make it a hybrid of the probit ... | Inferring parameters for a regression with features of both multivariate probit and ordinal regressi
Have you looked into the stats literature on reduced-rank vector generalized linear models? It seems you might be trying to identify the model by introducing constraints that in effect make it a hybri |
37,375 | Formal justification of Bayesian inference as a model for belief | So far I've seen two threads along these lines:
One of the earlier attempts is
Cox's Theorem (Cox, R. T. (1946). "Probability, Frequency and Reasonable Expectation". American Journal of Physics 14: 1–10), which essentially assumes Bayes theorem, and then derives the features of the resulting belief functions, and finds... | Formal justification of Bayesian inference as a model for belief | So far I've seen two threads along these lines:
One of the earlier attempts is
Cox's Theorem (Cox, R. T. (1946). "Probability, Frequency and Reasonable Expectation". American Journal of Physics 14: 1– | Formal justification of Bayesian inference as a model for belief
So far I've seen two threads along these lines:
One of the earlier attempts is
Cox's Theorem (Cox, R. T. (1946). "Probability, Frequency and Reasonable Expectation". American Journal of Physics 14: 1–10), which essentially assumes Bayes theorem, and then ... | Formal justification of Bayesian inference as a model for belief
So far I've seen two threads along these lines:
One of the earlier attempts is
Cox's Theorem (Cox, R. T. (1946). "Probability, Frequency and Reasonable Expectation". American Journal of Physics 14: 1– |
37,376 | How to define train and test sets in financial time series for estimating machine learning parameters | If you're still looking for insight regarding financial time series & machine learning, you might want to check out this article from the Journal of Economic Perspectives, which gives a great overview of various ML methods pertaining to Economics/Finance.
Essentially, the main problem you have is that most traditional ... | How to define train and test sets in financial time series for estimating machine learning parameter | If you're still looking for insight regarding financial time series & machine learning, you might want to check out this article from the Journal of Economic Perspectives, which gives a great overview | How to define train and test sets in financial time series for estimating machine learning parameters
If you're still looking for insight regarding financial time series & machine learning, you might want to check out this article from the Journal of Economic Perspectives, which gives a great overview of various ML met... | How to define train and test sets in financial time series for estimating machine learning parameter
If you're still looking for insight regarding financial time series & machine learning, you might want to check out this article from the Journal of Economic Perspectives, which gives a great overview |
37,377 | How to define train and test sets in financial time series for estimating machine learning parameters | Generally cross-validation is one of the methods to evaluate a model by splitting data into train and test data sets. Leave-one-out cross-validation splits the dataset, say n datapoints as (n-1) for train data and test on nth datapoint. this process is repeated until each data point serves as a test datapoint. This ens... | How to define train and test sets in financial time series for estimating machine learning parameter | Generally cross-validation is one of the methods to evaluate a model by splitting data into train and test data sets. Leave-one-out cross-validation splits the dataset, say n datapoints as (n-1) for t | How to define train and test sets in financial time series for estimating machine learning parameters
Generally cross-validation is one of the methods to evaluate a model by splitting data into train and test data sets. Leave-one-out cross-validation splits the dataset, say n datapoints as (n-1) for train data and test... | How to define train and test sets in financial time series for estimating machine learning parameter
Generally cross-validation is one of the methods to evaluate a model by splitting data into train and test data sets. Leave-one-out cross-validation splits the dataset, say n datapoints as (n-1) for t |
37,378 | How to describe and present the issue of perfect separation? | While performing my excavation activities on no-answer questions, I found this very sensible one, to which, I guess, by now the OP has found an answer.
But I realized that I had various questions of my own regarding the issue of perfect separation in logistic regression, and a (quick) search in the literature, did not ... | How to describe and present the issue of perfect separation? | While performing my excavation activities on no-answer questions, I found this very sensible one, to which, I guess, by now the OP has found an answer.
But I realized that I had various questions of m | How to describe and present the issue of perfect separation?
While performing my excavation activities on no-answer questions, I found this very sensible one, to which, I guess, by now the OP has found an answer.
But I realized that I had various questions of my own regarding the issue of perfect separation in logistic... | How to describe and present the issue of perfect separation?
While performing my excavation activities on no-answer questions, I found this very sensible one, to which, I guess, by now the OP has found an answer.
