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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37,601 | Post hoc test of adjusted means (after ANCOVA) | In STATISTICA (StatSoft), when performing ANCOVA, post-hoc values are related of adjusted means. Even though in top-X axis are present the "non-adjusted means".
Do the test... compare means and do the post-hoc with and without the covariates... P values are different. | Post hoc test of adjusted means (after ANCOVA) | In STATISTICA (StatSoft), when performing ANCOVA, post-hoc values are related of adjusted means. Even though in top-X axis are present the "non-adjusted means".
Do the test... compare means and do the | Post hoc test of adjusted means (after ANCOVA)
In STATISTICA (StatSoft), when performing ANCOVA, post-hoc values are related of adjusted means. Even though in top-X axis are present the "non-adjusted means".
Do the test... compare means and do the post-hoc with and without the covariates... P values are different. | Post hoc test of adjusted means (after ANCOVA)
In STATISTICA (StatSoft), when performing ANCOVA, post-hoc values are related of adjusted means. Even though in top-X axis are present the "non-adjusted means".
Do the test... compare means and do the |
37,602 | Prediction with Bayesian networks in R | I think everything is in the function bn.fit. Following up on your code, I got
> bn.fit(bn.hc, dat)
Bayesian network parameters
Parameters of node won (multinomial distribution)
Conditional probability table:
0 1
0.6666667 0.3333333
Parameters of node sold (multinomial distribution)
Condit... | Prediction with Bayesian networks in R | I think everything is in the function bn.fit. Following up on your code, I got
> bn.fit(bn.hc, dat)
Bayesian network parameters
Parameters of node won (multinomial distribution)
Conditional pro | Prediction with Bayesian networks in R
I think everything is in the function bn.fit. Following up on your code, I got
> bn.fit(bn.hc, dat)
Bayesian network parameters
Parameters of node won (multinomial distribution)
Conditional probability table:
0 1
0.6666667 0.3333333
Parameters of node ... | Prediction with Bayesian networks in R
I think everything is in the function bn.fit. Following up on your code, I got
> bn.fit(bn.hc, dat)
Bayesian network parameters
Parameters of node won (multinomial distribution)
Conditional pro |
37,603 | Dirichlet processes for supervised learning? | This question isn't getting too much attention, so I'm going to answer to update on what I've found and (hopefully) stimulate discussion. I've ran into an article I'm looking forward to reading that uses DPMs to do classification (Shahbaba and Neal, 2007) which they tested on protein fold data. Essentially it appears t... | Dirichlet processes for supervised learning? | This question isn't getting too much attention, so I'm going to answer to update on what I've found and (hopefully) stimulate discussion. I've ran into an article I'm looking forward to reading that u | Dirichlet processes for supervised learning?
This question isn't getting too much attention, so I'm going to answer to update on what I've found and (hopefully) stimulate discussion. I've ran into an article I'm looking forward to reading that uses DPMs to do classification (Shahbaba and Neal, 2007) which they tested o... | Dirichlet processes for supervised learning?
This question isn't getting too much attention, so I'm going to answer to update on what I've found and (hopefully) stimulate discussion. I've ran into an article I'm looking forward to reading that u |
37,604 | Dirichlet processes for supervised learning? | Take a look at the DPpackage of R. Dirichlet process can be used at least as a prior for a random effect, and to construct a nonparametric error distribution for regression. | Dirichlet processes for supervised learning? | Take a look at the DPpackage of R. Dirichlet process can be used at least as a prior for a random effect, and to construct a nonparametric error distribution for regression. | Dirichlet processes for supervised learning?
Take a look at the DPpackage of R. Dirichlet process can be used at least as a prior for a random effect, and to construct a nonparametric error distribution for regression. | Dirichlet processes for supervised learning?
Take a look at the DPpackage of R. Dirichlet process can be used at least as a prior for a random effect, and to construct a nonparametric error distribution for regression. |
37,605 | How important is using the exact method for ties in a Cox model, and how long should this take? | It is normal that the exact method takes such a long time: it has to do quite a lot. My own experience is that the approximate methods you refer to can be quite poor (i.e., leading to substantively different conclusions to the use of exact methods), but my own experiences are a bit atypical as they involve the applic... | How important is using the exact method for ties in a Cox model, and how long should this take? | It is normal that the exact method takes such a long time: it has to do quite a lot. My own experience is that the approximate methods you refer to can be quite poor (i.e., leading to substantively | How important is using the exact method for ties in a Cox model, and how long should this take?
It is normal that the exact method takes such a long time: it has to do quite a lot. My own experience is that the approximate methods you refer to can be quite poor (i.e., leading to substantively different conclusions to... | How important is using the exact method for ties in a Cox model, and how long should this take?
It is normal that the exact method takes such a long time: it has to do quite a lot. My own experience is that the approximate methods you refer to can be quite poor (i.e., leading to substantively |
37,606 | How to interpret coefficients in a vector autoregressive model? | It's often pretty hard interpret the coefficients of a VAR, specially if it includes many variables and lags. As one lag of a variable says one thing and another the opposite, there are no clear dynamics between the variables you wish to investigate, usually a VAR is accompanied with tools like the impulse response fun... | How to interpret coefficients in a vector autoregressive model? | It's often pretty hard interpret the coefficients of a VAR, specially if it includes many variables and lags. As one lag of a variable says one thing and another the opposite, there are no clear dynam | How to interpret coefficients in a vector autoregressive model?
It's often pretty hard interpret the coefficients of a VAR, specially if it includes many variables and lags. As one lag of a variable says one thing and another the opposite, there are no clear dynamics between the variables you wish to investigate, usual... | How to interpret coefficients in a vector autoregressive model?
It's often pretty hard interpret the coefficients of a VAR, specially if it includes many variables and lags. As one lag of a variable says one thing and another the opposite, there are no clear dynam |
37,607 | Estimating the number of times each of four pairs of dice was thrown | This reply addresses the first and third bullet points: Is the problem solvable? Can we frame it in a conventional way to allow for searching or application of conventional methods?
To address the latter question it helps to start generalizing the situation while retaining any special features that might be useful for ... | Estimating the number of times each of four pairs of dice was thrown | This reply addresses the first and third bullet points: Is the problem solvable? Can we frame it in a conventional way to allow for searching or application of conventional methods?
To address the lat | Estimating the number of times each of four pairs of dice was thrown
This reply addresses the first and third bullet points: Is the problem solvable? Can we frame it in a conventional way to allow for searching or application of conventional methods?
To address the latter question it helps to start generalizing the sit... | Estimating the number of times each of four pairs of dice was thrown
This reply addresses the first and third bullet points: Is the problem solvable? Can we frame it in a conventional way to allow for searching or application of conventional methods?
To address the lat |
37,608 | Estimating the number of times each of four pairs of dice was thrown | Let p be the probability of throwing a 1 on any die. Let ni be the probability of the outcome designated by i.
The probability of the occurrences 1,2,3 and 4 are all p$^2$ as the dice are rolled independently. The probability of occurrences 5, 6, 7, and 8 are all 2p(1-p) since for example in case 5 a red must roll a 1... | Estimating the number of times each of four pairs of dice was thrown | Let p be the probability of throwing a 1 on any die. Let ni be the probability of the outcome designated by i.
The probability of the occurrences 1,2,3 and 4 are all p$^2$ as the dice are rolled inde | Estimating the number of times each of four pairs of dice was thrown
Let p be the probability of throwing a 1 on any die. Let ni be the probability of the outcome designated by i.
The probability of the occurrences 1,2,3 and 4 are all p$^2$ as the dice are rolled independently. The probability of occurrences 5, 6, 7, ... | Estimating the number of times each of four pairs of dice was thrown
Let p be the probability of throwing a 1 on any die. Let ni be the probability of the outcome designated by i.
The probability of the occurrences 1,2,3 and 4 are all p$^2$ as the dice are rolled inde |
37,609 | Estimating the number of times each of four pairs of dice was thrown | Let $p$ be the probability of any die rolling a one. Then the probability of outcomes 1, 2, 3 and 4 are all $p^2$. Let $n_1$, $n_2$, $n_3$ and $n_4$ be number of observations for outcomes 1 through 4. Let $n_{rb}$, $n_{ry}$, $n_{gb}$ and $n_{gy}$ be the values we want to estimate, which are the actual number of times ... | Estimating the number of times each of four pairs of dice was thrown | Let $p$ be the probability of any die rolling a one. Then the probability of outcomes 1, 2, 3 and 4 are all $p^2$. Let $n_1$, $n_2$, $n_3$ and $n_4$ be number of observations for outcomes 1 through 4 | Estimating the number of times each of four pairs of dice was thrown
Let $p$ be the probability of any die rolling a one. Then the probability of outcomes 1, 2, 3 and 4 are all $p^2$. Let $n_1$, $n_2$, $n_3$ and $n_4$ be number of observations for outcomes 1 through 4. Let $n_{rb}$, $n_{ry}$, $n_{gb}$ and $n_{gy}$ be ... | Estimating the number of times each of four pairs of dice was thrown
Let $p$ be the probability of any die rolling a one. Then the probability of outcomes 1, 2, 3 and 4 are all $p^2$. Let $n_1$, $n_2$, $n_3$ and $n_4$ be number of observations for outcomes 1 through 4 |
37,610 | How to test that a set of distributions are located in a given order? | The Kruskal-Wallis procedure is the multi-group equivalent of the Wilcoxon rank-sum test, which is akin to one-way ANOVA without the normality assumption.
A nonparametric ordered alternative equivalent of the Kruskal-Wallis test is the Jonckheere-Terpstra test.
That is, where the Kruskal-Wallis tests against a general ... | How to test that a set of distributions are located in a given order? | The Kruskal-Wallis procedure is the multi-group equivalent of the Wilcoxon rank-sum test, which is akin to one-way ANOVA without the normality assumption.
A nonparametric ordered alternative equivalen | How to test that a set of distributions are located in a given order?
The Kruskal-Wallis procedure is the multi-group equivalent of the Wilcoxon rank-sum test, which is akin to one-way ANOVA without the normality assumption.
A nonparametric ordered alternative equivalent of the Kruskal-Wallis test is the Jonckheere-Ter... | How to test that a set of distributions are located in a given order?
The Kruskal-Wallis procedure is the multi-group equivalent of the Wilcoxon rank-sum test, which is akin to one-way ANOVA without the normality assumption.
A nonparametric ordered alternative equivalen |
37,611 | What software (paid or free) exists for learning large datasets? | You could try using Weka. It has implemented a large collection of classification algorithms. In your case you definitely want to experiment on the speed of algorithms given your dataset. The Naive Bayes and (Lib)SVM algorithms are known to be quite fast. Also try the LibLINEAR algorithm instead of LibSVM, it is someti... | What software (paid or free) exists for learning large datasets? | You could try using Weka. It has implemented a large collection of classification algorithms. In your case you definitely want to experiment on the speed of algorithms given your dataset. The Naive Ba | What software (paid or free) exists for learning large datasets?
You could try using Weka. It has implemented a large collection of classification algorithms. In your case you definitely want to experiment on the speed of algorithms given your dataset. The Naive Bayes and (Lib)SVM algorithms are known to be quite fast.... | What software (paid or free) exists for learning large datasets?
You could try using Weka. It has implemented a large collection of classification algorithms. In your case you definitely want to experiment on the speed of algorithms given your dataset. The Naive Ba |
37,612 | What software (paid or free) exists for learning large datasets? | Similar to Weka, you may also try SCaVis. You can create large data containers using Python language (or Java, Groovy, Rubu - they are all supported by SCaVis). I think if you do not want to create in-memory container, try to use PFile object that can scan your data line-by-line without loading all data to the memory | What software (paid or free) exists for learning large datasets? | Similar to Weka, you may also try SCaVis. You can create large data containers using Python language (or Java, Groovy, Rubu - they are all supported by SCaVis). I think if you do not want to create in | What software (paid or free) exists for learning large datasets?
Similar to Weka, you may also try SCaVis. You can create large data containers using Python language (or Java, Groovy, Rubu - they are all supported by SCaVis). I think if you do not want to create in-memory container, try to use PFile object that can sca... | What software (paid or free) exists for learning large datasets?
Similar to Weka, you may also try SCaVis. You can create large data containers using Python language (or Java, Groovy, Rubu - they are all supported by SCaVis). I think if you do not want to create in |
37,613 | How to analyse RCT where significant baseline differences exist despite randomisation? | If there is enough data to do this include the most significant baseline covariates in the model giving you a way to adjust for covaraite imbalance. There is an interesting book by Vance Berger that specifically addresses the issue of covariate imbalance in clinical trials and how to detect it. | How to analyse RCT where significant baseline differences exist despite randomisation? | If there is enough data to do this include the most significant baseline covariates in the model giving you a way to adjust for covaraite imbalance. There is an interesting book by Vance Berger that | How to analyse RCT where significant baseline differences exist despite randomisation?
If there is enough data to do this include the most significant baseline covariates in the model giving you a way to adjust for covaraite imbalance. There is an interesting book by Vance Berger that specifically addresses the issue ... | How to analyse RCT where significant baseline differences exist despite randomisation?
