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Three Ways to Run Bayesian Models in R

When I try write. If you are using library R2jags and function jags then function print powershell script examples download table of statistics that are stored in list element BUGSoutput and sublist summary.

You can access those data directly and store as other object or just use directly in function write. Learn more. Asked 7 years, 4 months ago. Active 7 axios cors 401, 4 months ago. Viewed 2k times. Jilber Urbina Active Oldest Votes. Didzis Elferts Didzis Elferts Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.

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I am trying to implement a few different count models in JAGS, but with the dependent variable taking large, positive values.

In comparison, achieving the requisite Rhat values when using dnegbin is proving not be an issue. In comparison to both, poisson-lognormal runs the fastest even on my empirical dataset. My understanding is that comparing the DIC values of NB2 and Poisson-Lognormal do not make sense because of the difference in parameterization.

R Tutorial: The posterior model

As a result, making the Poisson-Gamma model work would make for appropriate model comparison. So any thoughts on what might be affecting the computation would be much appreciated. I am sharing the the code for simulating a negative binomial depedent variable with its mean as a function of 2 covariates and a pre-defined size parameter of 1.

My initilization function randomizes the coefficient estimates using a standard normal distribution while the dispersion parameters are initialized using rexp 1. I remember reading in the JAGS v4. I tried using some truncation, but that did not help in the simulated study. Learn more. Asked 29 days ago.

Active 29 days ago. Viewed 12 times. Median Mean 3rd Qu. Active Oldest Votes. Sign up or log in Sign up using Google. Sign up using Facebook.This chapter focuses on a very simple model — one for which JAGS is overkill.

n eff jags

This allows us to get familiar with JAGS and the various tools to investigate JAGS models in a simple setting before moving on to more interesting models soon.

This can be useful if you need to find out particulars about things like the distributions that are availble in JAGS. Based on limited testing, it appears that things are good to go and you should not need to do this. The data sets provided as csv files by Kruschke also live in the CalvinBayes package, so you can read this file with. You should use better names when creating your own data sets.

We will primarily use R2jags. Kruschke primarily uses rjags. The main advantage of R2jags is that we can specify the model by creating a special kind of function.

Sometimes the parameterization are different. Notice that we are only giving the distribution name and its parameters. R2jags::jags can be used to run our JAGS model. We need to specify three things: 1 the model we are using as defined above2 the data we are using, 3 the parameters we want saved in the posterior sampling. The data do not need to be in a data frame, and this usually means a bit more work on our part to tell JAGS things like how much data there is.

We will prepare all the information JAGS needs about the data in a list using list. There are some additional, optional things we might want to control as well. More on those later. We can plot the posterior distribution, using posterior to extract the posterior samples as a data frame. It is also possible to generate posterior samples when we use the grid method. The mosaic package include the resample function that will sample rows of a data frame with replacement using specified probabilities given by the posterior, for example.

The coda package provides output analysis and diagnostics for MCMC algorithms. In order to use it, we must convert our JAGS object into something coda recognizes.

Categorical covariates in JAGS

We do with with the as. Note: Kruschke uses rjags without R2jagsso he does this step using rjags::coda. Both functions result in the same thing — posterior samples in a format that coda expects, but they have different starting points. The mcmc object we extracted with as. Here, for example is the bayesplot plot of the posterior distribution for theta.

By default, a vertical line segment is drawn at the median of the posterior distribution. One advantage of bayesplot is that the plots use the ggplot2 system and so interoperate well with ggformula. We can extract such a vector a couple different ways:. There are a number of options that allow you to add some additional information to the plot.

Here is an example. Sometimes we want to use more or longer chains or fewer or shorter chains if we are doing a quick preliminary check before running longer chains later. The default value of n. So in the example below, we end up with only samples per chain rather than the you might have expected. We can also control the starting point for the chains.In R, the class factor is used for categorical variables.

A factor has a levels attribute with the names of the categories, in alphabetical order by default, and the values are stored as integers giving the level number.

