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51,101
Fisher information of a statistic
There is no fisher information of the estimator, just the fisher information of a random sample $\theta$. In Wikipedia, it says: In mathematical statistics, the Fisher information (sometimes simply called information1) is a way of measuring the amount of information that an observable random variable X carries about a...
Fisher information of a statistic
There is no fisher information of the estimator, just the fisher information of a random sample $\theta$. In Wikipedia, it says: In mathematical statistics, the Fisher information (sometimes simply c
Fisher information of a statistic There is no fisher information of the estimator, just the fisher information of a random sample $\theta$. In Wikipedia, it says: In mathematical statistics, the Fisher information (sometimes simply called information1) is a way of measuring the amount of information that an observable...
Fisher information of a statistic There is no fisher information of the estimator, just the fisher information of a random sample $\theta$. In Wikipedia, it says: In mathematical statistics, the Fisher information (sometimes simply c
51,102
Fisher information of a statistic
I'm pretty sure that you've got some terminology mixed up. Fisher's Information is a function of the data, just like an estimator such as $\bar{X}_{n}$ that gives you an idea of how much information of the parameter of interest is contained in the sample you've acquired. You can compute Fisher's Information at an estim...
Fisher information of a statistic
I'm pretty sure that you've got some terminology mixed up. Fisher's Information is a function of the data, just like an estimator such as $\bar{X}_{n}$ that gives you an idea of how much information o
Fisher information of a statistic I'm pretty sure that you've got some terminology mixed up. Fisher's Information is a function of the data, just like an estimator such as $\bar{X}_{n}$ that gives you an idea of how much information of the parameter of interest is contained in the sample you've acquired. You can comput...
Fisher information of a statistic I'm pretty sure that you've got some terminology mixed up. Fisher's Information is a function of the data, just like an estimator such as $\bar{X}_{n}$ that gives you an idea of how much information o
51,103
Estimating distribution from censored data
In R: estimate=function(y,z,u=1e-9){ ys=sort(unique(y)) # Inf signifies x's never observed (as they are higher than max y) zs=c(sort(unique(z))[-1],Inf) counts=xtabs(~z+y) observed=rbind(counts[-1,],rep(0,length(ys))) marginalHidden=counts[1,] m=sapply(seq(ys),function(i)zs>ys[i]) d=rep(1/length(zs),len...
Estimating distribution from censored data
In R: estimate=function(y,z,u=1e-9){ ys=sort(unique(y)) # Inf signifies x's never observed (as they are higher than max y) zs=c(sort(unique(z))[-1],Inf) counts=xtabs(~z+y) observed=rbind(cou
Estimating distribution from censored data In R: estimate=function(y,z,u=1e-9){ ys=sort(unique(y)) # Inf signifies x's never observed (as they are higher than max y) zs=c(sort(unique(z))[-1],Inf) counts=xtabs(~z+y) observed=rbind(counts[-1,],rep(0,length(ys))) marginalHidden=counts[1,] m=sapply(seq(ys),fu...
Estimating distribution from censored data In R: estimate=function(y,z,u=1e-9){ ys=sort(unique(y)) # Inf signifies x's never observed (as they are higher than max y) zs=c(sort(unique(z))[-1],Inf) counts=xtabs(~z+y) observed=rbind(cou
51,104
Multiple measures mediation analysis
At least one method for doing this has been published in: Judd et al. Estimating and testing mediation and moderation in within-subject designs. Psychological methods (2001) vol. 6 (2) pp. 115-134 http://www.ncbi.nlm.nih.gov/pubmed/11411437 I haven't yet found a link to code that implements this method though.
Multiple measures mediation analysis
At least one method for doing this has been published in: Judd et al. Estimating and testing mediation and moderation in within-subject designs. Psychological methods (2001) vol. 6 (2) pp. 115-134 ht
Multiple measures mediation analysis At least one method for doing this has been published in: Judd et al. Estimating and testing mediation and moderation in within-subject designs. Psychological methods (2001) vol. 6 (2) pp. 115-134 http://www.ncbi.nlm.nih.gov/pubmed/11411437 I haven't yet found a link to code that i...
Multiple measures mediation analysis At least one method for doing this has been published in: Judd et al. Estimating and testing mediation and moderation in within-subject designs. Psychological methods (2001) vol. 6 (2) pp. 115-134 ht
51,105
Disadvantages of the Kullback-Leibler divergence
I'd like to add the first answer, which would be unsatisfying, to this question through the lens of deep learning mostly in NLP: First things first, Disadvantages of the Kullback-Leibler divergence Let's see the definition (in terms of your question): $$ KL(q||p)=\sum q(s)\log \frac{q(s)}{p(s)} $$ When $p(s) >...
Disadvantages of the Kullback-Leibler divergence
I'd like to add the first answer, which would be unsatisfying, to this question through the lens of deep learning mostly in NLP: First things first, Disadvantages of the Kullback-Leibler divergence
Disadvantages of the Kullback-Leibler divergence I'd like to add the first answer, which would be unsatisfying, to this question through the lens of deep learning mostly in NLP: First things first, Disadvantages of the Kullback-Leibler divergence Let's see the definition (in terms of your question): $$ KL(q||p...
Disadvantages of the Kullback-Leibler divergence I'd like to add the first answer, which would be unsatisfying, to this question through the lens of deep learning mostly in NLP: First things first, Disadvantages of the Kullback-Leibler divergence
51,106
Perfect separation error message for glm with binomial but not with quasibinomial family
That sounds strange, I would guess it is a numerical coincidence. The only difference in R's glm between binomial and quasibinomial family is in the calculation of standard errors, the estimation process is exactly the same. Or, it might be that the difference in calculation of standard errors cause differences in the ...
Perfect separation error message for glm with binomial but not with quasibinomial family
That sounds strange, I would guess it is a numerical coincidence. The only difference in R's glm between binomial and quasibinomial family is in the calculation of standard errors, the estimation proc
Perfect separation error message for glm with binomial but not with quasibinomial family That sounds strange, I would guess it is a numerical coincidence. The only difference in R's glm between binomial and quasibinomial family is in the calculation of standard errors, the estimation process is exactly the same. Or, it...
Perfect separation error message for glm with binomial but not with quasibinomial family That sounds strange, I would guess it is a numerical coincidence. The only difference in R's glm between binomial and quasibinomial family is in the calculation of standard errors, the estimation proc
51,107
Trees and Cross Validation - # misclass
It returns the sum of deviances from each of the 10 fits, for a range of complexity parameters. from reference Manual... "A copy of FUN applied to object, with component dev replaced by the cross-validated results from the sum of the dev components of each fit." from code... cvdev <- 0 for (i in unique(rand)) { tl...
Trees and Cross Validation - # misclass
It returns the sum of deviances from each of the 10 fits, for a range of complexity parameters. from reference Manual... "A copy of FUN applied to object, with component dev replaced by the cross-vali
Trees and Cross Validation - # misclass It returns the sum of deviances from each of the 10 fits, for a range of complexity parameters. from reference Manual... "A copy of FUN applied to object, with component dev replaced by the cross-validated results from the sum of the dev components of each fit." from code... cvd...
Trees and Cross Validation - # misclass It returns the sum of deviances from each of the 10 fits, for a range of complexity parameters. from reference Manual... "A copy of FUN applied to object, with component dev replaced by the cross-vali
51,108
Graphical representation of variance
I found this paper to be helpful. Hopefully you will find it useful too: https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467-9639.2010.00426.x Paraphrasing what's explained in the article, if you understand SD, you can imagine that the squared deviation (x - mean of x)^2 can be represented graphically as a square (...
Graphical representation of variance
I found this paper to be helpful. Hopefully you will find it useful too: https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467-9639.2010.00426.x Paraphrasing what's explained in the article, if you
Graphical representation of variance I found this paper to be helpful. Hopefully you will find it useful too: https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467-9639.2010.00426.x Paraphrasing what's explained in the article, if you understand SD, you can imagine that the squared deviation (x - mean of x)^2 can be ...
Graphical representation of variance I found this paper to be helpful. Hopefully you will find it useful too: https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467-9639.2010.00426.x Paraphrasing what's explained in the article, if you
51,109
Graphical representation of variance
One method that is helpful to is to visualize the center point of the data, the mean, and how much each raw data point's distance varies along that mean. One way of achieving this is simply drawing lines that start from where the mean is (where the data on average is centrally located) and finishing those lines where t...
Graphical representation of variance
One method that is helpful to is to visualize the center point of the data, the mean, and how much each raw data point's distance varies along that mean. One way of achieving this is simply drawing li
Graphical representation of variance One method that is helpful to is to visualize the center point of the data, the mean, and how much each raw data point's distance varies along that mean. One way of achieving this is simply drawing lines that start from where the mean is (where the data on average is centrally locat...
Graphical representation of variance One method that is helpful to is to visualize the center point of the data, the mean, and how much each raw data point's distance varies along that mean. One way of achieving this is simply drawing li
51,110
Unsupervised pre-training for Reinforcement Learning
I think, you should look into the Learning from Demonstration direction. The idea is pretty simple. Let's say, we want to teach a bot to play a video game. We record a human playing the game, and give the model this data in order to pre-train it then. There are lot's of possible ways of using this data. If you are inte...
Unsupervised pre-training for Reinforcement Learning
I think, you should look into the Learning from Demonstration direction. The idea is pretty simple. Let's say, we want to teach a bot to play a video game. We record a human playing the game, and give
Unsupervised pre-training for Reinforcement Learning I think, you should look into the Learning from Demonstration direction. The idea is pretty simple. Let's say, we want to teach a bot to play a video game. We record a human playing the game, and give the model this data in order to pre-train it then. There are lot's...
Unsupervised pre-training for Reinforcement Learning I think, you should look into the Learning from Demonstration direction. The idea is pretty simple. Let's say, we want to teach a bot to play a video game. We record a human playing the game, and give
51,111
Agreement in clustered sample data
What you are doing is introducing multiple comparisons. For a confirmatory analysis, we usually specify our primary analysis and we may fit some post-hoc or secondary analyses not to confirm the prior findings, but to understand limitations in the data. Without any description of the various analyses you have conducted...
Agreement in clustered sample data
What you are doing is introducing multiple comparisons. For a confirmatory analysis, we usually specify our primary analysis and we may fit some post-hoc or secondary analyses not to confirm the prior
Agreement in clustered sample data What you are doing is introducing multiple comparisons. For a confirmatory analysis, we usually specify our primary analysis and we may fit some post-hoc or secondary analyses not to confirm the prior findings, but to understand limitations in the data. Without any description of the ...
Agreement in clustered sample data What you are doing is introducing multiple comparisons. For a confirmatory analysis, we usually specify our primary analysis and we may fit some post-hoc or secondary analyses not to confirm the prior
51,112
Agreement in clustered sample data
Yes you probably cannot assume data from the same patient are independent but do you detect a within-patient effect (try ANOVA)? If you want to compare across patients you could try to normalise to control for per-patient effects? If you fit a linear mixed model with the patient as a random effect then you can get sig...
Agreement in clustered sample data
Yes you probably cannot assume data from the same patient are independent but do you detect a within-patient effect (try ANOVA)? If you want to compare across patients you could try to normalise to c
Agreement in clustered sample data Yes you probably cannot assume data from the same patient are independent but do you detect a within-patient effect (try ANOVA)? If you want to compare across patients you could try to normalise to control for per-patient effects? If you fit a linear mixed model with the patient as a...
Agreement in clustered sample data Yes you probably cannot assume data from the same patient are independent but do you detect a within-patient effect (try ANOVA)? If you want to compare across patients you could try to normalise to c
51,113
Constructing an interval estimate for a multivariate output
[I know this doesn't answer the question, nor provide sources; this was going to be a comment but got too long] I think your problem here is you haven't clearly defined "95% confidence interval", and your problem presents with more than one way of interpreting that. If you decide exactly what you mean by "95% confiden...