If there is enough data to do this include the most significant baseline covariates in the model giving you a way to adjust for covaraite imbalance. There is an interesting book by Vance Berger that |
37,614 | If only a two-way ANOVA main effect is significant, what is the appropriate follow-up? | You have no interaction and no main effect if IV1. Do NOT go looking at all comparisons of all means.
Even if you stick with IV2 I'm concerned that you're comparing significant and not significant and drawing conclusions and the difference between significant and not significant is likely not significant. Look at you... | If only a two-way ANOVA main effect is significant, what is the appropriate follow-up? | You have no interaction and no main effect if IV1. Do NOT go looking at all comparisons of all means.
Even if you stick with IV2 I'm concerned that you're comparing significant and not significant an | If only a two-way ANOVA main effect is significant, what is the appropriate follow-up?
You have no interaction and no main effect if IV1. Do NOT go looking at all comparisons of all means.
Even if you stick with IV2 I'm concerned that you're comparing significant and not significant and drawing conclusions and the dif... | If only a two-way ANOVA main effect is significant, what is the appropriate follow-up?
You have no interaction and no main effect if IV1. Do NOT go looking at all comparisons of all means.
Even if you stick with IV2 I'm concerned that you're comparing significant and not significant an |
37,615 | If only a two-way ANOVA main effect is significant, what is the appropriate follow-up? | I don't like the term appropriate post hoc analysis. Generally speaking if you tested and found a statistically significant main effect but no significant first order interactions you might be interested in some pairwise difference to identify why there is an effect. | If only a two-way ANOVA main effect is significant, what is the appropriate follow-up? | I don't like the term appropriate post hoc analysis. Generally speaking if you tested and found a statistically significant main effect but no significant first order interactions you might be intere | If only a two-way ANOVA main effect is significant, what is the appropriate follow-up?
I don't like the term appropriate post hoc analysis. Generally speaking if you tested and found a statistically significant main effect but no significant first order interactions you might be interested in some pairwise difference ... | If only a two-way ANOVA main effect is significant, what is the appropriate follow-up?
I don't like the term appropriate post hoc analysis. Generally speaking if you tested and found a statistically significant main effect but no significant first order interactions you might be intere |
37,616 | Estimating an underlying pdf from binomial trials | This is just a simple idea and is not something I have seen in the literature. I will take away the randomness of the flips by conditioning on the observed number for each coin. Take the usual estimate for pi (i.e. number of heads divided by the number of flips) for the ith randomly selected coin. This set of estima... | Estimating an underlying pdf from binomial trials | This is just a simple idea and is not something I have seen in the literature. I will take away the randomness of the flips by conditioning on the observed number for each coin. Take the usual estim | Estimating an underlying pdf from binomial trials
This is just a simple idea and is not something I have seen in the literature. I will take away the randomness of the flips by conditioning on the observed number for each coin. Take the usual estimate for pi (i.e. number of heads divided by the number of flips) for t... | Estimating an underlying pdf from binomial trials
This is just a simple idea and is not something I have seen in the literature. I will take away the randomness of the flips by conditioning on the observed number for each coin. Take the usual estim |
37,617 | Estimating an underlying pdf from binomial trials | Your problem can be generalized as follows:
The parameter $p$ is generated according to an unknown probability density.
You can measure $p$ only with a measurement error $\sigma$, which yields an estimator $\hat{p}$ for $p$ that has a known distribution (binomial distribution).
A simple approach is suggested by Glen_... | Estimating an underlying pdf from binomial trials | Your problem can be generalized as follows:
The parameter $p$ is generated according to an unknown probability density.
You can measure $p$ only with a measurement error $\sigma$, which yields an est | Estimating an underlying pdf from binomial trials
Your problem can be generalized as follows:
The parameter $p$ is generated according to an unknown probability density.
You can measure $p$ only with a measurement error $\sigma$, which yields an estimator $\hat{p}$ for $p$ that has a known distribution (binomial distr... | Estimating an underlying pdf from binomial trials
Your problem can be generalized as follows:
The parameter $p$ is generated according to an unknown probability density.
You can measure $p$ only with a measurement error $\sigma$, which yields an est |
37,618 | Can I have too much data? | It sounds like the networks you train with more data overfit to that data and hence perform worse on different data. The concept the networks are supposed to learn may be obvious from the small data set, but adding more data in the other set obscures it (or even transforms it into a different concept).
One way to mitig... | Can I have too much data? | It sounds like the networks you train with more data overfit to that data and hence perform worse on different data. The concept the networks are supposed to learn may be obvious from the small data s | Can I have too much data?
It sounds like the networks you train with more data overfit to that data and hence perform worse on different data. The concept the networks are supposed to learn may be obvious from the small data set, but adding more data in the other set obscures it (or even transforms it into a different ... | Can I have too much data?
It sounds like the networks you train with more data overfit to that data and hence perform worse on different data. The concept the networks are supposed to learn may be obvious from the small data s |
37,619 | Proportional hazards assumption | Peter is correct in it depends on what software you are using to check this, in the survival package with R there is the cox.ph() function.
Most assessments of the assumption will involve looking at the Schoenfeld residuals. If plotted against time there should be no noticeable pattern.
See Cox-Proportional Hazards st... | Proportional hazards assumption | Peter is correct in it depends on what software you are using to check this, in the survival package with R there is the cox.ph() function.
Most assessments of the assumption will involve looking at t | Proportional hazards assumption
Peter is correct in it depends on what software you are using to check this, in the survival package with R there is the cox.ph() function.
Most assessments of the assumption will involve looking at the Schoenfeld residuals. If plotted against time there should be no noticeable pattern.... | Proportional hazards assumption
Peter is correct in it depends on what software you are using to check this, in the survival package with R there is the cox.ph() function.
Most assessments of the assumption will involve looking at t |
37,620 | Fitting a line to a log-log plot | There is nothing inherently wrong with a log-log regression and economists have used them for ages to estimate elasticity. Yet if you want to allow for the power law effect but do not want to bother too much, you may apply this simple correction: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=881759 | Fitting a line to a log-log plot | There is nothing inherently wrong with a log-log regression and economists have used them for ages to estimate elasticity. Yet if you want to allow for the power law effect but do not want to bother t | Fitting a line to a log-log plot
There is nothing inherently wrong with a log-log regression and economists have used them for ages to estimate elasticity. Yet if you want to allow for the power law effect but do not want to bother too much, you may apply this simple correction: http://papers.ssrn.com/sol3/papers.cfm?a... | Fitting a line to a log-log plot
There is nothing inherently wrong with a log-log regression and economists have used them for ages to estimate elasticity. Yet if you want to allow for the power law effect but do not want to bother t |
37,621 | How to combine the results of several binary tests? | "I'm wondering what is the best way to combine these numbers in a way that will yield a final score that is (hopefully) more reliable than any single test." A very common way is to compute Cronbach's alpha and, more generally, to perform what some would call a "standard" reliability analysis. This would show to what ... | How to combine the results of several binary tests? | "I'm wondering what is the best way to combine these numbers in a way that will yield a final score that is (hopefully) more reliable than any single test." A very common way is to compute Cronbach's | How to combine the results of several binary tests?
"I'm wondering what is the best way to combine these numbers in a way that will yield a final score that is (hopefully) more reliable than any single test." A very common way is to compute Cronbach's alpha and, more generally, to perform what some would call a "stand... | How to combine the results of several binary tests?
"I'm wondering what is the best way to combine these numbers in a way that will yield a final score that is (hopefully) more reliable than any single test." A very common way is to compute Cronbach's |
37,622 | How to combine the results of several binary tests? | To simplify a bit, let's assume that you only have two diagnostic tests. You want to calculate
$$
\Pr(\text{Disease} \mid T_1,T_2) = \frac{\Pr(T_1,T_2 \mid \text{Disease})\Pr(\text{Disease})}{\Pr(T_1,T_2)}
$$
You suggested that the results of these tests are independent, conditional on person having a disease. If so,... | How to combine the results of several binary tests? | To simplify a bit, let's assume that you only have two diagnostic tests. You want to calculate
$$
\Pr(\text{Disease} \mid T_1,T_2) = \frac{\Pr(T_1,T_2 \mid \text{Disease})\Pr(\text{Disease})}{\Pr(T_1 | How to combine the results of several binary tests?
To simplify a bit, let's assume that you only have two diagnostic tests. You want to calculate
$$
\Pr(\text{Disease} \mid T_1,T_2) = \frac{\Pr(T_1,T_2 \mid \text{Disease})\Pr(\text{Disease})}{\Pr(T_1,T_2)}
$$
You suggested that the results of these tests are indepen... | How to combine the results of several binary tests?
To simplify a bit, let's assume that you only have two diagnostic tests. You want to calculate
$$
\Pr(\text{Disease} \mid T_1,T_2) = \frac{\Pr(T_1,T_2 \mid \text{Disease})\Pr(\text{Disease})}{\Pr(T_1 |
37,623 | Does similarity of coefficients and p-values regardless of whether dependent variable is transformed suggest untransformed model is reliable? | This looks like an example of the Li-Duan theorem:
Li, Duan. Regression analysis under link violation. Annals of
Statistics, 17:1009-1052, 1989
Which basically says that if your predictor variables are well behaved and you use the wrong link function (transformation on the response) then your coefficient estimates ... | Does similarity of coefficients and p-values regardless of whether dependent variable is transformed | This looks like an example of the Li-Duan theorem:
Li, Duan. Regression analysis under link violation. Annals of
Statistics, 17:1009-1052, 1989
Which basically says that if your predictor variable | Does similarity of coefficients and p-values regardless of whether dependent variable is transformed suggest untransformed model is reliable?
This looks like an example of the Li-Duan theorem:
Li, Duan. Regression analysis under link violation. Annals of
Statistics, 17:1009-1052, 1989
Which basically says that if... | Does similarity of coefficients and p-values regardless of whether dependent variable is transformed
This looks like an example of the Li-Duan theorem:
Li, Duan. Regression analysis under link violation. Annals of
Statistics, 17:1009-1052, 1989
Which basically says that if your predictor variable |
37,624 | Statistics for gambling machine validation | For a fair game successive plays should be independent. It sounds like they are asking you to perform a test that consecutive results are uncorrelated. You could do this by pairing the data let $R_1, R_2,...,R_{2n}$ be the first $2n$ results. Then you can form $n$ distnct pairs
$(R_1,R_2)$, $(R3, R4),...,(R_{2n-1}, R... | Statistics for gambling machine validation | For a fair game successive plays should be independent. It sounds like they are asking you to perform a test that consecutive results are uncorrelated. You could do this by pairing the data let $R_1, | Statistics for gambling machine validation
For a fair game successive plays should be independent. It sounds like they are asking you to perform a test that consecutive results are uncorrelated. You could do this by pairing the data let $R_1, R_2,...,R_{2n}$ be the first $2n$ results. Then you can form $n$ distnct pa... | Statistics for gambling machine validation
For a fair game successive plays should be independent. It sounds like they are asking you to perform a test that consecutive results are uncorrelated. You could do this by pairing the data let $R_1, |
37,625 | Should factor loadings be dominated by items' ranges of answer options? | The effect you mention happens because of response set, which can be controlled by the phrasing of the reactives, and the interest of the respondent, and the order of the questions. I've seen this happen in my own experience, but it's by no means inescapable: one good way to avoid the spurious tendency is to, say, put ... | Should factor loadings be dominated by items' ranges of answer options? | The effect you mention happens because of response set, which can be controlled by the phrasing of the reactives, and the interest of the respondent, and the order of the questions. I've seen this hap | Should factor loadings be dominated by items' ranges of answer options?
The effect you mention happens because of response set, which can be controlled by the phrasing of the reactives, and the interest of the respondent, and the order of the questions. I've seen this happen in my own experience, but it's by no means i... | Should factor loadings be dominated by items' ranges of answer options?
The effect you mention happens because of response set, which can be controlled by the phrasing of the reactives, and the interest of the respondent, and the order of the questions. I've seen this hap |
37,626 | How do I display detrended data from a linear regression? | As for me, it is terribly confusing, especially while you can do much simpler thing -- calculate price/carat to get a price of one carat, which would be way easier to interpret. | How do I display detrended data from a linear regression? | As for me, it is terribly confusing, especially while you can do much simpler thing -- calculate price/carat to get a price of one carat, which would be way easier to interpret. | How do I display detrended data from a linear regression?
As for me, it is terribly confusing, especially while you can do much simpler thing -- calculate price/carat to get a price of one carat, which would be way easier to interpret. | How do I display detrended data from a linear regression?
As for me, it is terribly confusing, especially while you can do much simpler thing -- calculate price/carat to get a price of one carat, which would be way easier to interpret. |
37,627 | How does a frequentist calculate the chance that group A beats group B regarding binary response | I will take this as an opportunity to explain some fundamental issues regarding the difference between frequentist and Bayesian statistics, by interpreting frequentist practices from a Bayesian standpoint.
