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I am a new user to WINBUGS. I am running a model with 2 chains. When my model has finished running I have the following posterior density plot of my parameter:

enter image description here

The plot only shows one distribution (i.e., one line). Since I used 2 MCMC chains, did WINBUGS just take the mean values and produced one single distribution? Also how can I get the 2 individual distributions for each chain. For example, something like this, where the red line is Chain #1 and blue line is Chain #2:

enter image description here

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The idea with MCMC is that you run the chains until well after they have converged to the same distribution. Then discard samples from before convergence. At which point you can't distinguish between samples from the two chains. So you throw all samples in one big pot.

If you still want to see how far apart the chains are, you could look at the convergence diagnostics.

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  • $\begingroup$ let's say we have a parameter K and we use the median of its estimated posterior distribution as K's point estimate. This is done with 2 chains in WINBUGS, so we have 2 posterior dist. for K. These 2 posterior dist. are very similar but numerically not exactly equivalent. What does WINBUGS use internally to give us the median point estimate of K? Is it the average of the 2 posterior distributions? $\endgroup$ – user121 Aug 15 '18 at 16:21
  • $\begingroup$ What you get with MCMC is samples from a distribution. After the chains have converged, you shouldn't be able to figure out which chain they came from just by looking at the values of the samples. I don't know what winbugs does internally for sure, but I'd bet a money it just pools the samples and calculates the statistic on the pool. $\endgroup$ – conjectures Aug 16 '18 at 8:47

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