Constructing an interval estimate for a multivariate output
[I know this doesn't answer the question, nor provide sources; this was going to be a comment but got too long] I think your problem here is you haven't clearly defined "95% confidence interval", and
Constructing an interval estimate for a multivariate output [I know this doesn't answer the question, nor provide sources; this was going to be a comment but got too long] I think your problem here is you haven't clearly defined "95% confidence interval", and your problem presents with more than one way of interpreting...
Constructing an interval estimate for a multivariate output [I know this doesn't answer the question, nor provide sources; this was going to be a comment but got too long] I think your problem here is you haven't clearly defined "95% confidence interval", and
51,114
A mixed-effects model for repeated measurements vs multiple time point-wise comparisons with a simpler test
Taking your second point first, your analysis of Day looked at the aggregate across days and there is no Day effect on average. There might be one on Day 2 but you really should have a justification for believing Day 2 more than other days. Point 1, that Day 1 isn't significant while Day 2 does show an effect is a mean...
A mixed-effects model for repeated measurements vs multiple time point-wise comparisons with a simpl
Taking your second point first, your analysis of Day looked at the aggregate across days and there is no Day effect on average. There might be one on Day 2 but you really should have a justification f
A mixed-effects model for repeated measurements vs multiple time point-wise comparisons with a simpler test Taking your second point first, your analysis of Day looked at the aggregate across days and there is no Day effect on average. There might be one on Day 2 but you really should have a justification for believing...
A mixed-effects model for repeated measurements vs multiple time point-wise comparisons with a simpl Taking your second point first, your analysis of Day looked at the aggregate across days and there is no Day effect on average. There might be one on Day 2 but you really should have a justification f
51,115
A mixed-effects model for repeated measurements vs multiple time point-wise comparisons with a simpler test
This may raise more questions for you than it answers, but consider that you can directly test A2 vs B2 by looking directly at the coefficients (plus their standard error) of your model and linearly combining them > summary(M) Linear mixed-effects model fit by REML ... Fixed effects: BW ~ Day * Group ...
A mixed-effects model for repeated measurements vs multiple time point-wise comparisons with a simpl
This may raise more questions for you than it answers, but consider that you can directly test A2 vs B2 by looking directly at the coefficients (plus their standard error) of your model and linearly c
A mixed-effects model for repeated measurements vs multiple time point-wise comparisons with a simpler test This may raise more questions for you than it answers, but consider that you can directly test A2 vs B2 by looking directly at the coefficients (plus their standard error) of your model and linearly combining the...
A mixed-effects model for repeated measurements vs multiple time point-wise comparisons with a simpl This may raise more questions for you than it answers, but consider that you can directly test A2 vs B2 by looking directly at the coefficients (plus their standard error) of your model and linearly c
51,116
Johansen test loading matrix
Loading matrix is the adjustment matrix ($α$ matrix). The elements of $α$ determine the speed of adjustment to the long-run equilibrium. Please see p.4 of this article to understand the relationship between adjustment matrix and cointegrating vector.
Johansen test loading matrix
Loading matrix is the adjustment matrix ($α$ matrix). The elements of $α$ determine the speed of adjustment to the long-run equilibrium. Please see p.4 of this article to understand the relationship
Johansen test loading matrix Loading matrix is the adjustment matrix ($α$ matrix). The elements of $α$ determine the speed of adjustment to the long-run equilibrium. Please see p.4 of this article to understand the relationship between adjustment matrix and cointegrating vector.
Johansen test loading matrix Loading matrix is the adjustment matrix ($α$ matrix). The elements of $α$ determine the speed of adjustment to the long-run equilibrium. Please see p.4 of this article to understand the relationship
51,117
Rolling out trial in phases, but not stepped wedge
Assuming your inferential focus is the treatment-control contrast, the solution you propose is a multicentre parallel randomised controlled trial design, where the centres are the communities, and there is no clear need to account for measurement times. A particular feature of the design you propose is that all partici...
Rolling out trial in phases, but not stepped wedge
Assuming your inferential focus is the treatment-control contrast, the solution you propose is a multicentre parallel randomised controlled trial design, where the centres are the communities, and the
Rolling out trial in phases, but not stepped wedge Assuming your inferential focus is the treatment-control contrast, the solution you propose is a multicentre parallel randomised controlled trial design, where the centres are the communities, and there is no clear need to account for measurement times. A particular fe...
Rolling out trial in phases, but not stepped wedge Assuming your inferential focus is the treatment-control contrast, the solution you propose is a multicentre parallel randomised controlled trial design, where the centres are the communities, and the
51,118
Uncertainty propagation in linear interpolation
Typically the uncertainties from counting measurements are made using Poisson statistics. The standard deviation of such a distribution is just the square root of the counts. I am not sure why your uncertainties are slightly off from this. Why do you need to interpolate the data at all? I am not too familiar with Reitv...
Uncertainty propagation in linear interpolation
Typically the uncertainties from counting measurements are made using Poisson statistics. The standard deviation of such a distribution is just the square root of the counts. I am not sure why your un
Uncertainty propagation in linear interpolation Typically the uncertainties from counting measurements are made using Poisson statistics. The standard deviation of such a distribution is just the square root of the counts. I am not sure why your uncertainties are slightly off from this. Why do you need to interpolate t...
Uncertainty propagation in linear interpolation Typically the uncertainties from counting measurements are made using Poisson statistics. The standard deviation of such a distribution is just the square root of the counts. I am not sure why your un
51,119
Lesser-known but powerful probabilistic inference algorithms
Indirect inference According to The New Palgrave Dictionary of Economics, Second Edition (entry by Anthony A. Smith, Jr), Indirect inference is a simulation-based method for estimating the parameters of economic models. Its hallmark is the use of an auxiliary model to capture aspects of the data upon which to base the...
Lesser-known but powerful probabilistic inference algorithms
Indirect inference According to The New Palgrave Dictionary of Economics, Second Edition (entry by Anthony A. Smith, Jr), Indirect inference is a simulation-based method for estimating the parameters
Lesser-known but powerful probabilistic inference algorithms Indirect inference According to The New Palgrave Dictionary of Economics, Second Edition (entry by Anthony A. Smith, Jr), Indirect inference is a simulation-based method for estimating the parameters of economic models. Its hallmark is the use of an auxiliar...
Lesser-known but powerful probabilistic inference algorithms Indirect inference According to The New Palgrave Dictionary of Economics, Second Edition (entry by Anthony A. Smith, Jr), Indirect inference is a simulation-based method for estimating the parameters
51,120
Prioritizing data collection
Have you thought about modelling this problem with decision bayesian networks (http://en.wikipedia.org/wiki/Influence_diagrams)? If you can define some utility function that you can optimise, given the decision you make, that is, which chemicals should be tested. This is a kind of a problem, when you take decisions und...
Prioritizing data collection
Have you thought about modelling this problem with decision bayesian networks (http://en.wikipedia.org/wiki/Influence_diagrams)? If you can define some utility function that you can optimise, given th
Prioritizing data collection Have you thought about modelling this problem with decision bayesian networks (http://en.wikipedia.org/wiki/Influence_diagrams)? If you can define some utility function that you can optimise, given the decision you make, that is, which chemicals should be tested. This is a kind of a problem...
Prioritizing data collection Have you thought about modelling this problem with decision bayesian networks (http://en.wikipedia.org/wiki/Influence_diagrams)? If you can define some utility function that you can optimise, given th
51,121
Kendall's coefficient of concordance (W) for ratings with a lot of ties
I don't have anything specific to say about Kendall's W but I don't get this concern about the ICC, the F test and the sample size. Your sample is not so small that testing would necessarily be impossible but why would you want to do such a test? To see if agreement is different from 0? This is quite a low bar and shou...
Kendall's coefficient of concordance (W) for ratings with a lot of ties
I don't have anything specific to say about Kendall's W but I don't get this concern about the ICC, the F test and the sample size. Your sample is not so small that testing would necessarily be imposs
Kendall's coefficient of concordance (W) for ratings with a lot of ties I don't have anything specific to say about Kendall's W but I don't get this concern about the ICC, the F test and the sample size. Your sample is not so small that testing would necessarily be impossible but why would you want to do such a test? T...
Kendall's coefficient of concordance (W) for ratings with a lot of ties I don't have anything specific to say about Kendall's W but I don't get this concern about the ICC, the F test and the sample size. Your sample is not so small that testing would necessarily be imposs
51,122
How to simulate a Cox proportional hazards model with change point and code it in R
Well, after a little research I found the answer to my question, so here is the code that allows the simulation: simulation <- function(n,lambda,changepoint, surv.df=TRUE) { # Define the covariate, restrictions and parameters. X <- rbinom(n,prob=1/3,size=1) E <- rexp(n,1) EL <- rexp(n,lambda) # Define the piecewise ...
How to simulate a Cox proportional hazards model with change point and code it in R
Well, after a little research I found the answer to my question, so here is the code that allows the simulation: simulation <- function(n,lambda,changepoint, surv.df=TRUE) { # Define the covariate, r
How to simulate a Cox proportional hazards model with change point and code it in R Well, after a little research I found the answer to my question, so here is the code that allows the simulation: simulation <- function(n,lambda,changepoint, surv.df=TRUE) { # Define the covariate, restrictions and parameters. X <- rb...
How to simulate a Cox proportional hazards model with change point and code it in R Well, after a little research I found the answer to my question, so here is the code that allows the simulation: simulation <- function(n,lambda,changepoint, surv.df=TRUE) { # Define the covariate, r
51,123
When should I use errors-in-variables?
Describing the nature and extent of measurement error is a very good practice for statisticians. The next important implication for practice is to interpret the results and findings in a contextually appropriate manner, which may confuse the reader somewhat, but doesn't convey false associations. For instance, suppose ...
When should I use errors-in-variables?
Describing the nature and extent of measurement error is a very good practice for statisticians. The next important implication for practice is to interpret the results and findings in a contextually
When should I use errors-in-variables? Describing the nature and extent of measurement error is a very good practice for statisticians. The next important implication for practice is to interpret the results and findings in a contextually appropriate manner, which may confuse the reader somewhat, but doesn't convey fal...
When should I use errors-in-variables? Describing the nature and extent of measurement error is a very good practice for statisticians. The next important implication for practice is to interpret the results and findings in a contextually
51,124
Statistics version of "What is..." columns in Notices
These days you often find such stuff in blogs! Here are two favourites of mine: andrewgelman.com normaldeviate.wordpress.com/
Statistics version of "What is..." columns in Notices
These days you often find such stuff in blogs! Here are two favourites of mine: andrewgelman.com normaldeviate.wordpress.com/
Statistics version of "What is..." columns in Notices These days you often find such stuff in blogs! Here are two favourites of mine: andrewgelman.com normaldeviate.wordpress.com/
Statistics version of "What is..." columns in Notices These days you often find such stuff in blogs! Here are two favourites of mine: andrewgelman.com normaldeviate.wordpress.com/
51,125
Comparison of two classifiers based on precision/recall/F1 only?
If all you have is P/R/F1 scores for the two systems/classifiers there's no way of testing whether the difference between the two is statistically significant. For the McNemar's test, as you suggested, you would need the predictions of the two systems. If you have other labeled data and the implementation of the two sy...
Comparison of two classifiers based on precision/recall/F1 only?
If all you have is P/R/F1 scores for the two systems/classifiers there's no way of testing whether the difference between the two is statistically significant. For the McNemar's test, as you suggested
Comparison of two classifiers based on precision/recall/F1 only? If all you have is P/R/F1 scores for the two systems/classifiers there's no way of testing whether the difference between the two is statistically significant. For the McNemar's test, as you suggested, you would need the predictions of the two systems. If...
Comparison of two classifiers based on precision/recall/F1 only? If all you have is P/R/F1 scores for the two systems/classifiers there's no way of testing whether the difference between the two is statistically significant. For the McNemar's test, as you suggested
51,126
Comparison of two classifiers based on precision/recall/F1 only?
You have different options about how to compare different classifiers in the text domain. However, you will need quality levels per class or per document. You can check this paper about Re-examining text categorisation methods.
Comparison of two classifiers based on precision/recall/F1 only?