But I realized that I had various questions of m |
37,379 | Simultaneous Z-test for the equality of two proportions (binomial distribution) | There is no simple test for what you are looking for, because you have to account for the unknown correlation of the 10 responses within a subject. Some options, many of which are usually not quite adequate, include:
Collapse the 10 answers to "at least one yes", and use a chi-square test - this might be reasonable fo... | Simultaneous Z-test for the equality of two proportions (binomial distribution) | There is no simple test for what you are looking for, because you have to account for the unknown correlation of the 10 responses within a subject. Some options, many of which are usually not quite ad | Simultaneous Z-test for the equality of two proportions (binomial distribution)
There is no simple test for what you are looking for, because you have to account for the unknown correlation of the 10 responses within a subject. Some options, many of which are usually not quite adequate, include:
Collapse the 10 answer... | Simultaneous Z-test for the equality of two proportions (binomial distribution)
There is no simple test for what you are looking for, because you have to account for the unknown correlation of the 10 responses within a subject. Some options, many of which are usually not quite ad |
37,380 | Simultaneous Z-test for the equality of two proportions (binomial distribution) | Perhaps a hierarchical log-linear model would work. Picture your data as a 2 x 10 x 2 array: the first dimension is agree/disagree; the second dimension contains the questions and the third dimension indexes the two groups. You fit a series of models until you get one that fits. Thus
condition on the margins only. Thi... | Simultaneous Z-test for the equality of two proportions (binomial distribution) | Perhaps a hierarchical log-linear model would work. Picture your data as a 2 x 10 x 2 array: the first dimension is agree/disagree; the second dimension contains the questions and the third dimension | Simultaneous Z-test for the equality of two proportions (binomial distribution)
Perhaps a hierarchical log-linear model would work. Picture your data as a 2 x 10 x 2 array: the first dimension is agree/disagree; the second dimension contains the questions and the third dimension indexes the two groups. You fit a series... | Simultaneous Z-test for the equality of two proportions (binomial distribution)
Perhaps a hierarchical log-linear model would work. Picture your data as a 2 x 10 x 2 array: the first dimension is agree/disagree; the second dimension contains the questions and the third dimension |
37,381 | What is the relationship between graphical models and hierarchical Bayesian models? | Firstly I would like you to see this example of modelling cancer rates.
https://stats.stackexchange.com/a/86231/29568
Graphical models are graphs which encode independencies between the random variables in the model. A graphical model with the assumptions on random variables can give us the joint distribution given t... | What is the relationship between graphical models and hierarchical Bayesian models? | Firstly I would like you to see this example of modelling cancer rates.
https://stats.stackexchange.com/a/86231/29568
Graphical models are graphs which encode independencies between the random varia | What is the relationship between graphical models and hierarchical Bayesian models?
Firstly I would like you to see this example of modelling cancer rates.
https://stats.stackexchange.com/a/86231/29568
Graphical models are graphs which encode independencies between the random variables in the model. A graphical model... | What is the relationship between graphical models and hierarchical Bayesian models?
Firstly I would like you to see this example of modelling cancer rates.
https://stats.stackexchange.com/a/86231/29568
Graphical models are graphs which encode independencies between the random varia |
37,382 | What is the relationship between graphical models and hierarchical Bayesian models? | There's a brief reference to this subject at section 2.4.1 in Graphical Models, Exponential Families, and Variational Inference | What is the relationship between graphical models and hierarchical Bayesian models? | There's a brief reference to this subject at section 2.4.1 in Graphical Models, Exponential Families, and Variational Inference | What is the relationship between graphical models and hierarchical Bayesian models?
There's a brief reference to this subject at section 2.4.1 in Graphical Models, Exponential Families, and Variational Inference | What is the relationship between graphical models and hierarchical Bayesian models?
There's a brief reference to this subject at section 2.4.1 in Graphical Models, Exponential Families, and Variational Inference |
37,383 | What is the relationship between graphical models and hierarchical Bayesian models? | My understanding is that a hierarchical model can be represented by a DAG. Hence all our knowledge about probabilistic graphical models applies. One difference (which is not really a difference) is that in hierarchical models, usually hyperpriors are included. Or at least hyperpriors are discussed in the context of hie... | What is the relationship between graphical models and hierarchical Bayesian models? | My understanding is that a hierarchical model can be represented by a DAG. Hence all our knowledge about probabilistic graphical models applies. One difference (which is not really a difference) is th | What is the relationship between graphical models and hierarchical Bayesian models?