In this example, we have observed data $D_1$ for the original and data $D_2$ for the combination case. One assume... | How does a frequentist calculate the chance that group A beats group B regarding binary response | I will take this as an opportunity to explain some fundamental issues regarding the difference between frequentist and Bayesian statistics, by interpreting frequentist practices from a Bayesian standp | How does a frequentist calculate the chance that group A beats group B regarding binary response
I will take this as an opportunity to explain some fundamental issues regarding the difference between frequentist and Bayesian statistics, by interpreting frequentist practices from a Bayesian standpoint.
In this example, ... | How does a frequentist calculate the chance that group A beats group B regarding binary response
I will take this as an opportunity to explain some fundamental issues regarding the difference between frequentist and Bayesian statistics, by interpreting frequentist practices from a Bayesian standp |
37,628 | Most powerful GoF test for normality | In generall I would advice to use more than just one test. Through statistic programms like R it isn't as much efford as just typing one line per test.
The Shapiro-Wilks and the Anderson-Darling-Test are both tests which operate on comparing the distribution functions or analyse the variance. For example the Cramér-vo... | Most powerful GoF test for normality | In generall I would advice to use more than just one test. Through statistic programms like R it isn't as much efford as just typing one line per test.
The Shapiro-Wilks and the Anderson-Darling-Test | Most powerful GoF test for normality
In generall I would advice to use more than just one test. Through statistic programms like R it isn't as much efford as just typing one line per test.
The Shapiro-Wilks and the Anderson-Darling-Test are both tests which operate on comparing the distribution functions or analyse th... | Most powerful GoF test for normality
In generall I would advice to use more than just one test. Through statistic programms like R it isn't as much efford as just typing one line per test.
The Shapiro-Wilks and the Anderson-Darling-Test |
37,629 | Most powerful GoF test for normality | If the only criterion is most powerful then nothing beats SnowsPenultimateNormalityTest which is in the TeachingDemos package for R. However that test has an unfair advantage in the power competition and some may consider it less capable in other areas, for one, it is of the class of functions for which the documentat... | Most powerful GoF test for normality | If the only criterion is most powerful then nothing beats SnowsPenultimateNormalityTest which is in the TeachingDemos package for R. However that test has an unfair advantage in the power competition | Most powerful GoF test for normality
If the only criterion is most powerful then nothing beats SnowsPenultimateNormalityTest which is in the TeachingDemos package for R. However that test has an unfair advantage in the power competition and some may consider it less capable in other areas, for one, it is of the class ... | Most powerful GoF test for normality
If the only criterion is most powerful then nothing beats SnowsPenultimateNormalityTest which is in the TeachingDemos package for R. However that test has an unfair advantage in the power competition |
37,630 | Can someone help me understand what type of problem I am looking at? Not sure if this classifies as hypothesis-testing | You can do a student test to see if the mean is different between the group 4,6 and the rest. Even if your sample size is small you will conclude in a difference. Note that it will tell you that group 4,6 is significantly different in average from the rest but it won't tell you that "The experiment was not conducted pr... | Can someone help me understand what type of problem I am looking at? Not sure if this classifies as | You can do a student test to see if the mean is different between the group 4,6 and the rest. Even if your sample size is small you will conclude in a difference. Note that it will tell you that group | Can someone help me understand what type of problem I am looking at? Not sure if this classifies as hypothesis-testing
You can do a student test to see if the mean is different between the group 4,6 and the rest. Even if your sample size is small you will conclude in a difference. Note that it will tell you that group ... | Can someone help me understand what type of problem I am looking at? Not sure if this classifies as
You can do a student test to see if the mean is different between the group 4,6 and the rest. Even if your sample size is small you will conclude in a difference. Note that it will tell you that group |
37,631 | How to model pairwise preference with both strong and weak preferences? | The difficulty with specifying a model to resolve this problem is one of how to interpret the strength of preference information. Does A vs B 999:1 mean that 999 times out of 1000 people will prefer A, or, does it mean that a person prefers A by a large amount relative to B?
If we take the interpretation that the data... | How to model pairwise preference with both strong and weak preferences? | The difficulty with specifying a model to resolve this problem is one of how to interpret the strength of preference information. Does A vs B 999:1 mean that 999 times out of 1000 people will prefer | How to model pairwise preference with both strong and weak preferences?
The difficulty with specifying a model to resolve this problem is one of how to interpret the strength of preference information. Does A vs B 999:1 mean that 999 times out of 1000 people will prefer A, or, does it mean that a person prefers A by a... | How to model pairwise preference with both strong and weak preferences?
The difficulty with specifying a model to resolve this problem is one of how to interpret the strength of preference information. Does A vs B 999:1 mean that 999 times out of 1000 people will prefer |
37,632 | When does the expected value or variance of the $t$ statistic exist? | The case of independent and identical distributions for the variables $X_i$ in the sample
The (non-central) t-distribution is proportional to the distribution of the inverse of the tangent of the angle of the sample $\vec{x}$ with the diagonal line $x_1 = x_2 = \dots = x_n$.
$$t = \frac{\sqrt{n-1}}{\text{tan}(\theta)}$... | When does the expected value or variance of the $t$ statistic exist? | The case of independent and identical distributions for the variables $X_i$ in the sample
The (non-central) t-distribution is proportional to the distribution of the inverse of the tangent of the angl | When does the expected value or variance of the $t$ statistic exist?
The case of independent and identical distributions for the variables $X_i$ in the sample
The (non-central) t-distribution is proportional to the distribution of the inverse of the tangent of the angle of the sample $\vec{x}$ with the diagonal line $x... | When does the expected value or variance of the $t$ statistic exist?
The case of independent and identical distributions for the variables $X_i$ in the sample
The (non-central) t-distribution is proportional to the distribution of the inverse of the tangent of the angl |
37,633 | When does the expected value or variance of the $t$ statistic exist? | One way to investigate this is by simulation. Since the question is about existence of moments, we could use some estimator of the tail index of the distribution of the T statistic, which is related to existence of expectation and other moments a definition of tail index here.
For an example I will simulate $N=100000$ ... | When does the expected value or variance of the $t$ statistic exist? | One way to investigate this is by simulation. Since the question is about existence of moments, we could use some estimator of the tail index of the distribution of the T statistic, which is related t | When does the expected value or variance of the $t$ statistic exist?
One way to investigate this is by simulation. Since the question is about existence of moments, we could use some estimator of the tail index of the distribution of the T statistic, which is related to existence of expectation and other moments a defi... | When does the expected value or variance of the $t$ statistic exist?
One way to investigate this is by simulation. Since the question is about existence of moments, we could use some estimator of the tail index of the distribution of the T statistic, which is related t |
37,634 | When does the expected value or variance of the $t$ statistic exist? | The distribution of Student's t statistic is known when the random
variable x follows a Normal distribution. Sometimes, however, we apply
it to random variables drawn from other distributions. I am curious if
there are known conditions, sufficient and necessary, that the
expectation of the t statistic, or its variance,... | When does the expected value or variance of the $t$ statistic exist? | The distribution of Student's t statistic is known when the random
variable x follows a Normal distribution. Sometimes, however, we apply
it to random variables drawn from other distributions. I am cu | When does the expected value or variance of the $t$ statistic exist?
The distribution of Student's t statistic is known when the random
variable x follows a Normal distribution. Sometimes, however, we apply
it to random variables drawn from other distributions. I am curious if
there are known conditions, sufficient and... | When does the expected value or variance of the $t$ statistic exist?
The distribution of Student's t statistic is known when the random
variable x follows a Normal distribution. Sometimes, however, we apply
it to random variables drawn from other distributions. I am cu |
37,635 | Help select prior function | This is a very common use-case for hierarchical models. These models have a lot of different names, so you'll sometimes see them called multi-level models or mixed-effects models. Hierarchical models aren't strictly Bayesian, but, in my experience, they are more common fit as Bayesian models than Frequentist.
The basic... | Help select prior function | This is a very common use-case for hierarchical models. These models have a lot of different names, so you'll sometimes see them called multi-level models or mixed-effects models. Hierarchical models | Help select prior function
This is a very common use-case for hierarchical models. These models have a lot of different names, so you'll sometimes see them called multi-level models or mixed-effects models. Hierarchical models aren't strictly Bayesian, but, in my experience, they are more common fit as Bayesian models ... | Help select prior function
This is a very common use-case for hierarchical models. These models have a lot of different names, so you'll sometimes see them called multi-level models or mixed-effects models. Hierarchical models |
37,636 | Sklar’s Extension Theorem and support restrictions | Reading Nelsen's 2006 "Introduction to Copulas":
$k$-dimensional sub-copulas are defined in a subset of $[0,1]^k$ (their domain). The same is said in Sklar's paper that the OP mentioned.
A Copula is the extension of a sub-copula to the whole $[0,1]^k$ (its domain).
Sklar's Theorem (the "core" one) then asserts that ev... | Sklar’s Extension Theorem and support restrictions | Reading Nelsen's 2006 "Introduction to Copulas":
$k$-dimensional sub-copulas are defined in a subset of $[0,1]^k$ (their domain). The same is said in Sklar's paper that the OP mentioned.
A Copula is | Sklar’s Extension Theorem and support restrictions
Reading Nelsen's 2006 "Introduction to Copulas":
$k$-dimensional sub-copulas are defined in a subset of $[0,1]^k$ (their domain). The same is said in Sklar's paper that the OP mentioned.
A Copula is the extension of a sub-copula to the whole $[0,1]^k$ (its domain).
Sk... | Sklar’s Extension Theorem and support restrictions
Reading Nelsen's 2006 "Introduction to Copulas":
$k$-dimensional sub-copulas are defined in a subset of $[0,1]^k$ (their domain). The same is said in Sklar's paper that the OP mentioned.
A Copula is |
37,637 | What does the term "regularization" refer to specifically? | I agree with the comment that regularization is a way to constrain parameters. In that regard, not only are $L_1$ and $L_2$ penalties regularization, but neural network dropout is regularization, since it forces certain parameters to be zero. Likewise, convolutional neural networks could be argued to perform regulariza... | What does the term "regularization" refer to specifically? | I agree with the comment that regularization is a way to constrain parameters. In that regard, not only are $L_1$ and $L_2$ penalties regularization, but neural network dropout is regularization, sinc | What does the term "regularization" refer to specifically?
I agree with the comment that regularization is a way to constrain parameters. In that regard, not only are $L_1$ and $L_2$ penalties regularization, but neural network dropout is regularization, since it forces certain parameters to be zero. Likewise, convolut... | What does the term "regularization" refer to specifically?
I agree with the comment that regularization is a way to constrain parameters. In that regard, not only are $L_1$ and $L_2$ penalties regularization, but neural network dropout is regularization, sinc |
37,638 | Is there a standard for statistical symbols? | So I found out that there is a standard. See
ISO 3534-1:2006 Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in probability
ISO 3534-2:2006
Statistics — Vocabulary and symbols — Part 2: Applied statistics
ISO 3534-3:2013 Statistics — Vocabulary and symbols — Part 3: Design of exp... | Is there a standard for statistical symbols? | So I found out that there is a standard. See
ISO 3534-1:2006 Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in probability
ISO 3534-2:2006
Statistics — Vocabul | Is there a standard for statistical symbols?
So I found out that there is a standard. See
ISO 3534-1:2006 Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in probability
ISO 3534-2:2006
Statistics — Vocabulary and symbols — Part 2: Applied statistics
ISO 3534-3:2013 Statistics — V... | Is there a standard for statistical symbols?
So I found out that there is a standard. See
ISO 3534-1:2006 Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in probability
ISO 3534-2:2006
Statistics — Vocabul |
37,639 | Is there a standard for statistical symbols? | According to the Oxford dictionary of statistical terms (and probably many other standard works) the term 'standard' has already been claimed by Karl Pearson in 1894.
Quote from Contributions to the mathematical theory of evolution (emphasis is mine)
In the case of a frequency-curve whose components are two normal cur... | Is there a standard for statistical symbols? | According to the Oxford dictionary of statistical terms (and probably many other standard works) the term 'standard' has already been claimed by Karl Pearson in 1894.
Quote from Contributions to the m | Is there a standard for statistical symbols?
According to the Oxford dictionary of statistical terms (and probably many other standard works) the term 'standard' has already been claimed by Karl Pearson in 1894.
Quote from Contributions to the mathematical theory of evolution (emphasis is mine)
In the case of a freque... | Is there a standard for statistical symbols?
According to the Oxford dictionary of statistical terms (and probably many other standard works) the term 'standard' has already been claimed by Karl Pearson in 1894.