You have different options about how to compare different classifiers in the text domain. However, you will need quality levels per class or per document. You can check this paper about Re-examining t
Comparison of two classifiers based on precision/recall/F1 only? You have different options about how to compare different classifiers in the text domain. However, you will need quality levels per class or per document. You can check this paper about Re-examining text categorisation methods.
Comparison of two classifiers based on precision/recall/F1 only? You have different options about how to compare different classifiers in the text domain. However, you will need quality levels per class or per document. You can check this paper about Re-examining t
51,127
Testing independence hypothesis in logistic regression
Yes, it is possible. You have to be somewhat careful about how to define the residuals. To be concrete, suppose we have a time series. Let the binary outcome be $y_t$ and the vector of regressors be $x_t$. An obvious thing is to take $\hat{\epsilon}_t = y_t - \frac{e^{x_t \hat{\beta}} } {1+e^{x_t \hat{\beta}} }$. Howev...
Testing independence hypothesis in logistic regression
Yes, it is possible. You have to be somewhat careful about how to define the residuals. To be concrete, suppose we have a time series. Let the binary outcome be $y_t$ and the vector of regressors be $
Testing independence hypothesis in logistic regression Yes, it is possible. You have to be somewhat careful about how to define the residuals. To be concrete, suppose we have a time series. Let the binary outcome be $y_t$ and the vector of regressors be $x_t$. An obvious thing is to take $\hat{\epsilon}_t = y_t - \frac...
Testing independence hypothesis in logistic regression Yes, it is possible. You have to be somewhat careful about how to define the residuals. To be concrete, suppose we have a time series. Let the binary outcome be $y_t$ and the vector of regressors be $
51,128
Testing two trendlines for statistical significance [closed]
you can try log transforming the data on either of both axis to get a normal distribution. Then do linear regression and compare the slopes to see if they are significantly different (calculate Z and then look up p-value in statistics table). Alternatively you can calculate area under the curve (AUC) using the trapezo...
Testing two trendlines for statistical significance [closed]
you can try log transforming the data on either of both axis to get a normal distribution. Then do linear regression and compare the slopes to see if they are significantly different (calculate Z and
Testing two trendlines for statistical significance [closed] you can try log transforming the data on either of both axis to get a normal distribution. Then do linear regression and compare the slopes to see if they are significantly different (calculate Z and then look up p-value in statistics table). Alternatively y...
Testing two trendlines for statistical significance [closed] you can try log transforming the data on either of both axis to get a normal distribution. Then do linear regression and compare the slopes to see if they are significantly different (calculate Z and
51,129
Clustering longitudinal (trajectory) data
If you have a particular longitudinal variable you are interested in, you could take an unsupervised approach on the covariates using either a mixed-effects regression tree or latent growth curve structural equation modeling tree. For SEM trees, see this for more info: http://brandmaier.de/semtree/user-guide/
Clustering longitudinal (trajectory) data
If you have a particular longitudinal variable you are interested in, you could take an unsupervised approach on the covariates using either a mixed-effects regression tree or latent growth curve stru
Clustering longitudinal (trajectory) data If you have a particular longitudinal variable you are interested in, you could take an unsupervised approach on the covariates using either a mixed-effects regression tree or latent growth curve structural equation modeling tree. For SEM trees, see this for more info: http://b...
Clustering longitudinal (trajectory) data If you have a particular longitudinal variable you are interested in, you could take an unsupervised approach on the covariates using either a mixed-effects regression tree or latent growth curve stru
51,130
Recommend classification algorithms to try
Can you describe simply what are these features ? If the features come from some complex data, like images or audio files, the size of your dataset allows you to use a classifier which learn itself the intermediate representation, for example deep neural networks. I don't know if R provides good ressources for deep lea...
Recommend classification algorithms to try
Can you describe simply what are these features ? If the features come from some complex data, like images or audio files, the size of your dataset allows you to use a classifier which learn itself th
Recommend classification algorithms to try Can you describe simply what are these features ? If the features come from some complex data, like images or audio files, the size of your dataset allows you to use a classifier which learn itself the intermediate representation, for example deep neural networks. I don't know...
Recommend classification algorithms to try Can you describe simply what are these features ? If the features come from some complex data, like images or audio files, the size of your dataset allows you to use a classifier which learn itself th
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Which model for panel data with dependent variables from [0,1]?
Addressing unobserved heterogeneity in panel models with fixed effects for fractional response variables (or nonlinear models in general) is not trivial due to the incidental parameter problem (for $N\rightarrow\infty$ and $T$ fixed), see for example Lancaster (2000) or this answer here at CrossValidated. If $T$ is sma...
Which model for panel data with dependent variables from [0,1]?
Addressing unobserved heterogeneity in panel models with fixed effects for fractional response variables (or nonlinear models in general) is not trivial due to the incidental parameter problem (for $N
Which model for panel data with dependent variables from [0,1]? Addressing unobserved heterogeneity in panel models with fixed effects for fractional response variables (or nonlinear models in general) is not trivial due to the incidental parameter problem (for $N\rightarrow\infty$ and $T$ fixed), see for example Lanca...
Which model for panel data with dependent variables from [0,1]? Addressing unobserved heterogeneity in panel models with fixed effects for fractional response variables (or nonlinear models in general) is not trivial due to the incidental parameter problem (for $N
51,132
Timeline of machine learning and data mining breakthroughs
This is far from complete, but Volker Tresp (Siemens) gives a nice timeline in the third slide of this talk.
Timeline of machine learning and data mining breakthroughs
This is far from complete, but Volker Tresp (Siemens) gives a nice timeline in the third slide of this talk.
Timeline of machine learning and data mining breakthroughs This is far from complete, but Volker Tresp (Siemens) gives a nice timeline in the third slide of this talk.
Timeline of machine learning and data mining breakthroughs This is far from complete, but Volker Tresp (Siemens) gives a nice timeline in the third slide of this talk.
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What optimization problem does least angle regression try to solve?
If I don't miss anything, LAR tries to solve the same optimization problem with LASSO in a way that the solutions for all possible equivalent $\epsilon$s are given (i.e., the so-called LASSO path)
What optimization problem does least angle regression try to solve?
If I don't miss anything, LAR tries to solve the same optimization problem with LASSO in a way that the solutions for all possible equivalent $\epsilon$s are given (i.e., the so-called LASSO path)
What optimization problem does least angle regression try to solve? If I don't miss anything, LAR tries to solve the same optimization problem with LASSO in a way that the solutions for all possible equivalent $\epsilon$s are given (i.e., the so-called LASSO path)
What optimization problem does least angle regression try to solve? If I don't miss anything, LAR tries to solve the same optimization problem with LASSO in a way that the solutions for all possible equivalent $\epsilon$s are given (i.e., the so-called LASSO path)
51,134
Linear regression in matrix notation
Note: In an attempt to add more details to my question, I ended up with a possible correct answer. Further comments will be highly appreciated Starting from: $$\nabla E_{D} = \sum_{n=1}^{N} \{y_{n}-\beta^{T}x_{n}\}x_{n}^{T}=0$$ Simplifying a bit: $$\sum_{n=1}^{N}y_{n}x_{n}^{T}=\beta^{T}\left(\sum_{n=1}^{N}x_{n}x_{n}^{...
Linear regression in matrix notation
Note: In an attempt to add more details to my question, I ended up with a possible correct answer. Further comments will be highly appreciated Starting from: $$\nabla E_{D} = \sum_{n=1}^{N} \{y_{n}-\
Linear regression in matrix notation Note: In an attempt to add more details to my question, I ended up with a possible correct answer. Further comments will be highly appreciated Starting from: $$\nabla E_{D} = \sum_{n=1}^{N} \{y_{n}-\beta^{T}x_{n}\}x_{n}^{T}=0$$ Simplifying a bit: $$\sum_{n=1}^{N}y_{n}x_{n}^{T}=\bet...
Linear regression in matrix notation Note: In an attempt to add more details to my question, I ended up with a possible correct answer. Further comments will be highly appreciated Starting from: $$\nabla E_{D} = \sum_{n=1}^{N} \{y_{n}-\
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Linear regression in matrix notation
I think I found the problem: when you went from the gradient to solving for $\beta$, you didn't reverse the order of the terms. The inversion should have been $$(x_nx^T_n)^{-1}=\frac{1}{x^T_nx_n},$$ so that $$\beta^T = \frac{\sum y_nx_n^T}{\sum x^T_nx_n}.$$ See the matrix cookbook (pdf) on page 5.
Linear regression in matrix notation
I think I found the problem: when you went from the gradient to solving for $\beta$, you didn't reverse the order of the terms. The inversion should have been $$(x_nx^T_n)^{-1}=\frac{1}{x^T_nx_n},$$ s
Linear regression in matrix notation I think I found the problem: when you went from the gradient to solving for $\beta$, you didn't reverse the order of the terms. The inversion should have been $$(x_nx^T_n)^{-1}=\frac{1}{x^T_nx_n},$$ so that $$\beta^T = \frac{\sum y_nx_n^T}{\sum x^T_nx_n}.$$ See the matrix cookbook (...
Linear regression in matrix notation I think I found the problem: when you went from the gradient to solving for $\beta$, you didn't reverse the order of the terms. The inversion should have been $$(x_nx^T_n)^{-1}=\frac{1}{x^T_nx_n},$$ s
51,136
Ftting a mixture of two Gaussians
Just so this thread gets an answer (since we can't access your data any more, I don't think much more answering will be happening): what you are doing seems to be perfectly fine. You could change your search for a quantile of a mixture to use KScorrect::qmixnorm(), as per Compute quantile function from a mixture of Nor...
Ftting a mixture of two Gaussians
Just so this thread gets an answer (since we can't access your data any more, I don't think much more answering will be happening): what you are doing seems to be perfectly fine. You could change your
Ftting a mixture of two Gaussians Just so this thread gets an answer (since we can't access your data any more, I don't think much more answering will be happening): what you are doing seems to be perfectly fine. You could change your search for a quantile of a mixture to use KScorrect::qmixnorm(), as per Compute quant...
Ftting a mixture of two Gaussians Just so this thread gets an answer (since we can't access your data any more, I don't think much more answering will be happening): what you are doing seems to be perfectly fine. You could change your
51,137
How to predict match outcome in team game based on participating players
By using Naive Bayes you assume that there is no such thing as team-play (Two players being best when play together). Keeping that in mind, you can do just the following: For each player evaluate number of games he wins divided by the total number of games. That will player's rate. Team's rate can be evaluated as a sum...
How to predict match outcome in team game based on participating players
By using Naive Bayes you assume that there is no such thing as team-play (Two players being best when play together). Keeping that in mind, you can do just the following: For each player evaluate numb
How to predict match outcome in team game based on participating players By using Naive Bayes you assume that there is no such thing as team-play (Two players being best when play together). Keeping that in mind, you can do just the following: For each player evaluate number of games he wins divided by the total number...
How to predict match outcome in team game based on participating players By using Naive Bayes you assume that there is no such thing as team-play (Two players being best when play together). Keeping that in mind, you can do just the following: For each player evaluate numb
51,138
How do I calculate the probabilities in this decision making scenario?
From probability theory: $P(T|You) = P(T \& You) / P(You)$ $P(T|Them) = P(T \& Them) / P(Them)$ $P(T) = P(T|You)P(You) + P(T|Them)P(Them)$ In your situation: $P(You) + P(Them) = 1$ The $P(You)$ is the probability that you're answering the question and $P(Them)$ is the probability that they are answering the questi...
How do I calculate the probabilities in this decision making scenario?
From probability theory: $P(T|You) = P(T \& You) / P(You)$ $P(T|Them) = P(T \& Them) / P(Them)$ $P(T) = P(T|You)P(You) + P(T|Them)P(Them)$ In your situation: $P(You) + P(Them) = 1$ The $P(You)$ is
How do I calculate the probabilities in this decision making scenario? From probability theory: $P(T|You) = P(T \& You) / P(You)$ $P(T|Them) = P(T \& Them) / P(Them)$ $P(T) = P(T|You)P(You) + P(T|Them)P(Them)$ In your situation: $P(You) + P(Them) = 1$ The $P(You)$ is the probability that you're answering the quest...