My understanding is that a hierarchical model can be represented by a DAG. Hence all our knowledge about probabilistic graphical models applies. One difference (which is not really a difference) is that in hierarchical models, usually h... | What is the relationship between graphical models and hierarchical Bayesian models?
My understanding is that a hierarchical model can be represented by a DAG. Hence all our knowledge about probabilistic graphical models applies. One difference (which is not really a difference) is th |
37,384 | Correct number of parameters of AR models for AIC / BIC ? | For AIC/BIC selection it doesn't really matter whether you choose to count the variance parameter, as long as you are consistent across models, because inference based on information-theoretic criteria only depends on the differences between the values for different models. Thus, adding 2 (for an additional parameter)... | Correct number of parameters of AR models for AIC / BIC ? | For AIC/BIC selection it doesn't really matter whether you choose to count the variance parameter, as long as you are consistent across models, because inference based on information-theoretic criteri | Correct number of parameters of AR models for AIC / BIC ?
For AIC/BIC selection it doesn't really matter whether you choose to count the variance parameter, as long as you are consistent across models, because inference based on information-theoretic criteria only depends on the differences between the values for diffe... | Correct number of parameters of AR models for AIC / BIC ?
For AIC/BIC selection it doesn't really matter whether you choose to count the variance parameter, as long as you are consistent across models, because inference based on information-theoretic criteri |
37,385 | Correct number of parameters of AR models for AIC / BIC ? | To obtain the AIC or BIC criteria in ARMA models, you need to find the number of estimated parameters in the model (except for the residual variance) including the constant term if it is estimated as mentioned in "Time Series Analysis and Forecasting by Example", by Søren Bisgaard, Murat Kulahci, page 164. So the numb... | Correct number of parameters of AR models for AIC / BIC ? | To obtain the AIC or BIC criteria in ARMA models, you need to find the number of estimated parameters in the model (except for the residual variance) including the constant term if it is estimated as | Correct number of parameters of AR models for AIC / BIC ?
To obtain the AIC or BIC criteria in ARMA models, you need to find the number of estimated parameters in the model (except for the residual variance) including the constant term if it is estimated as mentioned in "Time Series Analysis and Forecasting by Example"... | Correct number of parameters of AR models for AIC / BIC ?
To obtain the AIC or BIC criteria in ARMA models, you need to find the number of estimated parameters in the model (except for the residual variance) including the constant term if it is estimated as |
37,386 | Is Bonferroni correction too anti-conservative/liberal for some dependent hypotheses? | Bonferroni can't be liberal, regardless of dependence, if your p-values are computed correctly.
Let A be the event of Type I error in one test and let B be the event of Type I error in another test. The probability that A or B (or both) will occur is:
P(A or B) = P(A) + P(B) - P(A and B)
Because P(A and B) is a probabi... | Is Bonferroni correction too anti-conservative/liberal for some dependent hypotheses? | Bonferroni can't be liberal, regardless of dependence, if your p-values are computed correctly.
Let A be the event of Type I error in one test and let B be the event of Type I error in another test. T | Is Bonferroni correction too anti-conservative/liberal for some dependent hypotheses?
Bonferroni can't be liberal, regardless of dependence, if your p-values are computed correctly.
Let A be the event of Type I error in one test and let B be the event of Type I error in another test. The probability that A or B (or bot... | Is Bonferroni correction too anti-conservative/liberal for some dependent hypotheses?
Bonferroni can't be liberal, regardless of dependence, if your p-values are computed correctly.
Let A be the event of Type I error in one test and let B be the event of Type I error in another test. T |
37,387 | Is Bonferroni correction too anti-conservative/liberal for some dependent hypotheses? | I think I finally have the answer. I need an additional requirement on the distribution of $P(p_1,p_2|H_1=0, H_2=0)$. Before, I only required that $P(p_1|H_1=0)$ is uniform between 0 and 1. In this case my example is correct and Bonferroni would be too liberal. However, if I additionally require the uniformity of $P(p_... | Is Bonferroni correction too anti-conservative/liberal for some dependent hypotheses? | I think I finally have the answer. I need an additional requirement on the distribution of $P(p_1,p_2|H_1=0, H_2=0)$. Before, I only required that $P(p_1|H_1=0)$ is uniform between 0 and 1. In this ca | Is Bonferroni correction too anti-conservative/liberal for some dependent hypotheses?