Quote from Contributions to the m |
37,640 | Understanding how to find more "extreme" values when calculating p values in two sided hypothesis tests | Here are the probabilities for $0, 1, \dots, 10$ heads if we throw a coin $n=10$ times under your null hypothesis of $p=0.3$:
So let us assume that we have observed $n=5$ heads and wish to run a two-sided test. I have indicated the probability for observing $k=5$ under the null hypothesis of $p=0.3$ with the horizonta... | Understanding how to find more "extreme" values when calculating p values in two sided hypothesis te | Here are the probabilities for $0, 1, \dots, 10$ heads if we throw a coin $n=10$ times under your null hypothesis of $p=0.3$:
So let us assume that we have observed $n=5$ heads and wish to run a two- | Understanding how to find more "extreme" values when calculating p values in two sided hypothesis tests
Here are the probabilities for $0, 1, \dots, 10$ heads if we throw a coin $n=10$ times under your null hypothesis of $p=0.3$:
So let us assume that we have observed $n=5$ heads and wish to run a two-sided test. I ha... | Understanding how to find more "extreme" values when calculating p values in two sided hypothesis te
Here are the probabilities for $0, 1, \dots, 10$ heads if we throw a coin $n=10$ times under your null hypothesis of $p=0.3$:
So let us assume that we have observed $n=5$ heads and wish to run a two- |
37,641 | Why do model selection (AIC and LOO) outcomes differ between ML and bayesian approaches | Something strikes me as particularly odd when comparing different likelihoods via AIC.
Suppose I observed $x=2$. The log likelihood for a gaussian, gamma, and poisson each with mean and variance 1 is -0.91, -1, and -1. Should I assume this observation came from a gaussian simply because of the likelihood, ignoring ... | Why do model selection (AIC and LOO) outcomes differ between ML and bayesian approaches | Something strikes me as particularly odd when comparing different likelihoods via AIC.
Suppose I observed $x=2$. The log likelihood for a gaussian, gamma, and poisson each with mean and variance 1 | Why do model selection (AIC and LOO) outcomes differ between ML and bayesian approaches
Something strikes me as particularly odd when comparing different likelihoods via AIC.
Suppose I observed $x=2$. The log likelihood for a gaussian, gamma, and poisson each with mean and variance 1 is -0.91, -1, and -1. Should I ... | Why do model selection (AIC and LOO) outcomes differ between ML and bayesian approaches
Something strikes me as particularly odd when comparing different likelihoods via AIC.
Suppose I observed $x=2$. The log likelihood for a gaussian, gamma, and poisson each with mean and variance 1 |
37,642 | A reliance on repeated sampling ideas can lead to logical paradoxes that appear in common rather than esoteric procedures? | Say you have a measurement of real value interfered with noise.
The measurement is given by
$y(n) = x + \omega_n$
where $x$ is assumed to be a constant value. An unbiased estimator of $x$ can be the mean value:
$\hat{x}=\frac{\sum_n y(n)}{n}$
and the variance of the estimation should be:
$var(\hat{x})=\frac{\sigma_\ome... | A reliance on repeated sampling ideas can lead to logical paradoxes that appear in common rather tha | Say you have a measurement of real value interfered with noise.
The measurement is given by
$y(n) = x + \omega_n$
where $x$ is assumed to be a constant value. An unbiased estimator of $x$ can be the m | A reliance on repeated sampling ideas can lead to logical paradoxes that appear in common rather than esoteric procedures?
Say you have a measurement of real value interfered with noise.
The measurement is given by
$y(n) = x + \omega_n$
where $x$ is assumed to be a constant value. An unbiased estimator of $x$ can be th... | A reliance on repeated sampling ideas can lead to logical paradoxes that appear in common rather tha
Say you have a measurement of real value interfered with noise.
The measurement is given by
$y(n) = x + \omega_n$
where $x$ is assumed to be a constant value. An unbiased estimator of $x$ can be the m |
37,643 | Is it okay to perform PerMANOVA on PCA values? | I will leave it to others to decide if a permutational multivariate analysis of variance on principal components is 'acceptable' to them. But there isn't any logical error in computing such a statistic. It is simply composing functions of random variables. The more difficult question for you to ask yourself is whether ... | Is it okay to perform PerMANOVA on PCA values? | I will leave it to others to decide if a permutational multivariate analysis of variance on principal components is 'acceptable' to them. But there isn't any logical error in computing such a statisti | Is it okay to perform PerMANOVA on PCA values?
I will leave it to others to decide if a permutational multivariate analysis of variance on principal components is 'acceptable' to them. But there isn't any logical error in computing such a statistic. It is simply composing functions of random variables. The more difficu... | Is it okay to perform PerMANOVA on PCA values?
I will leave it to others to decide if a permutational multivariate analysis of variance on principal components is 'acceptable' to them. But there isn't any logical error in computing such a statisti |
37,644 | Bayesian Inference in the presence of multiple hypotheses | Arguments that Bayesians do not need to worry about type I errors are starting from the premise that the type I error rate does not matter/is not a relevant concept* and simply adhere to the likelihood principle**.
I don't think this kind of Bayesian viewpoint is compatible with coercing an inferential threshold, but ... | Bayesian Inference in the presence of multiple hypotheses | Arguments that Bayesians do not need to worry about type I errors are starting from the premise that the type I error rate does not matter/is not a relevant concept* and simply adhere to the likelihoo | Bayesian Inference in the presence of multiple hypotheses
Arguments that Bayesians do not need to worry about type I errors are starting from the premise that the type I error rate does not matter/is not a relevant concept* and simply adhere to the likelihood principle**.
I don't think this kind of Bayesian viewpoint ... | Bayesian Inference in the presence of multiple hypotheses
Arguments that Bayesians do not need to worry about type I errors are starting from the premise that the type I error rate does not matter/is not a relevant concept* and simply adhere to the likelihoo |
37,645 | Realistic/intuitive example where a nonadditive loss function is preferred over additive ones | One example that comes to mind is the area under the ROC curve (AUC). For binary classification problems where the model outputs a continuous score (e.g. logistic regression or SVMs), AUC gives the probability that the model will score a randomly selected 'positive' instance higher than a randomly selected 'negative' i... | Realistic/intuitive example where a nonadditive loss function is preferred over additive ones | One example that comes to mind is the area under the ROC curve (AUC). For binary classification problems where the model outputs a continuous score (e.g. logistic regression or SVMs), AUC gives the pr | Realistic/intuitive example where a nonadditive loss function is preferred over additive ones
One example that comes to mind is the area under the ROC curve (AUC). For binary classification problems where the model outputs a continuous score (e.g. logistic regression or SVMs), AUC gives the probability that the model w... | Realistic/intuitive example where a nonadditive loss function is preferred over additive ones
One example that comes to mind is the area under the ROC curve (AUC). For binary classification problems where the model outputs a continuous score (e.g. logistic regression or SVMs), AUC gives the pr |
37,646 | Realistic/intuitive example where a nonadditive loss function is preferred over additive ones | A sensible choice of loss could be the negative of utility. Within the framework of maximization of expected utility (MEU), we would have additive loss, since we would use average (over the set of test cases) negative loss as an estimate of expected utility. On the other hand, we could have nonadditive loss if we aband... | Realistic/intuitive example where a nonadditive loss function is preferred over additive ones | A sensible choice of loss could be the negative of utility. Within the framework of maximization of expected utility (MEU), we would have additive loss, since we would use average (over the set of tes | Realistic/intuitive example where a nonadditive loss function is preferred over additive ones
A sensible choice of loss could be the negative of utility. Within the framework of maximization of expected utility (MEU), we would have additive loss, since we would use average (over the set of test cases) negative loss as ... | Realistic/intuitive example where a nonadditive loss function is preferred over additive ones
A sensible choice of loss could be the negative of utility. Within the framework of maximization of expected utility (MEU), we would have additive loss, since we would use average (over the set of tes |
37,647 | If the Bayesian probability is not a belief, what is it? | Perhaps what the author was getting as is distinguishing between the posterior distribution and an individual's posterior distribution.
Suppose we knew as a fact that some of our parameters followed a given distribution before the data was distributed. Then based on those parameters, we observed some data conditional ... | If the Bayesian probability is not a belief, what is it? | Perhaps what the author was getting as is distinguishing between the posterior distribution and an individual's posterior distribution.
Suppose we knew as a fact that some of our parameters followed | If the Bayesian probability is not a belief, what is it?
Perhaps what the author was getting as is distinguishing between the posterior distribution and an individual's posterior distribution.
Suppose we knew as a fact that some of our parameters followed a given distribution before the data was distributed. Then base... | If the Bayesian probability is not a belief, what is it?
Perhaps what the author was getting as is distinguishing between the posterior distribution and an individual's posterior distribution.
Suppose we knew as a fact that some of our parameters followed |
37,648 | If the Bayesian probability is not a belief, what is it? | The problem is that you W can't be integrated out. Taken all the knowledge you have, W, we form our prior, p(Y|W). And with this, we can use Bayes theorem to get our posterior p(Y|XW). W just tags along with all our updates, but we don't actually know p(W). If we did have the probability of our prior beliefs we could i... | If the Bayesian probability is not a belief, what is it? | The problem is that you W can't be integrated out. Taken all the knowledge you have, W, we form our prior, p(Y|W). And with this, we can use Bayes theorem to get our posterior p(Y|XW). W just tags alo | If the Bayesian probability is not a belief, what is it?
The problem is that you W can't be integrated out. Taken all the knowledge you have, W, we form our prior, p(Y|W). And with this, we can use Bayes theorem to get our posterior p(Y|XW). W just tags along with all our updates, but we don't actually know p(W). If we... | If the Bayesian probability is not a belief, what is it?
The problem is that you W can't be integrated out. Taken all the knowledge you have, W, we form our prior, p(Y|W). And with this, we can use Bayes theorem to get our posterior p(Y|XW). W just tags alo |
37,649 | If the Bayesian probability is not a belief, what is it? | If the prior accurately reflects your beliefs about the parameter and you are willing to make the assumption that the model for the data is correct, then the posterior is the rational way to update your beliefs after seeing the data.
The assumption that your model for the data is correct is implicit and sometimes not ... | If the Bayesian probability is not a belief, what is it? | If the prior accurately reflects your beliefs about the parameter and you are willing to make the assumption that the model for the data is correct, then the posterior is the rational way to update yo | If the Bayesian probability is not a belief, what is it?
If the prior accurately reflects your beliefs about the parameter and you are willing to make the assumption that the model for the data is correct, then the posterior is the rational way to update your beliefs after seeing the data.
The assumption that your mod... | If the Bayesian probability is not a belief, what is it?
If the prior accurately reflects your beliefs about the parameter and you are willing to make the assumption that the model for the data is correct, then the posterior is the rational way to update yo |
37,650 | What is the idea behind Bayes By Backprop? | A VAE is a latent variable model. The encoder estimates for each input, the corresponding posterior distribution $P(z|x)$ on the latent space $z$. The objective is typically to obtain a density model $P(x)$ of the data.
In Bayes by Backprop, the setting is that you want estimate the posterior distribution over the weig... | What is the idea behind Bayes By Backprop? | A VAE is a latent variable model. The encoder estimates for each input, the corresponding posterior distribution $P(z|x)$ on the latent space $z$. The objective is typically to obtain a density model | What is the idea behind Bayes By Backprop?
A VAE is a latent variable model. The encoder estimates for each input, the corresponding posterior distribution $P(z|x)$ on the latent space $z$. The objective is typically to obtain a density model $P(x)$ of the data.
In Bayes by Backprop, the setting is that you want estima... | What is the idea behind Bayes By Backprop?
A VAE is a latent variable model. The encoder estimates for each input, the corresponding posterior distribution $P(z|x)$ on the latent space $z$. The objective is typically to obtain a density model |
37,651 | inferring most important features | There is a lot of options, it depends what exactly do you want.
Feature importance or permutation importance
Both methods tells you which features are most important for the model. It is a number for each feature. It is calculated after the model is fitted. It doesn't tell you anything about which values of a feature i... | inferring most important features | There is a lot of options, it depends what exactly do you want.
Feature importance or permutation importance
Both methods tells you which features are most important for the model. It is a number for | inferring most important features
There is a lot of options, it depends what exactly do you want.
Feature importance or permutation importance
Both methods tells you which features are most important for the model. It is a number for each feature. It is calculated after the model is fitted. It doesn't tell you anything... | inferring most important features
There is a lot of options, it depends what exactly do you want.
Feature importance or permutation importance
Both methods tells you which features are most important for the model. It is a number for |
37,652 | Does Leave One Out cross validation increase the chance of overfitting? | ML model will start to "memorize" data with increasing complexity of your algorithm (and its parameters), not the size of training set.
Cross-validation is used to estimate your model performance on data that was not used to train. If you use LOOCV (k=n) then your k models
will be (almost) identical. This gives you a ... | Does Leave One Out cross validation increase the chance of overfitting? | ML model will start to "memorize" data with increasing complexity of your algorithm (and its parameters), not the size of training set.
Cross-validation is used to estimate your model performance on d | Does Leave One Out cross validation increase the chance of overfitting?
ML model will start to "memorize" data with increasing complexity of your algorithm (and its parameters), not the size of training set.
Cross-validation is used to estimate your model performance on data that was not used to train. If you use LOOCV... | Does Leave One Out cross validation increase the chance of overfitting?
ML model will start to "memorize" data with increasing complexity of your algorithm (and its parameters), not the size of training set.