How do I calculate the probabilities in this decision making scenario? From probability theory: $P(T|You) = P(T \& You) / P(You)$ $P(T|Them) = P(T \& Them) / P(Them)$ $P(T) = P(T|You)P(You) + P(T|Them)P(Them)$ In your situation: $P(You) + P(Them) = 1$ The $P(You)$ is
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How do I calculate the probabilities in this decision making scenario?
Let's say there are only two choices A and B. If you make decision A, then the naive person is 30 percent correct in their choice; if you make decision B, then the naive person is 20 correct in their choice. Historically let 60% times A be the right answer. You making decision A happens $0.6 * 0.9 + 0.4 * 0.1$. Hence ...
How do I calculate the probabilities in this decision making scenario?
Let's say there are only two choices A and B. If you make decision A, then the naive person is 30 percent correct in their choice; if you make decision B, then the naive person is 20 correct in their
How do I calculate the probabilities in this decision making scenario? Let's say there are only two choices A and B. If you make decision A, then the naive person is 30 percent correct in their choice; if you make decision B, then the naive person is 20 correct in their choice. Historically let 60% times A be the right...
How do I calculate the probabilities in this decision making scenario? Let's say there are only two choices A and B. If you make decision A, then the naive person is 30 percent correct in their choice; if you make decision B, then the naive person is 20 correct in their
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Unbiased estimator from two SRS less duplicates
An option is to derive two independent HT estimates from each sample: $s_1$ and $s_2$: $\hat{t}_1 = \sum_{i \in s_1} \frac{y_i}{\pi_i} = \frac{N}{n} \sum_{i \in s_1} y_i$, $\hat{t}_2 = \sum_{i \in s_2} \frac{y_i}{\pi_i} = \frac{N}{m} \sum_{i \in s_2} y_i$. And then you can use average of both estimates to derive anothe...
Unbiased estimator from two SRS less duplicates
An option is to derive two independent HT estimates from each sample: $s_1$ and $s_2$: $\hat{t}_1 = \sum_{i \in s_1} \frac{y_i}{\pi_i} = \frac{N}{n} \sum_{i \in s_1} y_i$, $\hat{t}_2 = \sum_{i \in s_2
Unbiased estimator from two SRS less duplicates An option is to derive two independent HT estimates from each sample: $s_1$ and $s_2$: $\hat{t}_1 = \sum_{i \in s_1} \frac{y_i}{\pi_i} = \frac{N}{n} \sum_{i \in s_1} y_i$, $\hat{t}_2 = \sum_{i \in s_2} \frac{y_i}{\pi_i} = \frac{N}{m} \sum_{i \in s_2} y_i$. And then you ca...
Unbiased estimator from two SRS less duplicates An option is to derive two independent HT estimates from each sample: $s_1$ and $s_2$: $\hat{t}_1 = \sum_{i \in s_1} \frac{y_i}{\pi_i} = \frac{N}{n} \sum_{i \in s_1} y_i$, $\hat{t}_2 = \sum_{i \in s_2
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Unbiased estimator from two SRS less duplicates
There is other solution. You can compute the sampling probability for each individual to be sampled in combined sample $S$ by $$\pi_i = \frac{n}{N} + \frac{m}{N} - \frac{mn}{N^2} = \frac{n + m - \frac{mn}{N}}{N}$$ You can apply the standard HT-estimator for the population total now: $$\hat{t} = \sum_{i \in S} \frac{y_i...
Unbiased estimator from two SRS less duplicates
There is other solution. You can compute the sampling probability for each individual to be sampled in combined sample $S$ by $$\pi_i = \frac{n}{N} + \frac{m}{N} - \frac{mn}{N^2} = \frac{n + m - \frac
Unbiased estimator from two SRS less duplicates There is other solution. You can compute the sampling probability for each individual to be sampled in combined sample $S$ by $$\pi_i = \frac{n}{N} + \frac{m}{N} - \frac{mn}{N^2} = \frac{n + m - \frac{mn}{N}}{N}$$ You can apply the standard HT-estimator for the population...
Unbiased estimator from two SRS less duplicates There is other solution. You can compute the sampling probability for each individual to be sampled in combined sample $S$ by $$\pi_i = \frac{n}{N} + \frac{m}{N} - \frac{mn}{N^2} = \frac{n + m - \frac
51,142
Classification based on several marginal probabilities
Only $P(Y|X_n)$ and $P(X_n)$ are available in practice. For example, the $X_n$ are "whether a user has visited a specific website", and $Y$ is the gender. We have data of $X_n$, and we can buy the distribution of gender for some specific websites. Now I'll try the following approach: Assume that $P(X_1, X_2, ..., X_n|...
Classification based on several marginal probabilities
Only $P(Y|X_n)$ and $P(X_n)$ are available in practice. For example, the $X_n$ are "whether a user has visited a specific website", and $Y$ is the gender. We have data of $X_n$, and we can buy the dis
Classification based on several marginal probabilities Only $P(Y|X_n)$ and $P(X_n)$ are available in practice. For example, the $X_n$ are "whether a user has visited a specific website", and $Y$ is the gender. We have data of $X_n$, and we can buy the distribution of gender for some specific websites. Now I'll try the ...
Classification based on several marginal probabilities Only $P(Y|X_n)$ and $P(X_n)$ are available in practice. For example, the $X_n$ are "whether a user has visited a specific website", and $Y$ is the gender. We have data of $X_n$, and we can buy the dis
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Is there a standard name for probabilistic graphical models like this?
I think you need to recast your graphs into a different form. There is probably more than one way you could do this. A really important thing to notice about your model is that at any given time, you can make a best guess about the hidden state. What is special is at the next time step you can make an even better gue...
Is there a standard name for probabilistic graphical models like this?
I think you need to recast your graphs into a different form. There is probably more than one way you could do this. A really important thing to notice about your model is that at any given time, you
Is there a standard name for probabilistic graphical models like this? I think you need to recast your graphs into a different form. There is probably more than one way you could do this. A really important thing to notice about your model is that at any given time, you can make a best guess about the hidden state. W...
Is there a standard name for probabilistic graphical models like this? I think you need to recast your graphs into a different form. There is probably more than one way you could do this. A really important thing to notice about your model is that at any given time, you
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Particle filtering importance weights
Short Answer: No, you can't do that. It doesn't make sense. Notation: Let $s_{1:t}$ be the states from time $1$ to time $t$. Let $z_{1:t}$ denote the observations. Let $q(s_{1:t}|z_{1:t})$ be the proposal distribution that you sample from to approximate the entire sequence of unobserved states. This proposal distributi...
Particle filtering importance weights
Short Answer: No, you can't do that. It doesn't make sense. Notation: Let $s_{1:t}$ be the states from time $1$ to time $t$. Let $z_{1:t}$ denote the observations. Let $q(s_{1:t}|z_{1:t})$ be the prop
Particle filtering importance weights Short Answer: No, you can't do that. It doesn't make sense. Notation: Let $s_{1:t}$ be the states from time $1$ to time $t$. Let $z_{1:t}$ denote the observations. Let $q(s_{1:t}|z_{1:t})$ be the proposal distribution that you sample from to approximate the entire sequence of unobs...
Particle filtering importance weights Short Answer: No, you can't do that. It doesn't make sense. Notation: Let $s_{1:t}$ be the states from time $1$ to time $t$. Let $z_{1:t}$ denote the observations. Let $q(s_{1:t}|z_{1:t})$ be the prop
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Particle filtering importance weights
There is a reason why the weights turn out to be probabilities. In most simple implementations of SIR particle filters, the proposal distribution is the motion model. Under this setting the weight update equation simplifies to measurement likelihood. Check these resources: http://www.cs.berkeley.edu/~pabbeel/cs287-fa12...
Particle filtering importance weights
There is a reason why the weights turn out to be probabilities. In most simple implementations of SIR particle filters, the proposal distribution is the motion model. Under this setting the weight upd
Particle filtering importance weights There is a reason why the weights turn out to be probabilities. In most simple implementations of SIR particle filters, the proposal distribution is the motion model. Under this setting the weight update equation simplifies to measurement likelihood. Check these resources: http://w...
Particle filtering importance weights There is a reason why the weights turn out to be probabilities. In most simple implementations of SIR particle filters, the proposal distribution is the motion model. Under this setting the weight upd
51,146
lm() - model specification
Question 1 - There are two differences between the two approaches. First, by estimating it all together you are constraining the variance of the random part to be the same for each of variables 1, 2 and 5. If you fit the three models separately you will have a different estimate of the variance each time. A useful th...
lm() - model specification
Question 1 - There are two differences between the two approaches. First, by estimating it all together you are constraining the variance of the random part to be the same for each of variables 1, 2 a
lm() - model specification Question 1 - There are two differences between the two approaches. First, by estimating it all together you are constraining the variance of the random part to be the same for each of variables 1, 2 and 5. If you fit the three models separately you will have a different estimate of the varia...
lm() - model specification Question 1 - There are two differences between the two approaches. First, by estimating it all together you are constraining the variance of the random part to be the same for each of variables 1, 2 a
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lm() - model specification
I suggest that you use a model with a limited dependent variable. For example ordered probit, multinomial logit, negative binomial ...etc. The model choice depends on what you are modelling.
lm() - model specification
I suggest that you use a model with a limited dependent variable. For example ordered probit, multinomial logit, negative binomial ...etc. The model choice depends on what you are modelling.
lm() - model specification I suggest that you use a model with a limited dependent variable. For example ordered probit, multinomial logit, negative binomial ...etc. The model choice depends on what you are modelling.
lm() - model specification I suggest that you use a model with a limited dependent variable. For example ordered probit, multinomial logit, negative binomial ...etc. The model choice depends on what you are modelling.
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Constructing most powerful critical region basics
Anyway you look at it, the answer looks good. You have discovered that the log likelihood ratio is linear: $$\log\left(\frac{f(x;\theta_1)}{f(x;\theta_0)}\right) = 25\log(2) - x\log(3).$$ The left hand panel of the figure plots this. (Since only the shape of the log likelihood ratio matters, no value axis is shown.) ...
Constructing most powerful critical region basics
Anyway you look at it, the answer looks good. You have discovered that the log likelihood ratio is linear: $$\log\left(\frac{f(x;\theta_1)}{f(x;\theta_0)}\right) = 25\log(2) - x\log(3).$$ The left han
Constructing most powerful critical region basics Anyway you look at it, the answer looks good. You have discovered that the log likelihood ratio is linear: $$\log\left(\frac{f(x;\theta_1)}{f(x;\theta_0)}\right) = 25\log(2) - x\log(3).$$ The left hand panel of the figure plots this. (Since only the shape of the log li...
Constructing most powerful critical region basics Anyway you look at it, the answer looks good. You have discovered that the log likelihood ratio is linear: $$\log\left(\frac{f(x;\theta_1)}{f(x;\theta_0)}\right) = 25\log(2) - x\log(3).$$ The left han
51,149
Understanding output of a GEE model in R - Naive S.E vs. Robust S.E?
Naive SE is the same SE you would get if you perform GLM Robust SE is SE calculated using robust sandwich estimator. This vignettes explained GEE pretty well with an example https://cran.r-project.org/web/packages/HSAUR2/vignettes/Ch_analysing_longitudinal_dataII.pdf Hope that helps!
Understanding output of a GEE model in R - Naive S.E vs. Robust S.E?
Naive SE is the same SE you would get if you perform GLM Robust SE is SE calculated using robust sandwich estimator. This vignettes explained GEE pretty well with an example https://cran.r-project.or
Understanding output of a GEE model in R - Naive S.E vs. Robust S.E? Naive SE is the same SE you would get if you perform GLM Robust SE is SE calculated using robust sandwich estimator. This vignettes explained GEE pretty well with an example https://cran.r-project.org/web/packages/HSAUR2/vignettes/Ch_analysing_longit...
Understanding output of a GEE model in R - Naive S.E vs. Robust S.E? Naive SE is the same SE you would get if you perform GLM Robust SE is SE calculated using robust sandwich estimator. This vignettes explained GEE pretty well with an example https://cran.r-project.or
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What are the most popular domain adaptation methods (for transfer learning)?