I think I finally have the answer. I need an additional requirement on the distribution of $P(p_1,p_2|H_1=0, H_2=0)$. Before, I only required that $P(p_1|H_1=0)$ is uniform between 0 and 1. In this case my example is correct and Bonfe... | Is Bonferroni correction too anti-conservative/liberal for some dependent hypotheses?
I think I finally have the answer. I need an additional requirement on the distribution of $P(p_1,p_2|H_1=0, H_2=0)$. Before, I only required that $P(p_1|H_1=0)$ is uniform between 0 and 1. In this ca |
37,388 | Matrix Factorization Model for recommender systems how to determine number of latent features? | In response to your first question, cross validation is a widely used approach. One possible scheme is the following.
For each K value within a pre-selected range, use cross validation to estimate model performance (e.g. prediction accuracy). This will provide one estimated model performance metric per k-value. Then, s... | Matrix Factorization Model for recommender systems how to determine number of latent features? | In response to your first question, cross validation is a widely used approach. One possible scheme is the following.
For each K value within a pre-selected range, use cross validation to estimate mod | Matrix Factorization Model for recommender systems how to determine number of latent features?
In response to your first question, cross validation is a widely used approach. One possible scheme is the following.
For each K value within a pre-selected range, use cross validation to estimate model performance (e.g. pred... | Matrix Factorization Model for recommender systems how to determine number of latent features?
In response to your first question, cross validation is a widely used approach. One possible scheme is the following.
For each K value within a pre-selected range, use cross validation to estimate mod |
37,389 | Matrix Factorization Model for recommender systems how to determine number of latent features? | To answer your first question, I would do cross-validation, and for the second question, I would say you should look into tensor factorization. If you have multi-dimensional data representation, you may definitely consider tensor factorization which allows you to play with some additional data as another dimensions.
Yo... | Matrix Factorization Model for recommender systems how to determine number of latent features? | To answer your first question, I would do cross-validation, and for the second question, I would say you should look into tensor factorization. If you have multi-dimensional data representation, you m | Matrix Factorization Model for recommender systems how to determine number of latent features?
To answer your first question, I would do cross-validation, and for the second question, I would say you should look into tensor factorization. If you have multi-dimensional data representation, you may definitely consider te... | Matrix Factorization Model for recommender systems how to determine number of latent features?
To answer your first question, I would do cross-validation, and for the second question, I would say you should look into tensor factorization. If you have multi-dimensional data representation, you m |
37,390 | How do I combine multiple prior components and a likelihood? | I don't think there is anything wrong with your approach, but there are some technical details which makes your implementation incorrect. Now when you have a mixture prior, you will also get a mixture posterior. The easiest way to procede, I think, is to calculate the component posteriors and the component weights se... | How do I combine multiple prior components and a likelihood? | I don't think there is anything wrong with your approach, but there are some technical details which makes your implementation incorrect. Now when you have a mixture prior, you will also get a mixtur | How do I combine multiple prior components and a likelihood?
I don't think there is anything wrong with your approach, but there are some technical details which makes your implementation incorrect. Now when you have a mixture prior, you will also get a mixture posterior. The easiest way to procede, I think, is to ca... | How do I combine multiple prior components and a likelihood?
I don't think there is anything wrong with your approach, but there are some technical details which makes your implementation incorrect. Now when you have a mixture prior, you will also get a mixtur |
37,391 | Why does the log likelihood need to go to minus infinity when the parameter approaches the boundary of the parameter space? | in order for the maximum likelihood estimate to be valid, the log likelihood needs to go to minus infinity as the parameter goes to the boundary
This is equal to saying, the Likelihood of a parameter needs to become 0 at the boundary of the parameter space in order for the result to be valid.
Well first of all, you ca... | Why does the log likelihood need to go to minus infinity when the parameter approaches the boundary | in order for the maximum likelihood estimate to be valid, the log likelihood needs to go to minus infinity as the parameter goes to the boundary
This is equal to saying, the Likelihood of a parameter | Why does the log likelihood need to go to minus infinity when the parameter approaches the boundary of the parameter space?
in order for the maximum likelihood estimate to be valid, the log likelihood needs to go to minus infinity as the parameter goes to the boundary
This is equal to saying, the Likelihood of a param... | Why does the log likelihood need to go to minus infinity when the parameter approaches the boundary
in order for the maximum likelihood estimate to be valid, the log likelihood needs to go to minus infinity as the parameter goes to the boundary
This is equal to saying, the Likelihood of a parameter |
37,392 | Hidden Markov Model to predict the next state | You use the forward algorithm to predict $P(X_{t+1})$.