Cross-validation is used to estimate your model performance on d |
37,653 | Probability calibration metric for multiclass classifier | Following Guo et al., I ended up using the Expected Calibration Error, defined as $$\sum_{m=1}^M\frac{|{B_{m}|}}{n}\left|acc(B_m) - conf(B_m)\right|$$
In extending this to multiclass, one can either take the maximum probability for each prediction, or average across the top $n$ predictions, if desired. | Probability calibration metric for multiclass classifier | Following Guo et al., I ended up using the Expected Calibration Error, defined as $$\sum_{m=1}^M\frac{|{B_{m}|}}{n}\left|acc(B_m) - conf(B_m)\right|$$
In extending this to multiclass, one can either t | Probability calibration metric for multiclass classifier
Following Guo et al., I ended up using the Expected Calibration Error, defined as $$\sum_{m=1}^M\frac{|{B_{m}|}}{n}\left|acc(B_m) - conf(B_m)\right|$$
In extending this to multiclass, one can either take the maximum probability for each prediction, or average acr... | Probability calibration metric for multiclass classifier
Following Guo et al., I ended up using the Expected Calibration Error, defined as $$\sum_{m=1}^M\frac{|{B_{m}|}}{n}\left|acc(B_m) - conf(B_m)\right|$$
In extending this to multiclass, one can either t |
37,654 | Random rotation of a set of distinct points in $R^n$ | Restatement of the question.
Let $X_1,\ldots,X_M\in \mathbb R^n$ be deterministic vectors such that no two vectors $X_j$ and $X_k$ are identical in all components, and let $A$ be a random unitary matrix drawn from the circular real ensemble CRE$(n)$. Your question asks us to show that for all $1\leq i\leq n$, the rando... | Random rotation of a set of distinct points in $R^n$ | Restatement of the question.
Let $X_1,\ldots,X_M\in \mathbb R^n$ be deterministic vectors such that no two vectors $X_j$ and $X_k$ are identical in all components, and let $A$ be a random unitary matr | Random rotation of a set of distinct points in $R^n$
Restatement of the question.
Let $X_1,\ldots,X_M\in \mathbb R^n$ be deterministic vectors such that no two vectors $X_j$ and $X_k$ are identical in all components, and let $A$ be a random unitary matrix drawn from the circular real ensemble CRE$(n)$. Your question as... | Random rotation of a set of distinct points in $R^n$
Restatement of the question.
Let $X_1,\ldots,X_M\in \mathbb R^n$ be deterministic vectors such that no two vectors $X_j$ and $X_k$ are identical in all components, and let $A$ be a random unitary matr |
37,655 | Random rotation of a set of distinct points in $R^n$ | Consider
$y = Ux$
where $U$ is some random matrix (orthogonal or otherwise). Since you are interested in only the $m^{th}$ coordinate, only the $m^{th}$ row of $U$ is relevant to your work. Therefore, you are basically only interested in the properties of
$z_{i} = u^{T}x_{i}$,
where $u$ is the $m^{th}$ row of the mat... | Random rotation of a set of distinct points in $R^n$ | Consider
$y = Ux$
where $U$ is some random matrix (orthogonal or otherwise). Since you are interested in only the $m^{th}$ coordinate, only the $m^{th}$ row of $U$ is relevant to your work. Therefore | Random rotation of a set of distinct points in $R^n$
Consider
$y = Ux$
where $U$ is some random matrix (orthogonal or otherwise). Since you are interested in only the $m^{th}$ coordinate, only the $m^{th}$ row of $U$ is relevant to your work. Therefore, you are basically only interested in the properties of
$z_{i} = ... | Random rotation of a set of distinct points in $R^n$
Consider
$y = Ux$
where $U$ is some random matrix (orthogonal or otherwise). Since you are interested in only the $m^{th}$ coordinate, only the $m^{th}$ row of $U$ is relevant to your work. Therefore |
37,656 | Independence of random vectors | In the general case, no; there is a distinction in probability theory between pairwise independence and mutual independence. In the special case where the two random vectors have a joint multivariate normal distribution, yes; the dependence between the random vectors is only through the second moment of the distributi... | Independence of random vectors | In the general case, no; there is a distinction in probability theory between pairwise independence and mutual independence. In the special case where the two random vectors have a joint multivariate | Independence of random vectors
In the general case, no; there is a distinction in probability theory between pairwise independence and mutual independence. In the special case where the two random vectors have a joint multivariate normal distribution, yes; the dependence between the random vectors is only through the ... | Independence of random vectors
In the general case, no; there is a distinction in probability theory between pairwise independence and mutual independence. In the special case where the two random vectors have a joint multivariate |
37,657 | Train test split with time and person indexed data | Since this is a time-series data set the temporal issue is of utmost importance, meaning you really cannot use future data in order to predict past events. Thus, the split by Subject doesn't make much sense here since you'd be training your model with future observations but testing it on past ones (e.g. train on peri... | Train test split with time and person indexed data | Since this is a time-series data set the temporal issue is of utmost importance, meaning you really cannot use future data in order to predict past events. Thus, the split by Subject doesn't make much | Train test split with time and person indexed data
Since this is a time-series data set the temporal issue is of utmost importance, meaning you really cannot use future data in order to predict past events. Thus, the split by Subject doesn't make much sense here since you'd be training your model with future observatio... | Train test split with time and person indexed data
Since this is a time-series data set the temporal issue is of utmost importance, meaning you really cannot use future data in order to predict past events. Thus, the split by Subject doesn't make much |
37,658 | Train test split with time and person indexed data | I would go for a train/validation/test sets if you have enough data. Choose your validation set as close as possible as the test set, which should be as close as possible to testing the performance of your model in a productive environment.
In this case, is the main focus to predict the target for new subjects (then s... | Train test split with time and person indexed data | I would go for a train/validation/test sets if you have enough data. Choose your validation set as close as possible as the test set, which should be as close as possible to testing the performance of | Train test split with time and person indexed data
I would go for a train/validation/test sets if you have enough data. Choose your validation set as close as possible as the test set, which should be as close as possible to testing the performance of your model in a productive environment.
In this case, is the main f... | Train test split with time and person indexed data
I would go for a train/validation/test sets if you have enough data. Choose your validation set as close as possible as the test set, which should be as close as possible to testing the performance of |
37,659 | Train test split with time and person indexed data | Analysts trained in machine learning, whose main goal is optimizing computational efficiency when processing massive data, ignore any inherent variance and structure in data by treating each observation as iid (for a recent statement of this see Sirignano, et al., Deep Learning for Mortgage Risk, https://arxiv.org/pdf/... | Train test split with time and person indexed data | Analysts trained in machine learning, whose main goal is optimizing computational efficiency when processing massive data, ignore any inherent variance and structure in data by treating each observati | Train test split with time and person indexed data
Analysts trained in machine learning, whose main goal is optimizing computational efficiency when processing massive data, ignore any inherent variance and structure in data by treating each observation as iid (for a recent statement of this see Sirignano, et al., Deep... | Train test split with time and person indexed data
Analysts trained in machine learning, whose main goal is optimizing computational efficiency when processing massive data, ignore any inherent variance and structure in data by treating each observati |
37,660 | Why are (almost) all of my corrected (Benjamini-Hochberg) p-values equal? | From what I understand p.adjust("BH") returns the lowest alpha (FDR threshold) for which the test can be considered significant.
So, 0.3779828 means that the test will be significant only if you accept a FDR of 0.3779828 or higher. In this case you will have 11/12 tests considered significant, and you are accepting tha... | Why are (almost) all of my corrected (Benjamini-Hochberg) p-values equal? | From what I understand p.adjust("BH") returns the lowest alpha (FDR threshold) for which the test can be considered significant.
So, 0.3779828 means that the test will be significant only if you accep | Why are (almost) all of my corrected (Benjamini-Hochberg) p-values equal?
From what I understand p.adjust("BH") returns the lowest alpha (FDR threshold) for which the test can be considered significant.
So, 0.3779828 means that the test will be significant only if you accept a FDR of 0.3779828 or higher. In this case y... | Why are (almost) all of my corrected (Benjamini-Hochberg) p-values equal?
From what I understand p.adjust("BH") returns the lowest alpha (FDR threshold) for which the test can be considered significant.
So, 0.3779828 means that the test will be significant only if you accep |
37,661 | Is there current consensus on the value of the Information Bottleneck Principle to understanding Deep Learning? | What I will say here is that the proofs that compression guarantees a better lower bound on generalization are accepted, but it's not widely accepted if this lower bound is practically relevant.
For example, a model with better compression might increase the lower bound from 1.0 to 1.5, but it might not be relevant i... | Is there current consensus on the value of the Information Bottleneck Principle to understanding Dee | What I will say here is that the proofs that compression guarantees a better lower bound on generalization are accepted, but it's not widely accepted if this lower bound is practically relevant.
For | Is there current consensus on the value of the Information Bottleneck Principle to understanding Deep Learning?
What I will say here is that the proofs that compression guarantees a better lower bound on generalization are accepted, but it's not widely accepted if this lower bound is practically relevant.
For example... | Is there current consensus on the value of the Information Bottleneck Principle to understanding Dee
What I will say here is that the proofs that compression guarantees a better lower bound on generalization are accepted, but it's not widely accepted if this lower bound is practically relevant.
For |
37,662 | Guassian Process for Data Imputation | While I cannot answer all of your questions and I am unable to post a comment due to lack of reputation, in response to this:
Is there a defensible way to constrain the length scale parameters in the >model (the l's) based on the frequencies I am working with (1.5 Hz, .25 Hz and >the x-axis in seconds downsampled to 1... | Guassian Process for Data Imputation | While I cannot answer all of your questions and I am unable to post a comment due to lack of reputation, in response to this:
Is there a defensible way to constrain the length scale parameters in the | Guassian Process for Data Imputation
While I cannot answer all of your questions and I am unable to post a comment due to lack of reputation, in response to this:
Is there a defensible way to constrain the length scale parameters in the >model (the l's) based on the frequencies I am working with (1.5 Hz, .25 Hz and >t... | Guassian Process for Data Imputation
While I cannot answer all of your questions and I am unable to post a comment due to lack of reputation, in response to this:
Is there a defensible way to constrain the length scale parameters in the |
37,663 | How Do You Choose The Number of Bins To Use For A Chi-Squared GOF Test? | Is this discrepancy between outcomes for different bin sizes something
that I should have known about*, or is indicative of some larger
problem in my proposed data analysis?
The binning of the radioactive decay sample set is a red herring here. The real problem originates from the fact that chi-square (alongside o... | How Do You Choose The Number of Bins To Use For A Chi-Squared GOF Test? | Is this discrepancy between outcomes for different bin sizes something
that I should have known about*, or is indicative of some larger
problem in my proposed data analysis?
The binning of the ra | How Do You Choose The Number of Bins To Use For A Chi-Squared GOF Test?
Is this discrepancy between outcomes for different bin sizes something
that I should have known about*, or is indicative of some larger
problem in my proposed data analysis?
The binning of the radioactive decay sample set is a red herring here... | How Do You Choose The Number of Bins To Use For A Chi-Squared GOF Test?
Is this discrepancy between outcomes for different bin sizes something
that I should have known about*, or is indicative of some larger
problem in my proposed data analysis?
The binning of the ra |
37,664 | Why deep learning prefer the probability distribution with a sharp point? | These two distribution have a connection with deep learning via regularisation. In deep learning we are often concerned with regularising the parameters of a neural network because neural networks tend to overfit and we want to improve ability of the model to generalise to new data.
From a Bayesian perspective, fittin... | Why deep learning prefer the probability distribution with a sharp point? | These two distribution have a connection with deep learning via regularisation. In deep learning we are often concerned with regularising the parameters of a neural network because neural networks ten | Why deep learning prefer the probability distribution with a sharp point?
These two distribution have a connection with deep learning via regularisation. In deep learning we are often concerned with regularising the parameters of a neural network because neural networks tend to overfit and we want to improve ability of... | Why deep learning prefer the probability distribution with a sharp point?
These two distribution have a connection with deep learning via regularisation. In deep learning we are often concerned with regularising the parameters of a neural network because neural networks ten |
37,665 | Probability distribution models compatible with quantile regression | Question 1: In case of a single quantile, the quantile estimator is the maximum likelihood estimator of an asymmetric double exponential (a.k.a. Laplace) distribution that may look like this:
(Picture borrowed from Abeywardana "Deep Quantile Regression" (2018).)