Domain Adaptation is the process that attempts to alter the source domain in a way to bring the distribution of the source closer to that of the target domain. In many cases the Domain Adaptation methods are modifications of the basic algorithms from the area of the traditional Machine Learning, that they are trying to...
What are the most popular domain adaptation methods (for transfer learning)?
Domain Adaptation is the process that attempts to alter the source domain in a way to bring the distribution of the source closer to that of the target domain. In many cases the Domain Adaptation meth
What are the most popular domain adaptation methods (for transfer learning)? Domain Adaptation is the process that attempts to alter the source domain in a way to bring the distribution of the source closer to that of the target domain. In many cases the Domain Adaptation methods are modifications of the basic algorith...
What are the most popular domain adaptation methods (for transfer learning)? Domain Adaptation is the process that attempts to alter the source domain in a way to bring the distribution of the source closer to that of the target domain. In many cases the Domain Adaptation meth
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How to apply Isomap to test data?
Applying the mapping to test data is called the out-of-sample problem. Take a look at the following paper to see a solution for Isomap: Bengio, Yoshua, et al. Out-of-sample extensions for lle, isomap, mds, eigenmaps, and spectral clustering. Advances in neural information processing systems 16 (2004): 177-184.
How to apply Isomap to test data?
Applying the mapping to test data is called the out-of-sample problem. Take a look at the following paper to see a solution for Isomap: Bengio, Yoshua, et al. Out-of-sample extensions for lle, isomap,
How to apply Isomap to test data? Applying the mapping to test data is called the out-of-sample problem. Take a look at the following paper to see a solution for Isomap: Bengio, Yoshua, et al. Out-of-sample extensions for lle, isomap, mds, eigenmaps, and spectral clustering. Advances in neural information processing sy...
How to apply Isomap to test data? Applying the mapping to test data is called the out-of-sample problem. Take a look at the following paper to see a solution for Isomap: Bengio, Yoshua, et al. Out-of-sample extensions for lle, isomap,
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How to apply Isomap to test data?
As far as I know, the Isomap in scikit-learn implements out-of-sample isomap: http://scikit-learn.org/stable/modules/generated/sklearn.manifold.Isomap.html
How to apply Isomap to test data?
As far as I know, the Isomap in scikit-learn implements out-of-sample isomap: http://scikit-learn.org/stable/modules/generated/sklearn.manifold.Isomap.html
How to apply Isomap to test data? As far as I know, the Isomap in scikit-learn implements out-of-sample isomap: http://scikit-learn.org/stable/modules/generated/sklearn.manifold.Isomap.html
How to apply Isomap to test data? As far as I know, the Isomap in scikit-learn implements out-of-sample isomap: http://scikit-learn.org/stable/modules/generated/sklearn.manifold.Isomap.html
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How to apply Isomap to test data?
I solved the problem like this; solve Train*W = Y for W, map using Test*W. But other contributions are welcome.
How to apply Isomap to test data?
I solved the problem like this; solve Train*W = Y for W, map using Test*W. But other contributions are welcome.
How to apply Isomap to test data? I solved the problem like this; solve Train*W = Y for W, map using Test*W. But other contributions are welcome.
How to apply Isomap to test data? I solved the problem like this; solve Train*W = Y for W, map using Test*W. But other contributions are welcome.
51,154
Why arrange variables by causality in bivariate regression?
Distinguish two quantities that you might ask a regression to estimate: The expected value of $Y_{t+1}$ given that you observe $X_t$. This is always estimated by the regression of $Y_{t+1}$ on $X_t$ and targets the conditional distribution $P(Y_{t+1}\mid X_t)$. When you condition on different quantities you get (cor...
Why arrange variables by causality in bivariate regression?
Distinguish two quantities that you might ask a regression to estimate: The expected value of $Y_{t+1}$ given that you observe $X_t$. This is always estimated by the regression of $Y_{t+1}$ on $X_t$
Why arrange variables by causality in bivariate regression? Distinguish two quantities that you might ask a regression to estimate: The expected value of $Y_{t+1}$ given that you observe $X_t$. This is always estimated by the regression of $Y_{t+1}$ on $X_t$ and targets the conditional distribution $P(Y_{t+1}\mid X_t...
Why arrange variables by causality in bivariate regression? Distinguish two quantities that you might ask a regression to estimate: The expected value of $Y_{t+1}$ given that you observe $X_t$. This is always estimated by the regression of $Y_{t+1}$ on $X_t$
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Classification with increasing number of classes
This problem is sometimes called Open set recognition, or classification. There was a recent survey on open set recognition on Arxiv https://arxiv.org/pdf/1811.08581 The problem is also called zero shot learning https://en.wikipedia.org/wiki/Zero-shot_learning when the data points are images (I think)
Classification with increasing number of classes
This problem is sometimes called Open set recognition, or classification. There was a recent survey on open set recognition on Arxiv https://arxiv.org/pdf/1811.08581 The problem is also called zero sh
Classification with increasing number of classes This problem is sometimes called Open set recognition, or classification. There was a recent survey on open set recognition on Arxiv https://arxiv.org/pdf/1811.08581 The problem is also called zero shot learning https://en.wikipedia.org/wiki/Zero-shot_learning when the d...
Classification with increasing number of classes This problem is sometimes called Open set recognition, or classification. There was a recent survey on open set recognition on Arxiv https://arxiv.org/pdf/1811.08581 The problem is also called zero sh
51,156
Classification with increasing number of classes
It seems it is a clustering problem - if you don't know what and how many classes will you have, then unsupervised learning is for you. For example, if your trained classifier is very confident on some training example, then you conclude that it belongs to a known class. And if your classifier is unsure (say, it predic...
Classification with increasing number of classes
It seems it is a clustering problem - if you don't know what and how many classes will you have, then unsupervised learning is for you. For example, if your trained classifier is very confident on som
Classification with increasing number of classes It seems it is a clustering problem - if you don't know what and how many classes will you have, then unsupervised learning is for you. For example, if your trained classifier is very confident on some training example, then you conclude that it belongs to a known class....
Classification with increasing number of classes It seems it is a clustering problem - if you don't know what and how many classes will you have, then unsupervised learning is for you. For example, if your trained classifier is very confident on som
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Classification with increasing number of classes
You may treat all known classes as one class, and run some outlier detection / novel detection algorithms. For example, one class SVM Therefore we may have hierarchical classifiers, the first one to check if the data is some new species, if no, then second classifier will categorize data to $k$ known classes.
Classification with increasing number of classes
You may treat all known classes as one class, and run some outlier detection / novel detection algorithms. For example, one class SVM Therefore we may have hierarchical classifiers, the first one to c
Classification with increasing number of classes You may treat all known classes as one class, and run some outlier detection / novel detection algorithms. For example, one class SVM Therefore we may have hierarchical classifiers, the first one to check if the data is some new species, if no, then second classifier wil...
Classification with increasing number of classes You may treat all known classes as one class, and run some outlier detection / novel detection algorithms. For example, one class SVM Therefore we may have hierarchical classifiers, the first one to c
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Using doctor's data to identify hospitalisations
Machine learning idea: you could train a binary or one-class classifier of your choice to recognize what patterns in CPRD data indicate a hospitalization. You can use the HES data to label positive patterns in the CPRD data (e.g. those patterns that signify a hospitalization). I assume you could also use HES data to la...
Using doctor's data to identify hospitalisations
Machine learning idea: you could train a binary or one-class classifier of your choice to recognize what patterns in CPRD data indicate a hospitalization. You can use the HES data to label positive pa
Using doctor's data to identify hospitalisations Machine learning idea: you could train a binary or one-class classifier of your choice to recognize what patterns in CPRD data indicate a hospitalization. You can use the HES data to label positive patterns in the CPRD data (e.g. those patterns that signify a hospitaliza...
Using doctor's data to identify hospitalisations Machine learning idea: you could train a binary or one-class classifier of your choice to recognize what patterns in CPRD data indicate a hospitalization. You can use the HES data to label positive pa
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How do I analyse data with 2 independent variables and 2 dependent variables?
Are you interested in examining the correlation between the dependent variables in the same model? I can't speak to the multiple independent variables part of the question, but you could investigate using a linear mixed model with multiple response variables (if your data will be longitudinal). I don't know of a websit...
How do I analyse data with 2 independent variables and 2 dependent variables?
Are you interested in examining the correlation between the dependent variables in the same model? I can't speak to the multiple independent variables part of the question, but you could investigate u
How do I analyse data with 2 independent variables and 2 dependent variables? Are you interested in examining the correlation between the dependent variables in the same model? I can't speak to the multiple independent variables part of the question, but you could investigate using a linear mixed model with multiple re...
How do I analyse data with 2 independent variables and 2 dependent variables? Are you interested in examining the correlation between the dependent variables in the same model? I can't speak to the multiple independent variables part of the question, but you could investigate u
51,160
How do I analyse data with 2 independent variables and 2 dependent variables?
You probably know about this, but I often start at this point: http://www.ats.ucla.edu/stat/stata/whatstat/default.htm
How do I analyse data with 2 independent variables and 2 dependent variables?
You probably know about this, but I often start at this point: http://www.ats.ucla.edu/stat/stata/whatstat/default.htm
How do I analyse data with 2 independent variables and 2 dependent variables? You probably know about this, but I often start at this point: http://www.ats.ucla.edu/stat/stata/whatstat/default.htm
How do I analyse data with 2 independent variables and 2 dependent variables? You probably know about this, but I often start at this point: http://www.ats.ucla.edu/stat/stata/whatstat/default.htm
51,161
How do I analyse data with 2 independent variables and 2 dependent variables?
You said "How do I see what effect the two DV's have combined". So, I believe your two DV's are somehow related based on theory. In this case, running independent equations each for one DV is totally wrong! Imagine you want to measure "speaking skill" and one of your DV's is "accuracy of talking" and the other one is "...
How do I analyse data with 2 independent variables and 2 dependent variables?
You said "How do I see what effect the two DV's have combined". So, I believe your two DV's are somehow related based on theory. In this case, running independent equations each for one DV is totally
How do I analyse data with 2 independent variables and 2 dependent variables? You said "How do I see what effect the two DV's have combined". So, I believe your two DV's are somehow related based on theory. In this case, running independent equations each for one DV is totally wrong! Imagine you want to measure "speaki...
How do I analyse data with 2 independent variables and 2 dependent variables? You said "How do I see what effect the two DV's have combined". So, I believe your two DV's are somehow related based on theory. In this case, running independent equations each for one DV is totally
51,162
adjust rating based on number of experiences
If the rating is fairly predictable based on the number of people who've been to the restaurant, it occurs to me that one possibility is to build a model of the ratings given experiences. Then you could use the residuals (obviously, constant variance is fairly crucial here) instead of the raw data.
adjust rating based on number of experiences
If the rating is fairly predictable based on the number of people who've been to the restaurant, it occurs to me that one possibility is to build a model of the ratings given experiences. Then you co
adjust rating based on number of experiences If the rating is fairly predictable based on the number of people who've been to the restaurant, it occurs to me that one possibility is to build a model of the ratings given experiences. Then you could use the residuals (obviously, constant variance is fairly crucial here)...
adjust rating based on number of experiences If the rating is fairly predictable based on the number of people who've been to the restaurant, it occurs to me that one possibility is to build a model of the ratings given experiences. Then you co
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Visualizing probability of event over time, based on epoch time
Visualization options include circular histograms and circular kernel density plots. Basically, these are histograms or KDE visualizations wrapped around a circle, better to stress the cyclical nature of the variable, in your case that Sunday is much nearer to Monday than Wednesday. To the question of which times are m...
Visualizing probability of event over time, based on epoch time
Visualization options include circular histograms and circular kernel density plots. Basically, these are histograms or KDE visualizations wrapped around a circle, better to stress the cyclical nature
Visualizing probability of event over time, based on epoch time Visualization options include circular histograms and circular kernel density plots. Basically, these are histograms or KDE visualizations wrapped around a circle, better to stress the cyclical nature of the variable, in your case that Sunday is much neare...