$P(X_{t+1}|X_t, Y_{1:t} ) = \sum_{X} P(X_{t+1}|X_t) \cdot P(X_t|Y_{1:t}) $
So, you use the same principle for predicting $P(X_{t})$, but without being able to incorporate $Y_{t+1}$, since it is not observed yet. | Hidden Markov Model to predict the next state | You use the forward algorithm to predict $P(X_{t+1})$.
$P(X_{t+1}|X_t, Y_{1:t} ) = \sum_{X} P(X_{t+1}|X_t) \cdot P(X_t|Y_{1:t}) $
So, you use the same principle for predicting $P(X_{t})$, but without | Hidden Markov Model to predict the next state
You use the forward algorithm to predict $P(X_{t+1})$.
$P(X_{t+1}|X_t, Y_{1:t} ) = \sum_{X} P(X_{t+1}|X_t) \cdot P(X_t|Y_{1:t}) $
So, you use the same principle for predicting $P(X_{t})$, but without being able to incorporate $Y_{t+1}$, since it is not observed yet. | Hidden Markov Model to predict the next state
You use the forward algorithm to predict $P(X_{t+1})$.
$P(X_{t+1}|X_t, Y_{1:t} ) = \sum_{X} P(X_{t+1}|X_t) \cdot P(X_t|Y_{1:t}) $
So, you use the same principle for predicting $P(X_{t})$, but without |
37,393 | Hidden Markov Model to predict the next state | To get the probability over hidden states at t_2, just multiply your posterior over t_1 by your transition matrix.
https://stackoverflow.com/questions/15554923/how-to-perform-a-prediction-with-matlabs-hidden-markov-model-statistics-toolbo | Hidden Markov Model to predict the next state | To get the probability over hidden states at t_2, just multiply your posterior over t_1 by your transition matrix.
https://stackoverflow.com/questions/15554923/how-to-perform-a-prediction-with-matlabs | Hidden Markov Model to predict the next state
To get the probability over hidden states at t_2, just multiply your posterior over t_1 by your transition matrix.
https://stackoverflow.com/questions/15554923/how-to-perform-a-prediction-with-matlabs-hidden-markov-model-statistics-toolbo | Hidden Markov Model to predict the next state
To get the probability over hidden states at t_2, just multiply your posterior over t_1 by your transition matrix.
https://stackoverflow.com/questions/15554923/how-to-perform-a-prediction-with-matlabs |
37,394 | Power of a hypothesis test | I have not checked out your text, but your understanding is correct.
The alternative hypothesis (Ha) is usually stated vaguely as something like the difference between the two population means is not zero. But for the purpose of computing and interpreting power you need a definitive Ha, say that the difference between... | Power of a hypothesis test | I have not checked out your text, but your understanding is correct.
The alternative hypothesis (Ha) is usually stated vaguely as something like the difference between the two population means is not | Power of a hypothesis test
I have not checked out your text, but your understanding is correct.
The alternative hypothesis (Ha) is usually stated vaguely as something like the difference between the two population means is not zero. But for the purpose of computing and interpreting power you need a definitive Ha, say ... | Power of a hypothesis test
I have not checked out your text, but your understanding is correct.
The alternative hypothesis (Ha) is usually stated vaguely as something like the difference between the two population means is not |
37,395 | Power of a hypothesis test | It seems to me that it is the power of the test itself, rather than the power against either of the hypothesis. If there is very little data, the test will be unable to reject $H_0$ whether it is false or not, so the test itself has little power to reveal anything about the problem. If we have lots of data, we will b... | Power of a hypothesis test | It seems to me that it is the power of the test itself, rather than the power against either of the hypothesis. If there is very little data, the test will be unable to reject $H_0$ whether it is fal | Power of a hypothesis test
It seems to me that it is the power of the test itself, rather than the power against either of the hypothesis. If there is very little data, the test will be unable to reject $H_0$ whether it is false or not, so the test itself has little power to reveal anything about the problem. If we h... | Power of a hypothesis test
It seems to me that it is the power of the test itself, rather than the power against either of the hypothesis. If there is very little data, the test will be unable to reject $H_0$ whether it is fal |
37,396 | Meaning of Likelihood in layman's terms [duplicate] | Let's say the data comes from a distribution with a parameter $\theta$ whose value we don't know. You can think of the likelihood function ${L(\theta)}$, very roughly, as "the probability of observing the data given this value of $\theta$".