Thanks to @machazthegamer and @Dave for helpful links in... | Probability distribution models compatible with quantile regression | Question 1: In case of a single quantile, the quantile estimator is the maximum likelihood estimator of an asymmetric double exponential (a.k.a. Laplace) distribution that may look like this:
(Pictur | Probability distribution models compatible with quantile regression
Question 1: In case of a single quantile, the quantile estimator is the maximum likelihood estimator of an asymmetric double exponential (a.k.a. Laplace) distribution that may look like this:
(Picture borrowed from Abeywardana "Deep Quantile Regressio... | Probability distribution models compatible with quantile regression
Question 1: In case of a single quantile, the quantile estimator is the maximum likelihood estimator of an asymmetric double exponential (a.k.a. Laplace) distribution that may look like this:
(Pictur |
37,666 | Cases where TDA outperforms public benchmarks? | Comparisons between ML-at-large to topological data analysis (TDA) is difficult. This in part because much of what TDA attempts to do isn't even on the menu for most ML projects. One place (other than article databases of course) to look for examples of TDA is the Applied Algebraic Topology Research Network's website, ... | Cases where TDA outperforms public benchmarks? | Comparisons between ML-at-large to topological data analysis (TDA) is difficult. This in part because much of what TDA attempts to do isn't even on the menu for most ML projects. One place (other than | Cases where TDA outperforms public benchmarks?
Comparisons between ML-at-large to topological data analysis (TDA) is difficult. This in part because much of what TDA attempts to do isn't even on the menu for most ML projects. One place (other than article databases of course) to look for examples of TDA is the Applied ... | Cases where TDA outperforms public benchmarks?
Comparisons between ML-at-large to topological data analysis (TDA) is difficult. This in part because much of what TDA attempts to do isn't even on the menu for most ML projects. One place (other than |
37,667 | Cases where TDA outperforms public benchmarks? | As of 2016, it seems difficult to concretely answer the question. Perhaps an ambitious, risk-seeking, grad student will provide more insight on TDA's performance as compared with well-known benchmarks. | Cases where TDA outperforms public benchmarks? | As of 2016, it seems difficult to concretely answer the question. Perhaps an ambitious, risk-seeking, grad student will provide more insight on TDA's performance as compared with well-known benchmarks | Cases where TDA outperforms public benchmarks?
As of 2016, it seems difficult to concretely answer the question. Perhaps an ambitious, risk-seeking, grad student will provide more insight on TDA's performance as compared with well-known benchmarks. | Cases where TDA outperforms public benchmarks?
As of 2016, it seems difficult to concretely answer the question. Perhaps an ambitious, risk-seeking, grad student will provide more insight on TDA's performance as compared with well-known benchmarks |
37,668 | Choice of time-series model for store sales prediction | I will elaborate one point not mentioned by the other answers.
With many series for different stores/products, there might be competition/substitution effects so you could want to use some form of hierarchical forecasting. Specifically, some product might be possible substitues for other product, leading to negative co... | Choice of time-series model for store sales prediction | I will elaborate one point not mentioned by the other answers.
With many series for different stores/products, there might be competition/substitution effects so you could want to use some form of hie | Choice of time-series model for store sales prediction
I will elaborate one point not mentioned by the other answers.
With many series for different stores/products, there might be competition/substitution effects so you could want to use some form of hierarchical forecasting. Specifically, some product might be possib... | Choice of time-series model for store sales prediction
I will elaborate one point not mentioned by the other answers.
With many series for different stores/products, there might be competition/substitution effects so you could want to use some form of hie |
37,669 | Choice of time-series model for store sales prediction | For this type of problem of model selection / hyperparameter-optimization, I would recommend you look into cross-validation approaches. Especially since your primary goal seems to be out-of-sample prediction, you want to be careful about overfitting your training data.
I can't think of a reason why you couldn't have di... | Choice of time-series model for store sales prediction | For this type of problem of model selection / hyperparameter-optimization, I would recommend you look into cross-validation approaches. Especially since your primary goal seems to be out-of-sample pre | Choice of time-series model for store sales prediction
For this type of problem of model selection / hyperparameter-optimization, I would recommend you look into cross-validation approaches. Especially since your primary goal seems to be out-of-sample prediction, you want to be careful about overfitting your training d... | Choice of time-series model for store sales prediction
For this type of problem of model selection / hyperparameter-optimization, I would recommend you look into cross-validation approaches. Especially since your primary goal seems to be out-of-sample pre |
37,670 | Choice of time-series model for store sales prediction | ARIMA models easily incorporate empirically identified pulses ,level shifts and local time trends while incorporating parameter and error variance changes. HW models are a fixed procedure lacking the robustness and adaptability of ARIMA models with Intervention Detection and are bloated by incorporating unnecessary/non... | Choice of time-series model for store sales prediction | ARIMA models easily incorporate empirically identified pulses ,level shifts and local time trends while incorporating parameter and error variance changes. HW models are a fixed procedure lacking the | Choice of time-series model for store sales prediction
ARIMA models easily incorporate empirically identified pulses ,level shifts and local time trends while incorporating parameter and error variance changes. HW models are a fixed procedure lacking the robustness and adaptability of ARIMA models with Intervention Det... | Choice of time-series model for store sales prediction
ARIMA models easily incorporate empirically identified pulses ,level shifts and local time trends while incorporating parameter and error variance changes. HW models are a fixed procedure lacking the |
37,671 | Choice of time-series model for store sales prediction | It is useful to know which time-horizon you care about (a month, a week or a day in advance?), and how much data you have (can you reliably estimate yearly seasonality?).
Personally, I've found ARIMA to be unintuitive and full of traps, and I haven't had much success with it. If you have daily data and care about dail... | Choice of time-series model for store sales prediction | It is useful to know which time-horizon you care about (a month, a week or a day in advance?), and how much data you have (can you reliably estimate yearly seasonality?).
Personally, I've found ARIMA | Choice of time-series model for store sales prediction
It is useful to know which time-horizon you care about (a month, a week or a day in advance?), and how much data you have (can you reliably estimate yearly seasonality?).
Personally, I've found ARIMA to be unintuitive and full of traps, and I haven't had much succ... | Choice of time-series model for store sales prediction
It is useful to know which time-horizon you care about (a month, a week or a day in advance?), and how much data you have (can you reliably estimate yearly seasonality?).
Personally, I've found ARIMA |
37,672 | How to get multivariate credible interval estimate(s) / highest density regions (HDR) after MCMC | I have found a Matlab Wrapper for ANN. ANN is a library for approximate nearest neighbor searches (homepage). Besides the usual parameters of a spatial index region query, it uses an additional error parameter eps which gives the "approximateness" of the search: A returned nearest neighbor will be at most 1+eps times f... | How to get multivariate credible interval estimate(s) / highest density regions (HDR) after MCMC | I have found a Matlab Wrapper for ANN. ANN is a library for approximate nearest neighbor searches (homepage). Besides the usual parameters of a spatial index region query, it uses an additional error | How to get multivariate credible interval estimate(s) / highest density regions (HDR) after MCMC
I have found a Matlab Wrapper for ANN. ANN is a library for approximate nearest neighbor searches (homepage). Besides the usual parameters of a spatial index region query, it uses an additional error parameter eps which giv... | How to get multivariate credible interval estimate(s) / highest density regions (HDR) after MCMC
I have found a Matlab Wrapper for ANN. ANN is a library for approximate nearest neighbor searches (homepage). Besides the usual parameters of a spatial index region query, it uses an additional error |
37,673 | How to interpret the estimate from Wilcoxon signed rank paired test? | From the documentation for the wilcox.test package:
Optionally (if argument conf.int is true), a nonparametric confidence interval and an estimator for the pseudomedian (one-sample case) or for the difference of the location parameters x-y is computed. (The pseudomedian of a distribution F is the median of the distrib... | How to interpret the estimate from Wilcoxon signed rank paired test? | From the documentation for the wilcox.test package:
Optionally (if argument conf.int is true), a nonparametric confidence interval and an estimator for the pseudomedian (one-sample case) or for the d | How to interpret the estimate from Wilcoxon signed rank paired test?
From the documentation for the wilcox.test package:
Optionally (if argument conf.int is true), a nonparametric confidence interval and an estimator for the pseudomedian (one-sample case) or for the difference of the location parameters x-y is compute... | How to interpret the estimate from Wilcoxon signed rank paired test?
From the documentation for the wilcox.test package:
Optionally (if argument conf.int is true), a nonparametric confidence interval and an estimator for the pseudomedian (one-sample case) or for the d |
37,674 | Best way to average F-score with unbalanced classes | "I am not sure which one is right"
There is no right or wrong here.
A classifier's performance can be represented using an $n\cdot n$ matrix. When trying to represent the performance using a single metric you lose some information.
In other words, since it is impossible to recover the confusion matrix based on a sing... | Best way to average F-score with unbalanced classes | "I am not sure which one is right"
There is no right or wrong here.
A classifier's performance can be represented using an $n\cdot n$ matrix. When trying to represent the performance using a single | Best way to average F-score with unbalanced classes
"I am not sure which one is right"
There is no right or wrong here.
A classifier's performance can be represented using an $n\cdot n$ matrix. When trying to represent the performance using a single metric you lose some information.
In other words, since it is imposs... | Best way to average F-score with unbalanced classes
"I am not sure which one is right"
There is no right or wrong here.
A classifier's performance can be represented using an $n\cdot n$ matrix. When trying to represent the performance using a single |
37,675 | Nonparametric nonlinear regression with prediction uncertainty (besides Gaussian Processes) | A Matérn covariance matrix with $ν=5/2$ is almost converging to a Squared Exponential kernel.
So I think that a Radial Basis Function (RBF) based approach is perfect in this scenario. It is fast, it works for the kind of black-box function that you have, and you can get measures of uncertainty.
You can alternatively us... | Nonparametric nonlinear regression with prediction uncertainty (besides Gaussian Processes) | A Matérn covariance matrix with $ν=5/2$ is almost converging to a Squared Exponential kernel.
So I think that a Radial Basis Function (RBF) based approach is perfect in this scenario. It is fast, it w | Nonparametric nonlinear regression with prediction uncertainty (besides Gaussian Processes)
A Matérn covariance matrix with $ν=5/2$ is almost converging to a Squared Exponential kernel.
So I think that a Radial Basis Function (RBF) based approach is perfect in this scenario. It is fast, it works for the kind of black-b... | Nonparametric nonlinear regression with prediction uncertainty (besides Gaussian Processes)
A Matérn covariance matrix with $ν=5/2$ is almost converging to a Squared Exponential kernel.
So I think that a Radial Basis Function (RBF) based approach is perfect in this scenario. It is fast, it w |
37,676 | Does the determination of the mean and SD imply the loss of one or two degrees of freedom? | The T-distribution is defined as the distribution of the ratio of a standard normal random variable and an independent scaled-chi random variable. Its degrees-of-freedom-parameter is equal to the degrees-of-freedom parameter for the chi random variable in its denominator. So the DF parameter is a matter of determinin... | Does the determination of the mean and SD imply the loss of one or two degrees of freedom? | The T-distribution is defined as the distribution of the ratio of a standard normal random variable and an independent scaled-chi random variable. Its degrees-of-freedom-parameter is equal to the deg | Does the determination of the mean and SD imply the loss of one or two degrees of freedom?
The T-distribution is defined as the distribution of the ratio of a standard normal random variable and an independent scaled-chi random variable. Its degrees-of-freedom-parameter is equal to the degrees-of-freedom parameter for... | Does the determination of the mean and SD imply the loss of one or two degrees of freedom?
The T-distribution is defined as the distribution of the ratio of a standard normal random variable and an independent scaled-chi random variable. Its degrees-of-freedom-parameter is equal to the deg |
37,677 | Does the determination of the mean and SD imply the loss of one or two degrees of freedom? | Let's consider an example to understand degrees of freedom:
Pretend we have 5 observations, $(1, 2, 1, 3, 5)$. If I tell you the mean of this data set ($2.4$) but not the values of the observations themselves, you can make up four values without changing the mean. If you pick $(3, 4, 3, 5)$ as your first four observati... | Does the determination of the mean and SD imply the loss of one or two degrees of freedom? | Let's consider an example to understand degrees of freedom:
Pretend we have 5 observations, $(1, 2, 1, 3, 5)$. If I tell you the mean of this data set ($2.4$) but not the values of the observations th | Does the determination of the mean and SD imply the loss of one or two degrees of freedom?
Let's consider an example to understand degrees of freedom:
Pretend we have 5 observations, $(1, 2, 1, 3, 5)$. If I tell you the mean of this data set ($2.4$) but not the values of the observations themselves, you can make up fou... | Does the determination of the mean and SD imply the loss of one or two degrees of freedom?
Let's consider an example to understand degrees of freedom:
Pretend we have 5 observations, $(1, 2, 1, 3, 5)$. If I tell you the mean of this data set ($2.4$) but not the values of the observations th |
37,678 | Heteroskedasticity and Distribution of the Dependent Variable in Linear Models | This is the solution for the problem above:
In brief, for my case, the heteroskedasticity is caused by at least two different sources:
Group's differences which OLS and all the family of "mono-level" regression model hardly can account for;
Wrong specification of the model functional form: more in detail (as suggested... | Heteroskedasticity and Distribution of the Dependent Variable in Linear Models | This is the solution for the problem above:
In brief, for my case, the heteroskedasticity is caused by at least two different sources:
Group's differences which OLS and all the family of "mono-level" | Heteroskedasticity and Distribution of the Dependent Variable in Linear Models
This is the solution for the problem above:
In brief, for my case, the heteroskedasticity is caused by at least two different sources:
Group's differences which OLS and all the family of "mono-level" regression model hardly can account for;... | Heteroskedasticity and Distribution of the Dependent Variable in Linear Models
This is the solution for the problem above:
In brief, for my case, the heteroskedasticity is caused by at least two different sources:
Group's differences which OLS and all the family of "mono-level" |
37,679 | How do I statistically rephrase this question | Darts is the simplest of games. Each player starts with a score of 501 and takes turns to throw 3 darts. The score for each turn is calculated and deducted from the players total. Bullseye scores 50, the outer ring scores 25 and a dart in the double or treble ring counts double or treble the segment score.