Visualizing probability of event over time, based on epoch time Visualization options include circular histograms and circular kernel density plots. Basically, these are histograms or KDE visualizations wrapped around a circle, better to stress the cyclical nature
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Prediction/generalisation error derivation
OK, I got it: $E[(Y-\hat{f})^2] = E[\epsilon^2 + 2f\epsilon -2\epsilon\hat{f} + f^2 - 2f\hat{f} + \hat{f}^2]$ $E[(Y-\hat{f})^2] = \sigma_\epsilon^2 + f^2 - 2fE\hat{f} + E[\hat{f}^2]$ Note that: $E[(\hat{f}-E\hat{f})^2] = E[\hat{f}^2] - 2E\hat{f}E\hat{f} + (E[\hat{f}])^2$ $E[(\hat{f}-E\hat{f})^2] = E[\hat{f}^2] - (E[\ha...
Prediction/generalisation error derivation
OK, I got it: $E[(Y-\hat{f})^2] = E[\epsilon^2 + 2f\epsilon -2\epsilon\hat{f} + f^2 - 2f\hat{f} + \hat{f}^2]$ $E[(Y-\hat{f})^2] = \sigma_\epsilon^2 + f^2 - 2fE\hat{f} + E[\hat{f}^2]$ Note that: $E[(\h
Prediction/generalisation error derivation OK, I got it: $E[(Y-\hat{f})^2] = E[\epsilon^2 + 2f\epsilon -2\epsilon\hat{f} + f^2 - 2f\hat{f} + \hat{f}^2]$ $E[(Y-\hat{f})^2] = \sigma_\epsilon^2 + f^2 - 2fE\hat{f} + E[\hat{f}^2]$ Note that: $E[(\hat{f}-E\hat{f})^2] = E[\hat{f}^2] - 2E\hat{f}E\hat{f} + (E[\hat{f}])^2$ $E[(\...
Prediction/generalisation error derivation OK, I got it: $E[(Y-\hat{f})^2] = E[\epsilon^2 + 2f\epsilon -2\epsilon\hat{f} + f^2 - 2f\hat{f} + \hat{f}^2]$ $E[(Y-\hat{f})^2] = \sigma_\epsilon^2 + f^2 - 2fE\hat{f} + E[\hat{f}^2]$ Note that: $E[(\h
51,165
Reporting chi-square tests for weighted data
Personally, I always report the unweighted n, not the weighted values, and some restricted surveys ask you to round n to the nearest 50, but that depends on the survey. My 2 cents CS
Reporting chi-square tests for weighted data
Personally, I always report the unweighted n, not the weighted values, and some restricted surveys ask you to round n to the nearest 50, but that depends on the survey. My 2 cents CS
Reporting chi-square tests for weighted data Personally, I always report the unweighted n, not the weighted values, and some restricted surveys ask you to round n to the nearest 50, but that depends on the survey. My 2 cents CS
Reporting chi-square tests for weighted data Personally, I always report the unweighted n, not the weighted values, and some restricted surveys ask you to round n to the nearest 50, but that depends on the survey. My 2 cents CS
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Derivation of the formula for partial correlation coefficient of second order
You can find a proof of the general case in Section 2.5.3 (pp. 42-43) of Anderson (1984). The proof covers about a page and half to obtain the general formula $$\rho_{ij\cdot q+1,...,p} = \frac {\rho_{ij\cdot q+2,...,p} - \rho_{i, q+1\cdot q+2,...,p} \rho_{j, q+1\cdot q+2,...,p}} { \sqrt{1 - \rho^2_{i,q+1\cdot q+2,......
Derivation of the formula for partial correlation coefficient of second order
You can find a proof of the general case in Section 2.5.3 (pp. 42-43) of Anderson (1984). The proof covers about a page and half to obtain the general formula $$\rho_{ij\cdot q+1,...,p} = \frac {\rho
Derivation of the formula for partial correlation coefficient of second order You can find a proof of the general case in Section 2.5.3 (pp. 42-43) of Anderson (1984). The proof covers about a page and half to obtain the general formula $$\rho_{ij\cdot q+1,...,p} = \frac {\rho_{ij\cdot q+2,...,p} - \rho_{i, q+1\cdot q...
Derivation of the formula for partial correlation coefficient of second order You can find a proof of the general case in Section 2.5.3 (pp. 42-43) of Anderson (1984). The proof covers about a page and half to obtain the general formula $$\rho_{ij\cdot q+1,...,p} = \frac {\rho
51,167
Parameter estimation of a power spectrum equal to a power law + white noise
do a spectrum estimate(How? depends on your process, you might need some multi tapering method.) and fit your function to it. use wavelet, calculate wavelet variance, which is like spectrum but integrated over a band, then fit the integrated line to it. Similar to wavelet, but make use of the fact that wavelet approxim...
Parameter estimation of a power spectrum equal to a power law + white noise
do a spectrum estimate(How? depends on your process, you might need some multi tapering method.) and fit your function to it. use wavelet, calculate wavelet variance, which is like spectrum but integr
Parameter estimation of a power spectrum equal to a power law + white noise do a spectrum estimate(How? depends on your process, you might need some multi tapering method.) and fit your function to it. use wavelet, calculate wavelet variance, which is like spectrum but integrated over a band, then fit the integrated li...
Parameter estimation of a power spectrum equal to a power law + white noise do a spectrum estimate(How? depends on your process, you might need some multi tapering method.) and fit your function to it. use wavelet, calculate wavelet variance, which is like spectrum but integr
51,168
Residual, linear least squares and quality engineering
I did not go through your question completely, it is quite long. But I think it concerns with multiple regression and goodness of fit analysis. I would recommend reading chapter 3 titled 'Diagnostics and Remedial Measures' from textbook 'Applied Linear Statistical Models'.
Residual, linear least squares and quality engineering
I did not go through your question completely, it is quite long. But I think it concerns with multiple regression and goodness of fit analysis. I would recommend reading chapter 3 titled 'Diagnostics
Residual, linear least squares and quality engineering I did not go through your question completely, it is quite long. But I think it concerns with multiple regression and goodness of fit analysis. I would recommend reading chapter 3 titled 'Diagnostics and Remedial Measures' from textbook 'Applied Linear Statistical ...
Residual, linear least squares and quality engineering I did not go through your question completely, it is quite long. But I think it concerns with multiple regression and goodness of fit analysis. I would recommend reading chapter 3 titled 'Diagnostics
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Is the following an error-in-variance problem, and is there a recommended R (or SAS) package for it?
Your situation sounds very much like the situation I described with the last two questions I wrote here. I think those questions and the responses will help if you haven't already read them. If there are two variables that are linearly related and each is observed with measurement error then you have an error-in-vari...
Is the following an error-in-variance problem, and is there a recommended R (or SAS) package for it?
Your situation sounds very much like the situation I described with the last two questions I wrote here. I think those questions and the responses will help if you haven't already read them. If ther
Is the following an error-in-variance problem, and is there a recommended R (or SAS) package for it? Your situation sounds very much like the situation I described with the last two questions I wrote here. I think those questions and the responses will help if you haven't already read them. If there are two variables...
Is the following an error-in-variance problem, and is there a recommended R (or SAS) package for it? Your situation sounds very much like the situation I described with the last two questions I wrote here. I think those questions and the responses will help if you haven't already read them. If ther
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How can the robustness of observational studies be increased?
The weakness of observational studies is the lack of randomization. The best way to make these studies valid (not biased), is to do them by matching cases to controls through methods such as propensity scoring. This makes each experimental case very similar to its control case in terms of the various covariates that ...
How can the robustness of observational studies be increased?
The weakness of observational studies is the lack of randomization. The best way to make these studies valid (not biased), is to do them by matching cases to controls through methods such as propensi
How can the robustness of observational studies be increased? The weakness of observational studies is the lack of randomization. The best way to make these studies valid (not biased), is to do them by matching cases to controls through methods such as propensity scoring. This makes each experimental case very simila...
How can the robustness of observational studies be increased? The weakness of observational studies is the lack of randomization. The best way to make these studies valid (not biased), is to do them by matching cases to controls through methods such as propensi
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Measurement error in dependent variable?
Essentially what you have is an error term with a nonzero mean. Consequently the assumptions required for OLS to be appropriate are violated. So you should use OLS directly. However if q is known subtract it from the Y^$_i$s and apply OLS using the variance of the error term which is σ$^2$$_ν$+σ$^2$$_e$. Given that t...
Measurement error in dependent variable?
Essentially what you have is an error term with a nonzero mean. Consequently the assumptions required for OLS to be appropriate are violated. So you should use OLS directly. However if q is known su
Measurement error in dependent variable? Essentially what you have is an error term with a nonzero mean. Consequently the assumptions required for OLS to be appropriate are violated. So you should use OLS directly. However if q is known subtract it from the Y^$_i$s and apply OLS using the variance of the error term w...
Measurement error in dependent variable? Essentially what you have is an error term with a nonzero mean. Consequently the assumptions required for OLS to be appropriate are violated. So you should use OLS directly. However if q is known su
51,172
How is the intercept calculated in a generalized linear model and why is it different from a linear model?
The difference in estimated intercepts is not because of the overdispersion in the data. Peter Flom's comment is the correct answer. To see this, change the lm() model into a glm() model with a gaussian family: glm(data ~ 1, family = gaussian) glm(data ~ 1, family = gaussian(link="log"),start=c(20)) The canonical link...
How is the intercept calculated in a generalized linear model and why is it different from a linear
The difference in estimated intercepts is not because of the overdispersion in the data. Peter Flom's comment is the correct answer. To see this, change the lm() model into a glm() model with a gaussi
How is the intercept calculated in a generalized linear model and why is it different from a linear model? The difference in estimated intercepts is not because of the overdispersion in the data. Peter Flom's comment is the correct answer. To see this, change the lm() model into a glm() model with a gaussian family: gl...
How is the intercept calculated in a generalized linear model and why is it different from a linear The difference in estimated intercepts is not because of the overdispersion in the data. Peter Flom's comment is the correct answer. To see this, change the lm() model into a glm() model with a gaussi
51,173
Edge correction of Ripley's K-function for two 1D point processes?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted. Have you seen Gavin's K1D code? In his vignette, sync...
Edge correction of Ripley's K-function for two 1D point processes?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Edge correction of Ripley's K-function for two 1D point processes? Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted. ...
Edge correction of Ripley's K-function for two 1D point processes? Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
51,174
MCMC for structured matrix
First of all, lets simplify things. assume, that we have a zero-mean Gaussian Markov field with an unknown covariance matrix $\Sigma$ $$X\mid \Sigma\sim N\left ( 0,\Sigma \right )$$ Conditional independence of two variables $X_{i}$ and $X_{j}$, given the rest, is garantued iff the $(i,j)$ element of the precision matri...
MCMC for structured matrix
First of all, lets simplify things. assume, that we have a zero-mean Gaussian Markov field with an unknown covariance matrix $\Sigma$ $$X\mid \Sigma\sim N\left ( 0,\Sigma \right )$$ Conditional indepe
MCMC for structured matrix First of all, lets simplify things. assume, that we have a zero-mean Gaussian Markov field with an unknown covariance matrix $\Sigma$ $$X\mid \Sigma\sim N\left ( 0,\Sigma \right )$$ Conditional independence of two variables $X_{i}$ and $X_{j}$, given the rest, is garantued iff the $(i,j)$ ele...
MCMC for structured matrix First of all, lets simplify things. assume, that we have a zero-mean Gaussian Markov field with an unknown covariance matrix $\Sigma$ $$X\mid \Sigma\sim N\left ( 0,\Sigma \right )$$ Conditional indepe
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Likelihood test for dividing a distribution into two separate distributions
If I were approaching this I would: Try to use a random forest of gradient boosted trees to predict the patients (or patient characteristics of interest) based only on the amino acids. These tools handle categorical inputs. This would allow reduction of the region of interest from being 600-dimension (or whatever) to...