I'll generate some simulated data for a logistic regression model as that generalises to a lot of our other models. We have four players with different degrees of skill and a continuous covariate which does nothing. I've used character strings for the player names and then for the levels of the player factor they appear in the summarywhich I think is much safer than using numbers for categories.

A factor can easily be converted to integers if necessary, as in the call to rbinom above. Note that the number of observations per category varies, something that happens often with real data.

Notice that we have coefficients for Bob, Chan and Dora, but not for Andy. The intercept refers to Andy's plays and the other coefficients give the difference between Andy and each of the other players. It isn't possible to have an intercept and a coefficient for each player, as they would be confounded: you could add any value you liked to the intercept provided you subtracted the same value from the player coefficients and you'd get exactly the same result.

To begin with, let's run a JAGS model with no covariates. In this case we need to estimate a single probability of success, p, and do not need the logit link. Here I'm using a Beta prior, which is the appropriate distribution for a probability, as it is restricted to the range of 0 to 1. Beta 1,1 is a uniform prior with little information, and no one is likely to question its choice, except to suggest a more informative prior.

n eff jags

Many people use Uniform 0,1 for a uniform prior instead of Beta 1,1 ; that's mathematically equivalent, but is not recognised as a probability by JAGS. If we have only one covariate and that covariate is categorical, the simplest strategy is to estimate a value for p for each category. We do not use the logit link, and dealing directly with p simplifies interpretation and discussion of priors.

Again I'm using a Beta 1,1 prior, which could easily be replaced by an informative beta prior, a different one for each player if you wanted. This is used as the index into the p vector so that the right p is used for each observation in the success vector. The posterior means are close to the actual proportion of successes in the data, though pulled somewhat towards 0. With more than one covariate we do need to use the logit link. There are several strategies, but with only one categorical covariate, we can keep it simple by using a different intercept for each category.

So we might be able to provide a sensible prior for probability of success. In the code below, I've specified a uniform prior, Beta 1,1for the intercepts on the probability scale, then converted to logit for use in the regression.

You could use an informative Beta prior for each player if you wished. These may not be appropriate for your reported analysis, but it is easy to see if the prior is constraining the posterior. The method above won't work if you have more than one categorical covariate. An alternative is to use the strategy adopted by default by glm : the model has an intercept which refers to one of the categories, and coefficients for the difference between this reference category and each of the others.

We adapt our code by adding the intercept, b0and setting the coefficient for the reference category to zero. But I have no intuitive feel for how you would choose priors for the differences on the logit scale among players.

The data list, JAGSdatais the same and we add b0 to the parameters in wanted. The output looks like this:. Notice that the effective sample sizes, n. The main reason for this is that the reference category, Andy, has relatively few observations, only 25 out of That means that it's difficult to estimate the intercept and hence difficult to estimate the other coefficients. We can improve things by making Bob, who has the most observations, the reference category. That could be done by changing the JAGS code set bPlay[2] but it's easier to change the data by releveling the player factor so that Bob comes first:.

Choosing a reference category can make interpretation of the output difficult, especially if there are several categorical covariates, each with its own reference category.I have been experiencing some problems with mixing and effective sample size running Weibull models in JAGS, especially in regard to the shape parameter and any covariates estimated as a function of the Weibull hazard.

Besides noticing this problem in my own data, I have also noticed it here in the mice data as well. I am not sure what could be causing this problem, but there seems to be high correlation among some parameters. Yes this is a known problem. Unfortunately the MICE example runs very slowly due to the poor mixing of the shape parameter of the Weibull distribution. The underlying problem here is the choice of parameterization.

The usual parameterization of the Weibull distribution e. In survival analysis this corresponds to the accelerated life model where the second parameter scale corresponds to the scaling of time.

However, the accelerated life model is not popular in biostatistics, where the proportional hazards model is ubiquitous in survival analysis.

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Hence the BUGS authors chose the alternate parameterization that corresponds to the proportional hazards model The Weibull distribution is unique in having both an accelerated life parameterization and a proportional hazards parameterization. The variables veh. It turns out that the proportional hazards parameterization is not a good one for Gibbs sampling when we try to update r and each element of mu[i] separately.