Image from ... | How do I statistically rephrase this question | Darts is the simplest of games. Each player starts with a score of 501 and takes turns to throw 3 darts. The score for each turn is calculated and deducted from the players total. Bullseye scores 50, | How do I statistically rephrase this question
Darts is the simplest of games. Each player starts with a score of 501 and takes turns to throw 3 darts. The score for each turn is calculated and deducted from the players total. Bullseye scores 50, the outer ring scores 25 and a dart in the double or treble ring counts do... | How do I statistically rephrase this question
Darts is the simplest of games. Each player starts with a score of 501 and takes turns to throw 3 darts. The score for each turn is calculated and deducted from the players total. Bullseye scores 50, |
37,680 | Is there any meaningfully robust approach to conduct a network meta-analysis of diagnostic test accuracy studies? | So this does not go unanswered here, based on comments from @GGA and from the OP's further research, are some references which the OP edited into the question as an update.
Upon feedback from GGA and extensive search, we can mention as potentially suitable approaches: a Bayesian method proposed by Menten and Lesaffre ... | Is there any meaningfully robust approach to conduct a network meta-analysis of diagnostic test accu | So this does not go unanswered here, based on comments from @GGA and from the OP's further research, are some references which the OP edited into the question as an update.
Upon feedback from GGA and | Is there any meaningfully robust approach to conduct a network meta-analysis of diagnostic test accuracy studies?
So this does not go unanswered here, based on comments from @GGA and from the OP's further research, are some references which the OP edited into the question as an update.
Upon feedback from GGA and exten... | Is there any meaningfully robust approach to conduct a network meta-analysis of diagnostic test accu
So this does not go unanswered here, based on comments from @GGA and from the OP's further research, are some references which the OP edited into the question as an update.
Upon feedback from GGA and |
37,681 | Dirichlet process mixture MCMC | $$
P(c_i=c|\vec{c_{-i}},y_i,\phi) =\frac{p(\vec{c_i},y_i,\phi)}{p(\vec{c_{-i}},y_i,\phi)} = \frac{p(y_i|\vec{c_{i}},\phi)p(\vec{c_{i}},\phi)}{p(y_i|\vec{c_{-i}},\phi)p(\vec{c_{-i}},\phi)} \\ = \frac{p(y_i|c_i,\phi)p(c_i|\vec{c_{-i},\phi})p(\vec{c_{-i}},\phi)}{p(y_i|\vec{c_{-i}},\phi)p(\vec{c_{-i}},\phi)} \\= \frac{p(y_... | Dirichlet process mixture MCMC | $$
P(c_i=c|\vec{c_{-i}},y_i,\phi) =\frac{p(\vec{c_i},y_i,\phi)}{p(\vec{c_{-i}},y_i,\phi)} = \frac{p(y_i|\vec{c_{i}},\phi)p(\vec{c_{i}},\phi)}{p(y_i|\vec{c_{-i}},\phi)p(\vec{c_{-i}},\phi)} \\ = \frac{p | Dirichlet process mixture MCMC
$$
P(c_i=c|\vec{c_{-i}},y_i,\phi) =\frac{p(\vec{c_i},y_i,\phi)}{p(\vec{c_{-i}},y_i,\phi)} = \frac{p(y_i|\vec{c_{i}},\phi)p(\vec{c_{i}},\phi)}{p(y_i|\vec{c_{-i}},\phi)p(\vec{c_{-i}},\phi)} \\ = \frac{p(y_i|c_i,\phi)p(c_i|\vec{c_{-i},\phi})p(\vec{c_{-i}},\phi)}{p(y_i|\vec{c_{-i}},\phi)p(\ve... | Dirichlet process mixture MCMC
$$
P(c_i=c|\vec{c_{-i}},y_i,\phi) =\frac{p(\vec{c_i},y_i,\phi)}{p(\vec{c_{-i}},y_i,\phi)} = \frac{p(y_i|\vec{c_{i}},\phi)p(\vec{c_{i}},\phi)}{p(y_i|\vec{c_{-i}},\phi)p(\vec{c_{-i}},\phi)} \\ = \frac{p |
37,682 | The Effect of Stopword Filtering prior to Word Embedding Training | One common approach is to simply subsample the most common words in the corpus. This way they have less effect on the model but you don't have to completely get rid of them. It can also speed up training because you spend less time dealing with stopwords that don't carry all that much information compared to the amount... | The Effect of Stopword Filtering prior to Word Embedding Training | One common approach is to simply subsample the most common words in the corpus. This way they have less effect on the model but you don't have to completely get rid of them. It can also speed up train | The Effect of Stopword Filtering prior to Word Embedding Training
One common approach is to simply subsample the most common words in the corpus. This way they have less effect on the model but you don't have to completely get rid of them. It can also speed up training because you spend less time dealing with stopwords... | The Effect of Stopword Filtering prior to Word Embedding Training
One common approach is to simply subsample the most common words in the corpus. This way they have less effect on the model but you don't have to completely get rid of them. It can also speed up train |
37,683 | KDE for censored data | Yes, it's possible. In order to do anything with censored data you need to assume at least 'censoring at random', which says that the hazard for observations censored at time $t$ is the same conditional on covariates as for uncensored observations still alive at time $t$.
The main difference from ordinary uncensore... | KDE for censored data | Yes, it's possible. In order to do anything with censored data you need to assume at least 'censoring at random', which says that the hazard for observations censored at time $t$ is the same condition | KDE for censored data
Yes, it's possible. In order to do anything with censored data you need to assume at least 'censoring at random', which says that the hazard for observations censored at time $t$ is the same conditional on covariates as for uncensored observations still alive at time $t$.
The main difference f... | KDE for censored data
Yes, it's possible. In order to do anything with censored data you need to assume at least 'censoring at random', which says that the hazard for observations censored at time $t$ is the same condition |
37,684 | KDE for censored data | Kernel density estimates probability density function of the empirical distribution, it doesn't "know" and "care" about the underlying distribution. By "empirical" we mean here that it uses only the observed data and makes minimal distributional assumptions. Obviously, if it uses the observed data, it cannot say anythi... | KDE for censored data | Kernel density estimates probability density function of the empirical distribution, it doesn't "know" and "care" about the underlying distribution. By "empirical" we mean here that it uses only the o | KDE for censored data
Kernel density estimates probability density function of the empirical distribution, it doesn't "know" and "care" about the underlying distribution. By "empirical" we mean here that it uses only the observed data and makes minimal distributional assumptions. Obviously, if it uses the observed data... | KDE for censored data
Kernel density estimates probability density function of the empirical distribution, it doesn't "know" and "care" about the underlying distribution. By "empirical" we mean here that it uses only the o |
37,685 | Can one compute the autocorrelation of covariance matrices sampled by MCMC? | The way I see it, when drawing $p \times p$ matrices $S_1, S_2, \dots S_n$ from a Wishart distribution, you are really drawing $p\cdot (p+1)/2$ specifically related univariate random variables at each time step. I.e., only the $\text{vech}(S_i)$ part of any $S_i$ [ = the upper triangular part] is random, and symmetry g... | Can one compute the autocorrelation of covariance matrices sampled by MCMC? | The way I see it, when drawing $p \times p$ matrices $S_1, S_2, \dots S_n$ from a Wishart distribution, you are really drawing $p\cdot (p+1)/2$ specifically related univariate random variables at each | Can one compute the autocorrelation of covariance matrices sampled by MCMC?
The way I see it, when drawing $p \times p$ matrices $S_1, S_2, \dots S_n$ from a Wishart distribution, you are really drawing $p\cdot (p+1)/2$ specifically related univariate random variables at each time step. I.e., only the $\text{vech}(S_i)... | Can one compute the autocorrelation of covariance matrices sampled by MCMC?
The way I see it, when drawing $p \times p$ matrices $S_1, S_2, \dots S_n$ from a Wishart distribution, you are really drawing $p\cdot (p+1)/2$ specifically related univariate random variables at each |
37,686 | Distribution for Paired Elo Matches Drawn from Normal Distribution | Looking at the MGF of $Z$
\begin{align*}
\mathbb E[e^{tZ}] &= \mathbb E[\mathbb E[e^{tZ}|X_1,X_2]]\\
&= \mathbb E\left[e^{tX_1} \frac{e^{X_1}}{e^{X_1}+e^{X_2}} +
e^{tX_2} \frac{e^{X_2}}{e^{X_2}+e^{X_1}}\right]\\
&= \mathbb E\left[e^{tX_1} \frac{e^{X_1}}{e^{X_1}+e^{X_2}}\right] +
\mathbb E\left[e^{tX_2} \frac{e^{X_2}}{... | Distribution for Paired Elo Matches Drawn from Normal Distribution | Looking at the MGF of $Z$
\begin{align*}
\mathbb E[e^{tZ}] &= \mathbb E[\mathbb E[e^{tZ}|X_1,X_2]]\\
&= \mathbb E\left[e^{tX_1} \frac{e^{X_1}}{e^{X_1}+e^{X_2}} +
e^{tX_2} \frac{e^{X_2}}{e^{X_2}+e^{X_ | Distribution for Paired Elo Matches Drawn from Normal Distribution
Looking at the MGF of $Z$
\begin{align*}
\mathbb E[e^{tZ}] &= \mathbb E[\mathbb E[e^{tZ}|X_1,X_2]]\\
&= \mathbb E\left[e^{tX_1} \frac{e^{X_1}}{e^{X_1}+e^{X_2}} +
e^{tX_2} \frac{e^{X_2}}{e^{X_2}+e^{X_1}}\right]\\
&= \mathbb E\left[e^{tX_1} \frac{e^{X_1}... | Distribution for Paired Elo Matches Drawn from Normal Distribution
Looking at the MGF of $Z$
\begin{align*}
\mathbb E[e^{tZ}] &= \mathbb E[\mathbb E[e^{tZ}|X_1,X_2]]\\
&= \mathbb E\left[e^{tX_1} \frac{e^{X_1}}{e^{X_1}+e^{X_2}} +
e^{tX_2} \frac{e^{X_2}}{e^{X_2}+e^{X_ |
37,687 | Distribution for Paired Elo Matches Drawn from Normal Distribution | A proof will have to wait, but some simulations indicate that the distribution of the Elo score of the winner is normal:
Here is the R code:
N <- 1e7
set.seed(7*11*13)
X1 <- rnorm(N); X2 <- rnorm(N)
Y <- runif(N)
Z <- ifelse(Y<= 1/(1+exp(X2-X1)), X1, X2)
(mu <-mean(Z))
[1] 0.363302
(sigma <- sd(Z))
[1] 0.9316078 | Distribution for Paired Elo Matches Drawn from Normal Distribution | A proof will have to wait, but some simulations indicate that the distribution of the Elo score of the winner is normal:
Here is the R code:
N <- 1e7
set.seed(7*11*13)
X1 <- rnorm(N); X2 <- rnorm(N)
| Distribution for Paired Elo Matches Drawn from Normal Distribution
A proof will have to wait, but some simulations indicate that the distribution of the Elo score of the winner is normal:
Here is the R code:
N <- 1e7
set.seed(7*11*13)
X1 <- rnorm(N); X2 <- rnorm(N)
Y <- runif(N)
Z <- ifelse(Y<= 1/(1+exp(X2-X1)), X1, X... | Distribution for Paired Elo Matches Drawn from Normal Distribution
A proof will have to wait, but some simulations indicate that the distribution of the Elo score of the winner is normal:
Here is the R code:
N <- 1e7
set.seed(7*11*13)
X1 <- rnorm(N); X2 <- rnorm(N)
|
37,688 | Log of Average v. Average of Log | If you maintain the assumption that the daily dependent variable $Y_{ji}$ of month $i$ follows a log-normal distribution, this means that
$$\ln Y_{ji} \sim \mathbf N (\mu_{ji}, \sigma_{ji}^2)$$
Then, denoting $d_i$ the number of days of month $i$, we also have
$$ \frac {1}{d_i} \ln Y_{ji} \sim \mathbf N\left(\frac {\m... | Log of Average v. Average of Log | If you maintain the assumption that the daily dependent variable $Y_{ji}$ of month $i$ follows a log-normal distribution, this means that
$$\ln Y_{ji} \sim \mathbf N (\mu_{ji}, \sigma_{ji}^2)$$
Then, | Log of Average v. Average of Log
If you maintain the assumption that the daily dependent variable $Y_{ji}$ of month $i$ follows a log-normal distribution, this means that
$$\ln Y_{ji} \sim \mathbf N (\mu_{ji}, \sigma_{ji}^2)$$
Then, denoting $d_i$ the number of days of month $i$, we also have
$$ \frac {1}{d_i} \ln Y_{j... | Log of Average v. Average of Log
If you maintain the assumption that the daily dependent variable $Y_{ji}$ of month $i$ follows a log-normal distribution, this means that
$$\ln Y_{ji} \sim \mathbf N (\mu_{ji}, \sigma_{ji}^2)$$
Then, |
37,689 | Log of Average v. Average of Log | The question is what is log-normally distributed?