Likelihood test for dividing a distribution into two separate distributions
If I were approaching this I would: Try to use a random forest of gradient boosted trees to predict the patients (or patient characteristics of interest) based only on the amino acids. These tools ha
Likelihood test for dividing a distribution into two separate distributions If I were approaching this I would: Try to use a random forest of gradient boosted trees to predict the patients (or patient characteristics of interest) based only on the amino acids. These tools handle categorical inputs. This would allow r...
Likelihood test for dividing a distribution into two separate distributions If I were approaching this I would: Try to use a random forest of gradient boosted trees to predict the patients (or patient characteristics of interest) based only on the amino acids. These tools ha
51,176
What are finite window effects?
This is a guess but an educated one. Since the authors are referring to a histogram of interarrival times they might be referring to a smoothed version of the histogram. A kernel density estimate is one way to smooth a histogram. The bandwidth of the kernel is called the window. Based on the article that Peter Flom ...
What are finite window effects?
This is a guess but an educated one. Since the authors are referring to a histogram of interarrival times they might be referring to a smoothed version of the histogram. A kernel density estimate is
What are finite window effects? This is a guess but an educated one. Since the authors are referring to a histogram of interarrival times they might be referring to a smoothed version of the histogram. A kernel density estimate is one way to smooth a histogram. The bandwidth of the kernel is called the window. Based...
What are finite window effects? This is a guess but an educated one. Since the authors are referring to a histogram of interarrival times they might be referring to a smoothed version of the histogram. A kernel density estimate is
51,177
Model for circular statistics
This book by Nick Fisher is very popular. It covers many circular distributions including Cardioid, wrapped Cauchy, wrapped Normal and von MIses distribution. I don't know if it tells you how to generate observations from these distributions, but it gives you a lot of distributions, theory and methods. Statistical An...
Model for circular statistics
This book by Nick Fisher is very popular. It covers many circular distributions including Cardioid, wrapped Cauchy, wrapped Normal and von MIses distribution. I don't know if it tells you how to gen
Model for circular statistics This book by Nick Fisher is very popular. It covers many circular distributions including Cardioid, wrapped Cauchy, wrapped Normal and von MIses distribution. I don't know if it tells you how to generate observations from these distributions, but it gives you a lot of distributions, theo...
Model for circular statistics This book by Nick Fisher is very popular. It covers many circular distributions including Cardioid, wrapped Cauchy, wrapped Normal and von MIses distribution. I don't know if it tells you how to gen
51,178
Sample size for multiple regression: How much more data do I need?
Consider this: given no population effect, and given an initial sample effect classified as significant and a 2nd-stage effect (controlling for dummy variable) classified as non-significant, what is the probability that a researcher will continue to amass more observations to the point where the effect in question app...
Sample size for multiple regression: How much more data do I need?
Consider this: given no population effect, and given an initial sample effect classified as significant and a 2nd-stage effect (controlling for dummy variable) classified as non-significant, what is
Sample size for multiple regression: How much more data do I need? Consider this: given no population effect, and given an initial sample effect classified as significant and a 2nd-stage effect (controlling for dummy variable) classified as non-significant, what is the probability that a researcher will continue to am...
Sample size for multiple regression: How much more data do I need? Consider this: given no population effect, and given an initial sample effect classified as significant and a 2nd-stage effect (controlling for dummy variable) classified as non-significant, what is
51,179
Calculating and comparing histograms of complex numbers
If I have a 1D sequence of complex numbers with real and imaginary parts, how can I compute the histogram of this sequence? Do I separately compute the histogram of both the real and imaginary parts? A complex number is just an ordered pair of real numbers (i.e., a two-element vector of real numbers) with extended def...
Calculating and comparing histograms of complex numbers
If I have a 1D sequence of complex numbers with real and imaginary parts, how can I compute the histogram of this sequence? Do I separately compute the histogram of both the real and imaginary parts?
Calculating and comparing histograms of complex numbers If I have a 1D sequence of complex numbers with real and imaginary parts, how can I compute the histogram of this sequence? Do I separately compute the histogram of both the real and imaginary parts? A complex number is just an ordered pair of real numbers (i.e.,...
Calculating and comparing histograms of complex numbers If I have a 1D sequence of complex numbers with real and imaginary parts, how can I compute the histogram of this sequence? Do I separately compute the histogram of both the real and imaginary parts?
51,180
Finding the correct data mining approach
I am in agreement with the commentators, this is a simple time-series problem. If you are unconcerned with seasonal changes, I'm not sure what you expect to get out of simple day and hourly counts. ARIMA is what you want. If you really need something that is specifically machine learningish, just try basic Bayesian m...
Finding the correct data mining approach
I am in agreement with the commentators, this is a simple time-series problem. If you are unconcerned with seasonal changes, I'm not sure what you expect to get out of simple day and hourly counts. A
Finding the correct data mining approach I am in agreement with the commentators, this is a simple time-series problem. If you are unconcerned with seasonal changes, I'm not sure what you expect to get out of simple day and hourly counts. ARIMA is what you want. If you really need something that is specifically machi...
Finding the correct data mining approach I am in agreement with the commentators, this is a simple time-series problem. If you are unconcerned with seasonal changes, I'm not sure what you expect to get out of simple day and hourly counts. A
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Gaussian Process goodness of fit
What do you think would cause the change? Is it a change in the mean, the variance or something else? The type of change you expect should determine the parameter you should test for change. Is this a sudden change? If so this could be done using intervention analysis for time series such as is done with Box Jenkins mo...
Gaussian Process goodness of fit
What do you think would cause the change? Is it a change in the mean, the variance or something else? The type of change you expect should determine the parameter you should test for change. Is this a
Gaussian Process goodness of fit What do you think would cause the change? Is it a change in the mean, the variance or something else? The type of change you expect should determine the parameter you should test for change. Is this a sudden change? If so this could be done using intervention analysis for time series su...
Gaussian Process goodness of fit What do you think would cause the change? Is it a change in the mean, the variance or something else? The type of change you expect should determine the parameter you should test for change. Is this a
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Gaussian Process goodness of fit
So following is the solution I came up with. Please correct me if I'm wrong :) Assumptions The model change is abrupt. Idea My idea was the following: We determine the goodness of the fit by means of a model comparison. So we create a very simple model for which we know how to calculate the likelihood. As soon as this ...
Gaussian Process goodness of fit
So following is the solution I came up with. Please correct me if I'm wrong :) Assumptions The model change is abrupt. Idea My idea was the following: We determine the goodness of the fit by means of
Gaussian Process goodness of fit So following is the solution I came up with. Please correct me if I'm wrong :) Assumptions The model change is abrupt. Idea My idea was the following: We determine the goodness of the fit by means of a model comparison. So we create a very simple model for which we know how to calculate...
Gaussian Process goodness of fit So following is the solution I came up with. Please correct me if I'm wrong :) Assumptions The model change is abrupt. Idea My idea was the following: We determine the goodness of the fit by means of
51,183
Risk assesment and non-statistician's perception of percentages
As mentioned in the comment @Tim, prospect theory proposes that probabilities are perceived in a particular way, such as in this figure: The "weighted probability" could also be called subjective probability or perceived probability. This function suggests you might be justified to propose three categories of low prob...
Risk assesment and non-statistician's perception of percentages
As mentioned in the comment @Tim, prospect theory proposes that probabilities are perceived in a particular way, such as in this figure: The "weighted probability" could also be called subjective pro
Risk assesment and non-statistician's perception of percentages As mentioned in the comment @Tim, prospect theory proposes that probabilities are perceived in a particular way, such as in this figure: The "weighted probability" could also be called subjective probability or perceived probability. This function suggest...
Risk assesment and non-statistician's perception of percentages As mentioned in the comment @Tim, prospect theory proposes that probabilities are perceived in a particular way, such as in this figure: The "weighted probability" could also be called subjective pro
51,184
Risk assesment and non-statistician's perception of percentages
I imagine this would depend on the background of the individual. Someone with a strong statisticsl background would probably have a lower threshold on what is a reasoanbly high percentage than somone who doesn't.
Risk assesment and non-statistician's perception of percentages
I imagine this would depend on the background of the individual. Someone with a strong statisticsl background would probably have a lower threshold on what is a reasoanbly high percentage than somone
Risk assesment and non-statistician's perception of percentages I imagine this would depend on the background of the individual. Someone with a strong statisticsl background would probably have a lower threshold on what is a reasoanbly high percentage than somone who doesn't.
Risk assesment and non-statistician's perception of percentages I imagine this would depend on the background of the individual. Someone with a strong statisticsl background would probably have a lower threshold on what is a reasoanbly high percentage than somone
51,185
Method to estimate the prediction interval for GLM and negative binomial distribution
It makes sense if you're taking the $\theta$ as known. If you want to incorporate the uncertainty in $\theta$ you would either simulate from the joint distribution (asymptotically Gaussian) of the other parameters and $\theta$, or you could simulate one conditionally on the other (since $\theta$ is an input to the GLM,...
Method to estimate the prediction interval for GLM and negative binomial distribution
It makes sense if you're taking the $\theta$ as known. If you want to incorporate the uncertainty in $\theta$ you would either simulate from the joint distribution (asymptotically Gaussian) of the oth
Method to estimate the prediction interval for GLM and negative binomial distribution It makes sense if you're taking the $\theta$ as known. If you want to incorporate the uncertainty in $\theta$ you would either simulate from the joint distribution (asymptotically Gaussian) of the other parameters and $\theta$, or you...
Method to estimate the prediction interval for GLM and negative binomial distribution It makes sense if you're taking the $\theta$ as known. If you want to incorporate the uncertainty in $\theta$ you would either simulate from the joint distribution (asymptotically Gaussian) of the oth
51,186
How to compare response to same question asked at different time points?
It depends on several things. One is what your scale was. Unless it can plausibly be treated as a continuous scale, a t test could not be appropriate. Some purists argue that you should never treat an ordinal scale as continuous for such purposes. The other, probably more important issue, is what you are interested i...
How to compare response to same question asked at different time points?
It depends on several things. One is what your scale was. Unless it can plausibly be treated as a continuous scale, a t test could not be appropriate. Some purists argue that you should never treat
How to compare response to same question asked at different time points? It depends on several things. One is what your scale was. Unless it can plausibly be treated as a continuous scale, a t test could not be appropriate. Some purists argue that you should never treat an ordinal scale as continuous for such purpose...
How to compare response to same question asked at different time points? It depends on several things. One is what your scale was. Unless it can plausibly be treated as a continuous scale, a t test could not be appropriate. Some purists argue that you should never treat
51,187
How to compare response to same question asked at different time points?
One approach is to visualize the changes by individuals. I can't recall the name of this chart type offhand, but this would be a chart in which each individual response to the first question is plotted in its y-axis position on the left side, and each response is plotted for the second question on the right side, with ...
How to compare response to same question asked at different time points?
One approach is to visualize the changes by individuals. I can't recall the name of this chart type offhand, but this would be a chart in which each individual response to the first question is plotte
How to compare response to same question asked at different time points? One approach is to visualize the changes by individuals. I can't recall the name of this chart type offhand, but this would be a chart in which each individual response to the first question is plotted in its y-axis position on the left side, and ...
How to compare response to same question asked at different time points? One approach is to visualize the changes by individuals. I can't recall the name of this chart type offhand, but this would be a chart in which each individual response to the first question is plotte
51,188
How to compare response to same question asked at different time points?
Your outcomes are paired ordered categories, so the t-test is not appropriate, but the generalizations of McNemar's test would be. Read the linked page to get the general idea, then follow the "Related Tests" links to find which is best for your situation.
How to compare response to same question asked at different time points?
Your outcomes are paired ordered categories, so the t-test is not appropriate, but the generalizations of McNemar's test would be. Read the linked page to get the general idea, then follow the "Relat
How to compare response to same question asked at different time points? Your outcomes are paired ordered categories, so the t-test is not appropriate, but the generalizations of McNemar's test would be. Read the linked page to get the general idea, then follow the "Related Tests" links to find which is best for your ...