From this comes the maximum likelihood principle: when we want to estimate $\th... | Meaning of Likelihood in layman's terms [duplicate] | Let's say the data comes from a distribution with a parameter $\theta$ whose value we don't know. You can think of the likelihood function ${L(\theta)}$, very roughly, as "the probability of observing | Meaning of Likelihood in layman's terms [duplicate]
Let's say the data comes from a distribution with a parameter $\theta$ whose value we don't know. You can think of the likelihood function ${L(\theta)}$, very roughly, as "the probability of observing the data given this value of $\theta$".
From this comes the maximum... | Meaning of Likelihood in layman's terms [duplicate]
Let's say the data comes from a distribution with a parameter $\theta$ whose value we don't know. You can think of the likelihood function ${L(\theta)}$, very roughly, as "the probability of observing |
37,397 | Survey design chi square | If you are going along the path of stacking the data sets together, then you should define super-strata corresponding to the two data sets/waves, so that svydesign() knows that they are independent. Thus your new svydesign will have strata = cross of year and strata, the PSUs from the original designs, and the weights ... | Survey design chi square | If you are going along the path of stacking the data sets together, then you should define super-strata corresponding to the two data sets/waves, so that svydesign() knows that they are independent. T | Survey design chi square
If you are going along the path of stacking the data sets together, then you should define super-strata corresponding to the two data sets/waves, so that svydesign() knows that they are independent. Thus your new svydesign will have strata = cross of year and strata, the PSUs from the original ... | Survey design chi square
If you are going along the path of stacking the data sets together, then you should define super-strata corresponding to the two data sets/waves, so that svydesign() knows that they are independent. T |
37,398 | When to use sample median as an estimator for the median of a lognormal distribution? | Apparently the concept of unbiasedness has already been discussed a long time ago. I feel it is a topic worth of dicussion as mean-unbiasedness is a standard requirement for a good estimator but for small sample it does not mean as much as in large sample estimations.
I post these two references as an answer to my seco... | When to use sample median as an estimator for the median of a lognormal distribution? | Apparently the concept of unbiasedness has already been discussed a long time ago. I feel it is a topic worth of dicussion as mean-unbiasedness is a standard requirement for a good estimator but for s | When to use sample median as an estimator for the median of a lognormal distribution?
Apparently the concept of unbiasedness has already been discussed a long time ago. I feel it is a topic worth of dicussion as mean-unbiasedness is a standard requirement for a good estimator but for small sample it does not mean as mu... | When to use sample median as an estimator for the median of a lognormal distribution?
Apparently the concept of unbiasedness has already been discussed a long time ago. I feel it is a topic worth of dicussion as mean-unbiasedness is a standard requirement for a good estimator but for s |
37,399 | Force-directed methods to draw graphs | If the subgraphs are not connected to each other, as in your picture, then their relative placement is arbitrary. Fruchterman-Reingold layout is only based on connections. | Force-directed methods to draw graphs | If the subgraphs are not connected to each other, as in your picture, then their relative placement is arbitrary. Fruchterman-Reingold layout is only based on connections. | Force-directed methods to draw graphs
If the subgraphs are not connected to each other, as in your picture, then their relative placement is arbitrary. Fruchterman-Reingold layout is only based on connections. | Force-directed methods to draw graphs
If the subgraphs are not connected to each other, as in your picture, then their relative placement is arbitrary. Fruchterman-Reingold layout is only based on connections. |
37,400 | Choosing non-informative priors | Jeffreys priors are indeed unmanageable outside standard families and not even necessarily recommended in high dimensions. If the model is complex enough, priors should take advantage of the hierarchical structures underlying this model...
Using the actual data to produce or select a "prior" is a contradiction in term... | Choosing non-informative priors | Jeffreys priors are indeed unmanageable outside standard families and not even necessarily recommended in high dimensions. If the model is complex enough, priors should take advantage of the hierarchi | Choosing non-informative priors
Jeffreys priors are indeed unmanageable outside standard families and not even necessarily recommended in high dimensions. If the model is complex enough, priors should take advantage of the hierarchical structures underlying this model...
Using the actual data to produce or select a "p... | Choosing non-informative priors
Jeffreys priors are indeed unmanageable outside standard families and not even necessarily recommended in high dimensions. If the model is complex enough, priors should take advantage of the hierarchi |
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