I'm assuming it's monthly series. In this case get the average, then log.
If you thought that the daily series are log-normally distributed, then your average monthly series would be very close to normal distribution if there is no large autocorrelation. | Log of Average v. Average of Log | The question is what is log-normally distributed?
I'm assuming it's monthly series. In this case get the average, then log.
If you thought that the daily series are log-normally distributed, then you | Log of Average v. Average of Log
The question is what is log-normally distributed?
I'm assuming it's monthly series. In this case get the average, then log.
If you thought that the daily series are log-normally distributed, then your average monthly series would be very close to normal distribution if there is no larg... | Log of Average v. Average of Log
The question is what is log-normally distributed?
I'm assuming it's monthly series. In this case get the average, then log.
If you thought that the daily series are log-normally distributed, then you |
37,690 | Calculating and plotting confidence interval for Theil-Sen estimator | The following R code is copied verbatim from Appendix C, page C-20 of U.S. EPA's Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities; Unified Guidance; March 2009 (EPA 530/R-09-007; https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=P10055GQ.TXT). The code was written by Kirk M. Cameron, Ph.D. of MacStat Co... | Calculating and plotting confidence interval for Theil-Sen estimator | The following R code is copied verbatim from Appendix C, page C-20 of U.S. EPA's Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities; Unified Guidance; March 2009 (EPA 530/R-09-007; | Calculating and plotting confidence interval for Theil-Sen estimator
The following R code is copied verbatim from Appendix C, page C-20 of U.S. EPA's Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities; Unified Guidance; March 2009 (EPA 530/R-09-007; https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=P10055... | Calculating and plotting confidence interval for Theil-Sen estimator
The following R code is copied verbatim from Appendix C, page C-20 of U.S. EPA's Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities; Unified Guidance; March 2009 (EPA 530/R-09-007; |
37,691 | Covariance estimation of overlapping time series | I faced a similar problem earlier and found some related literature, e.g.
Britten‐Jones, Mark, Anthony Neuberger, and Ingmar Nolte. "Improved inference in regression with overlapping observations." Journal of Business Finance & Accounting 38.5‐6 (2011): 657-683.
Harri, Ardian, and B. Wade Brorsen. "The overlapping dat... | Covariance estimation of overlapping time series | I faced a similar problem earlier and found some related literature, e.g.
Britten‐Jones, Mark, Anthony Neuberger, and Ingmar Nolte. "Improved inference in regression with overlapping observations." J | Covariance estimation of overlapping time series
I faced a similar problem earlier and found some related literature, e.g.
Britten‐Jones, Mark, Anthony Neuberger, and Ingmar Nolte. "Improved inference in regression with overlapping observations." Journal of Business Finance & Accounting 38.5‐6 (2011): 657-683.
Harri, ... | Covariance estimation of overlapping time series
I faced a similar problem earlier and found some related literature, e.g.
Britten‐Jones, Mark, Anthony Neuberger, and Ingmar Nolte. "Improved inference in regression with overlapping observations." J |
37,692 | Covariance estimation of overlapping time series | If I understand the question well, then in the univariate case the autocorrelation matrix is a Toeplitz matrix.
In the mulitvariate case the the matrix will be a block Toeplitz matrix. In a block Toeplitz matrix all the variables are grouped per time t. That is blocks of correlations for the variables on h=0 on the d... | Covariance estimation of overlapping time series | If I understand the question well, then in the univariate case the autocorrelation matrix is a Toeplitz matrix.
In the mulitvariate case the the matrix will be a block Toeplitz matrix. In a block Toe | Covariance estimation of overlapping time series
If I understand the question well, then in the univariate case the autocorrelation matrix is a Toeplitz matrix.
In the mulitvariate case the the matrix will be a block Toeplitz matrix. In a block Toeplitz matrix all the variables are grouped per time t. That is blocks ... | Covariance estimation of overlapping time series
If I understand the question well, then in the univariate case the autocorrelation matrix is a Toeplitz matrix.
In the mulitvariate case the the matrix will be a block Toeplitz matrix. In a block Toe |
37,693 | Is the true linear regressor equal to the average linear regressor? | I am not sure what you are doing here, so only a quick comment. In general, for two random variables $Z$ and $W$, $E(ZW)\neq E(Z)E(W)$. I am not sure what your operator $E_D$ does but my guess it is that this property applies to $E_D$ too. So, the last line does not follows from the previous one. | Is the true linear regressor equal to the average linear regressor? | I am not sure what you are doing here, so only a quick comment. In general, for two random variables $Z$ and $W$, $E(ZW)\neq E(Z)E(W)$. I am not sure what your operator $E_D$ does but my guess it is t | Is the true linear regressor equal to the average linear regressor?
I am not sure what you are doing here, so only a quick comment. In general, for two random variables $Z$ and $W$, $E(ZW)\neq E(Z)E(W)$. I am not sure what your operator $E_D$ does but my guess it is that this property applies to $E_D$ too. So, the last... | Is the true linear regressor equal to the average linear regressor?
I am not sure what you are doing here, so only a quick comment. In general, for two random variables $Z$ and $W$, $E(ZW)\neq E(Z)E(W)$. I am not sure what your operator $E_D$ does but my guess it is t |
37,694 | Why does value iteration converge to the optimal value function in **finite** amount of steps? | According to Section VI in "An Introduction To Reinforcement Learning" written by Sutton and Barto, this is an experienced conclusion, not a strictly-proved theorem. So it implies that they believe in some special MDP model cases, it's possible that the convergence couldn't happen.
Please correct me if my understanding... | Why does value iteration converge to the optimal value function in **finite** amount of steps? | According to Section VI in "An Introduction To Reinforcement Learning" written by Sutton and Barto, this is an experienced conclusion, not a strictly-proved theorem. So it implies that they believe in | Why does value iteration converge to the optimal value function in **finite** amount of steps?
According to Section VI in "An Introduction To Reinforcement Learning" written by Sutton and Barto, this is an experienced conclusion, not a strictly-proved theorem. So it implies that they believe in some special MDP model c... | Why does value iteration converge to the optimal value function in **finite** amount of steps?
According to Section VI in "An Introduction To Reinforcement Learning" written by Sutton and Barto, this is an experienced conclusion, not a strictly-proved theorem. So it implies that they believe in |
37,695 | Why does value iteration converge to the optimal value function in **finite** amount of steps? | An example: $S = \{s\}, A = \{a\}, R = \frac{1}{2}$. By taking the only action $a$, the next state should be $s$ again.
Let's assume initial $V(s): = 0$. Updating by bellman formula: $V(s)= \frac{1}{2}, \frac{3}{4}, \frac{7}{8}...$ | Why does value iteration converge to the optimal value function in **finite** amount of steps? | An example: $S = \{s\}, A = \{a\}, R = \frac{1}{2}$. By taking the only action $a$, the next state should be $s$ again.
Let's assume initial $V(s): = 0$. Updating by bellman formula: $V(s)= \frac{1}{2 | Why does value iteration converge to the optimal value function in **finite** amount of steps?
An example: $S = \{s\}, A = \{a\}, R = \frac{1}{2}$. By taking the only action $a$, the next state should be $s$ again.
Let's assume initial $V(s): = 0$. Updating by bellman formula: $V(s)= \frac{1}{2}, \frac{3}{4}, \frac{7}{... | Why does value iteration converge to the optimal value function in **finite** amount of steps?
An example: $S = \{s\}, A = \{a\}, R = \frac{1}{2}$. By taking the only action $a$, the next state should be $s$ again.
Let's assume initial $V(s): = 0$. Updating by bellman formula: $V(s)= \frac{1}{2 |
37,696 | Review paper on particle filter | This appears to be a dissertation thesis or something close to that, not published in a scholarly journal but by Hamilton University, as clarified in ref. 2 of Feng et al. | Review paper on particle filter | This appears to be a dissertation thesis or something close to that, not published in a scholarly journal but by Hamilton University, as clarified in ref. 2 of Feng et al. | Review paper on particle filter
This appears to be a dissertation thesis or something close to that, not published in a scholarly journal but by Hamilton University, as clarified in ref. 2 of Feng et al. | Review paper on particle filter
This appears to be a dissertation thesis or something close to that, not published in a scholarly journal but by Hamilton University, as clarified in ref. 2 of Feng et al. |
37,697 | What is the probability of observing some function given a gaussian process? | I looked into the in the case of a 1D GP and the parametric function $y = f(x)$ a few months ago. This was my findings:
In order to get the probability of a function, $y = f(x)$, we have to perform a line integral through the probability distribution provided by the GP. This line integral would therefore be the probabi... | What is the probability of observing some function given a gaussian process? | I looked into the in the case of a 1D GP and the parametric function $y = f(x)$ a few months ago. This was my findings:
In order to get the probability of a function, $y = f(x)$, we have to perform a | What is the probability of observing some function given a gaussian process?
I looked into the in the case of a 1D GP and the parametric function $y = f(x)$ a few months ago. This was my findings:
In order to get the probability of a function, $y = f(x)$, we have to perform a line integral through the probability distr... | What is the probability of observing some function given a gaussian process?
I looked into the in the case of a 1D GP and the parametric function $y = f(x)$ a few months ago. This was my findings:
In order to get the probability of a function, $y = f(x)$, we have to perform a |
37,698 | Nonparametric tolerance intervals for discrete variables | The variable of interest is multinomially distributed with class (cell) probabilities: $p_1, p_2, ..., p_{10}$. Further, the classes are endowed with a natural order.
First attempt: smallest "predictive interval" containing $90\%$
p = [p1, ..., p10] # empirical proportions summing to 1
l = 1
u = length(p)
c... | Nonparametric tolerance intervals for discrete variables | The variable of interest is multinomially distributed with class (cell) probabilities: $p_1, p_2, ..., p_{10}$. Further, the classes are endowed with a natural order.
First attempt: smallest "predicti | Nonparametric tolerance intervals for discrete variables
The variable of interest is multinomially distributed with class (cell) probabilities: $p_1, p_2, ..., p_{10}$. Further, the classes are endowed with a natural order.
First attempt: smallest "predictive interval" containing $90\%$
p = [p1, ..., p10] # empiric... | Nonparametric tolerance intervals for discrete variables
The variable of interest is multinomially distributed with class (cell) probabilities: $p_1, p_2, ..., p_{10}$. Further, the classes are endowed with a natural order.
First attempt: smallest "predicti |
37,699 | Plotting a "posterior median surface" | It is very likely that the author used a Gaussian process to produce the interpolation. I think that is true because an exercise in the book describes a very similar problem to this one and requires a plot based on a Gaussian process.
I tried it and I think the resulting plot shares features with the posterior median ... | Plotting a "posterior median surface" | It is very likely that the author used a Gaussian process to produce the interpolation. I think that is true because an exercise in the book describes a very similar problem to this one and requires a | Plotting a "posterior median surface"
It is very likely that the author used a Gaussian process to produce the interpolation. I think that is true because an exercise in the book describes a very similar problem to this one and requires a plot based on a Gaussian process.
I tried it and I think the resulting plot shar... | Plotting a "posterior median surface"
It is very likely that the author used a Gaussian process to produce the interpolation. I think that is true because an exercise in the book describes a very similar problem to this one and requires a |
37,700 | Motivating likelihood ratio test vs Wald test for paper reviewer | Wald vs likelihood ratio is secondary to the fact that comparing $y\sim B$ to $y\sim A+B$ is a test of $A$, not a test of $B$. I hope this is a typo in the referee report.
Agresti’s Foundations of Linear and Generalized Linear Models gives some reasons to prefer likelihood ratio testing to Wald testing in logistic regr... | Motivating likelihood ratio test vs Wald test for paper reviewer | Wald vs likelihood ratio is secondary to the fact that comparing $y\sim B$ to $y\sim A+B$ is a test of $A$, not a test of $B$. I hope this is a typo in the referee report.
Agresti’s Foundations of Lin | Motivating likelihood ratio test vs Wald test for paper reviewer
Wald vs likelihood ratio is secondary to the fact that comparing $y\sim B$ to $y\sim A+B$ is a test of $A$, not a test of $B$. I hope this is a typo in the referee report.
Agresti’s Foundations of Linear and Generalized Linear Models gives some reasons to... | Motivating likelihood ratio test vs Wald test for paper reviewer
Wald vs likelihood ratio is secondary to the fact that comparing $y\sim B$ to $y\sim A+B$ is a test of $A$, not a test of $B$. I hope this is a typo in the referee report.
Agresti’s Foundations of Lin |
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