How to compare response to same question asked at different time points? Your outcomes are paired ordered categories, so the t-test is not appropriate, but the generalizations of McNemar's test would be. Read the linked page to get the general idea, then follow the "Relat
51,189
Variance stabilization "rule" for MCMC jumps...anyone?
As far as I know, in general it strongly depends on the landscape of your observable. Last year, me and my supervisors presented one way to adaptively obtain the step-sizes for one particular example of landscapes - Fractal Landscapes occurring in chaotic systems. However, I'm not aware of a systematic way to approach ...
Variance stabilization "rule" for MCMC jumps...anyone?
As far as I know, in general it strongly depends on the landscape of your observable. Last year, me and my supervisors presented one way to adaptively obtain the step-sizes for one particular example
Variance stabilization "rule" for MCMC jumps...anyone? As far as I know, in general it strongly depends on the landscape of your observable. Last year, me and my supervisors presented one way to adaptively obtain the step-sizes for one particular example of landscapes - Fractal Landscapes occurring in chaotic systems. ...
Variance stabilization "rule" for MCMC jumps...anyone? As far as I know, in general it strongly depends on the landscape of your observable. Last year, me and my supervisors presented one way to adaptively obtain the step-sizes for one particular example
51,190
How to assess correlation when each variable is measured by independent replicates?
From your description I think the only viable way to go is what you don't want to do: Use the bucket as the level of analyses. That is, aggregate the 3 measurements within each bucket and you have your pairings. With this approach you should effectively aggegate out the measurement error. I made a small simulation and ...
How to assess correlation when each variable is measured by independent replicates?
From your description I think the only viable way to go is what you don't want to do: Use the bucket as the level of analyses. That is, aggregate the 3 measurements within each bucket and you have you
How to assess correlation when each variable is measured by independent replicates? From your description I think the only viable way to go is what you don't want to do: Use the bucket as the level of analyses. That is, aggregate the 3 measurements within each bucket and you have your pairings. With this approach you s...
How to assess correlation when each variable is measured by independent replicates? From your description I think the only viable way to go is what you don't want to do: Use the bucket as the level of analyses. That is, aggregate the 3 measurements within each bucket and you have you
51,191
Abusing Linear Models under Multicollinearity: Simulation for 'realistic' movement of predictors
Try lavaan. It's an R package that is supposed to being built to handle link functions as well. The problem with your question is the lack of a purpose. Statistical modeling is very difficult to translate and interpret when dealing with variables and abstract hypotheses. X and Z are correlated. If there is large varia...
Abusing Linear Models under Multicollinearity: Simulation for 'realistic' movement of predictors
Try lavaan. It's an R package that is supposed to being built to handle link functions as well. The problem with your question is the lack of a purpose. Statistical modeling is very difficult to trans
Abusing Linear Models under Multicollinearity: Simulation for 'realistic' movement of predictors Try lavaan. It's an R package that is supposed to being built to handle link functions as well. The problem with your question is the lack of a purpose. Statistical modeling is very difficult to translate and interpret when...
Abusing Linear Models under Multicollinearity: Simulation for 'realistic' movement of predictors Try lavaan. It's an R package that is supposed to being built to handle link functions as well. The problem with your question is the lack of a purpose. Statistical modeling is very difficult to trans
51,192
Confidence interval for the biggest difference between means
To estimate confidence intervals we could use simulations of the distribution of the biggest difference of the mean when we place half the means on one end and the other half on the other end. It would look for instance like this. Then based on some observed range you can compute which boundaries associate with that, ...
Confidence interval for the biggest difference between means
To estimate confidence intervals we could use simulations of the distribution of the biggest difference of the mean when we place half the means on one end and the other half on the other end. It woul
Confidence interval for the biggest difference between means To estimate confidence intervals we could use simulations of the distribution of the biggest difference of the mean when we place half the means on one end and the other half on the other end. It would look for instance like this. Then based on some observed...
Confidence interval for the biggest difference between means To estimate confidence intervals we could use simulations of the distribution of the biggest difference of the mean when we place half the means on one end and the other half on the other end. It woul
51,193
Classifier success rate and confidence intervals
Under the assumption that your data is normally distributed, then the standard error can be used as it is the error that is expected from normally distributed data with the same expectation (mean). We are interested in how many samples fall into the "tails" of the distribution - i.e. how many samples fall outside of a ...
Classifier success rate and confidence intervals
Under the assumption that your data is normally distributed, then the standard error can be used as it is the error that is expected from normally distributed data with the same expectation (mean). We
Classifier success rate and confidence intervals Under the assumption that your data is normally distributed, then the standard error can be used as it is the error that is expected from normally distributed data with the same expectation (mean). We are interested in how many samples fall into the "tails" of the distri...
Classifier success rate and confidence intervals Under the assumption that your data is normally distributed, then the standard error can be used as it is the error that is expected from normally distributed data with the same expectation (mean). We
51,194
Non-parametric test for repeated measures and post-hoc single comparisons in R?
It may be worth looking at the Brunner-Munzel-Test, see e.g. Brunner, Munzel, Puri (1999) "Rank-score tests in factorial designs with repeated measures", Journal of Multivariate Analysis. You can use it even if you have any kind of ordinal scale and not too small sample sizes. Yet I'm not sure about your particular mod...
Non-parametric test for repeated measures and post-hoc single comparisons in R?
It may be worth looking at the Brunner-Munzel-Test, see e.g. Brunner, Munzel, Puri (1999) "Rank-score tests in factorial designs with repeated measures", Journal of Multivariate Analysis. You can use
Non-parametric test for repeated measures and post-hoc single comparisons in R? It may be worth looking at the Brunner-Munzel-Test, see e.g. Brunner, Munzel, Puri (1999) "Rank-score tests in factorial designs with repeated measures", Journal of Multivariate Analysis. You can use it even if you have any kind of ordinal ...
Non-parametric test for repeated measures and post-hoc single comparisons in R? It may be worth looking at the Brunner-Munzel-Test, see e.g. Brunner, Munzel, Puri (1999) "Rank-score tests in factorial designs with repeated measures", Journal of Multivariate Analysis. You can use
51,195
Can I somehow compute variance explained by PC after Oblique rotation in PCA?
I think you're on solid ground. Another useful thing to do is to call up a loading plot ('/plot rotation'), then to reanalyze using varimax rotation and again ask for a loading plot. But I hope you're analyzing objective data and not opinion data: using PCA on the latter is well-known to be a mistake, because it tre...
Can I somehow compute variance explained by PC after Oblique rotation in PCA?
I think you're on solid ground. Another useful thing to do is to call up a loading plot ('/plot rotation'), then to reanalyze using varimax rotation and again ask for a loading plot. But I hope you'
Can I somehow compute variance explained by PC after Oblique rotation in PCA? I think you're on solid ground. Another useful thing to do is to call up a loading plot ('/plot rotation'), then to reanalyze using varimax rotation and again ask for a loading plot. But I hope you're analyzing objective data and not opinio...
Can I somehow compute variance explained by PC after Oblique rotation in PCA? I think you're on solid ground. Another useful thing to do is to call up a loading plot ('/plot rotation'), then to reanalyze using varimax rotation and again ask for a loading plot. But I hope you'
51,196
Kullback–Leibler divergence between two Wishart distributions
I think it's a typo and $a_s = a, B_s = B$. I don't know what the $\tilde\Gamma$ notation is supposed to represent. If you set it this way, this is consistent with the equations at http://people.ee.duke.edu/~shji/papers/AL_TPAMI.pdf on page 25.
Kullback–Leibler divergence between two Wishart distributions
I think it's a typo and $a_s = a, B_s = B$. I don't know what the $\tilde\Gamma$ notation is supposed to represent. If you set it this way, this is consistent with the equations at http://people.ee.du
Kullback–Leibler divergence between two Wishart distributions I think it's a typo and $a_s = a, B_s = B$. I don't know what the $\tilde\Gamma$ notation is supposed to represent. If you set it this way, this is consistent with the equations at http://people.ee.duke.edu/~shji/papers/AL_TPAMI.pdf on page 25.
Kullback–Leibler divergence between two Wishart distributions I think it's a typo and $a_s = a, B_s = B$. I don't know what the $\tilde\Gamma$ notation is supposed to represent. If you set it this way, this is consistent with the equations at http://people.ee.du
51,197
What is the distribution of the sample variance of the Skellam distribution?
Some of the comments have pointed out that there may be better ways to solve your problem that do not involve finding the distribution of the sample variance of the Skellam distribution. Here I will answer the title question irrespective of those other issues. The exact distribution of the sample variance from a Skel...
What is the distribution of the sample variance of the Skellam distribution?
Some of the comments have pointed out that there may be better ways to solve your problem that do not involve finding the distribution of the sample variance of the Skellam distribution. Here I will
What is the distribution of the sample variance of the Skellam distribution? Some of the comments have pointed out that there may be better ways to solve your problem that do not involve finding the distribution of the sample variance of the Skellam distribution. Here I will answer the title question irrespective of t...
What is the distribution of the sample variance of the Skellam distribution? Some of the comments have pointed out that there may be better ways to solve your problem that do not involve finding the distribution of the sample variance of the Skellam distribution. Here I will
51,198
What is the distribution of the sample variance of the Skellam distribution?
I'm not sure what the problem is: sample variance is a random variable. I would guess it is distributed as a (re-scaled) Chi-square for this distribution. For a fixed number of samples, the standard error of the variance statistic will be proportional to the population variance you are trying to estimate. Thus I would ...
What is the distribution of the sample variance of the Skellam distribution?
I'm not sure what the problem is: sample variance is a random variable. I would guess it is distributed as a (re-scaled) Chi-square for this distribution. For a fixed number of samples, the standard e
What is the distribution of the sample variance of the Skellam distribution? I'm not sure what the problem is: sample variance is a random variable. I would guess it is distributed as a (re-scaled) Chi-square for this distribution. For a fixed number of samples, the standard error of the variance statistic will be prop...
What is the distribution of the sample variance of the Skellam distribution? I'm not sure what the problem is: sample variance is a random variable. I would guess it is distributed as a (re-scaled) Chi-square for this distribution. For a fixed number of samples, the standard e
51,199
Sample-size calculations for Benjamini-Hochberg, Westfall-Young, Holm-Bonferroni methods
What is typically done (though it is easier said than done), is this: do a pilot study which gives you an idea of the data you're handling based on this (or if a pilot study is not an option, knowledge about the domain), create a data generating model so you can sample data that 'looks like' the true data. Make this s...
Sample-size calculations for Benjamini-Hochberg, Westfall-Young, Holm-Bonferroni methods
What is typically done (though it is easier said than done), is this: do a pilot study which gives you an idea of the data you're handling based on this (or if a pilot study is not an option, knowled
Sample-size calculations for Benjamini-Hochberg, Westfall-Young, Holm-Bonferroni methods What is typically done (though it is easier said than done), is this: do a pilot study which gives you an idea of the data you're handling based on this (or if a pilot study is not an option, knowledge about the domain), create a ...
Sample-size calculations for Benjamini-Hochberg, Westfall-Young, Holm-Bonferroni methods What is typically done (though it is easier said than done), is this: do a pilot study which gives you an idea of the data you're handling based on this (or if a pilot study is not an option, knowled
51,200
How to model the relationship between geocoded and ungeocoded sales data?
I don't have a succinct answer, but I do have advice and comments too long for a single comment... Having 70% of your sales come from transactions with a name and zip code (making it possible to match to an address in a given trade area) seems to be really really good. I would recommend not getting too bogged down with...
How to model the relationship between geocoded and ungeocoded sales data?
I don't have a succinct answer, but I do have advice and comments too long for a single comment... Having 70% of your sales come from transactions with a name and zip code (making it possible to match
How to model the relationship between geocoded and ungeocoded sales data? I don't have a succinct answer, but I do have advice and comments too long for a single comment... Having 70% of your sales come from transactions with a name and zip code (making it possible to match to an address in a given trade area) seems to...
How to model the relationship between geocoded and ungeocoded sales data? I don't have a succinct answer, but I do have advice and comments too long for a single comment... Having 70% of your sales come from transactions with a name and zip code (making it possible to match