You can use the accelerated life parameterization with a parameter transformation. Instead of putting a prior on beta[i] directly, define it in terms of the shape parameter r and the log of the scale parameter, given a vague normal prior:. This does improve the mixing for the shape parameter considerably, and I don't get a message about low effective sample size. I have a couple of factors in the Weibull model that I am fitting to my data that I am using to predict survival probability up to a certain time.

I will see if I can incorporate these factors into this reparameterization to solve the mixing problem. Help Create Join Login. Operations Management. IT Management. Project Management.

Services Business VoIP. Resources Blog Articles Deals. Menu Help Create Join Login. Weibull model: problem with slow mixing and effective sample size. Forum: Open Discussion.

Creator: Daniel Eacker. Created: Updated: Daniel Eacker - Dear JAGS users, I have been experiencing some problems with mixing and effective sample size running Weibull models in JAGS, especially in regard to the shape parameter and any covariates estimated as a function of the Weibull hazard. Here is the mice data: sp. If you would like to refer to this comment somewhere else in this project, copy and paste the following link:.

Martyn Plummer - Oh no! Some styles failed to load. Sign Up No, Thank you.You can report issue about the content on this page here Want to share your content on R-bloggers? In this post I want to analyze a first order pharmocokinetcs problem: the data of study problem 9, chapter 3 of Rowland and Tozer Clinical pharmacokinetics and pharmacodynamics, 4th edition with Jags.

It is a surprising simple set of data, but still there is enough to play around with. The data is simple enough. This model has as feature that the non-informative priors are directly on the parameters which are in PK analysis important; distribution volume and clearance. Using a package The package PKfit does offer these calculations. It is also completely menu operated, hence no code in this blog part.

It does offer the possibility to specify error as shown here. Since I wanted to have some idea about the distribution of the parameters I have added this plot.

Want to share your content on R-bloggers? The numbers are slightly off compared to the book, but the expectation is that students use graph paper and a ruler. For each parameter, n. DIC is an estimate of expected predictive error lower deviance is better.

The results are fairly close to the first calculation, although the standard deviations are a bit larger. The question which is the better obviously depends on the expectations or knowledge on measurement error. The book states the data is adapted from a paper Chow et al.

I find classic regression to be a bit more convenient to help me with the structure of the error. Nonlinear regression model. The package PKfit does offer these calculations.

n eff jags

Time Observed Calculated Wt. Estimate Std. Residual standard error: 0. In hindsight the first Bayesian model is the one I prefer. To leave a comment for the author, please follow the link and comment on their blog: Wiekvoet. Never miss an update! Subscribe to R-bloggers to receive e-mails with the latest R posts. You will not see this message again.You can report issue about the content on this page here Want to share your content on R-bloggers?

In that period I have seen one example where JAGS could not get me decent samples in the sense of low Rhat and high number of effective samples but that was data which I could not blog about. Hence this post. It appears that Stan did not really do much better. What did appear is that results in this kind of difficult problem can vary depending on the inits and random samples used in the chain.

This probably means more samples helps, but that is not the topic of this post. In effect I expect most readers of this blog to know about both Stan and JAGS, but a few lines about them seem not amiss. Stan and JAGS can be used for the same kind of problems, but they are quite different.

Stan on the other hand, is a program where a model has clearly defined parts, where order of statements is of influence. Stan is compiled, which takes some time by itself. R is then used for pre-processing data, setting up the model and finally summarizing the samples. Stan is supposed to be more efficient, hence needing less samples to obtain a posterior result of similar quality.

In addition, JAGS has no compilation time. The plus of Stan though is highly organized model code. The model describes the number of shootings per state, hierarchically under regions.

n eff jags

This means there is a binomial probability of interest, the states, under beta distributed regions. The beta has uninformative priors. After some tweaking the models should be equivalent. This means that the JAGS model is slightly different from previous posts. The number of samples chosen is with burn-in for JAGS and with half burn-in for Stan.

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