How to test the convergence in bugs model?

Question

I want to explain the convergence in a bugs model with the command plot(). An example of the output is in the follow figure

I don't sure that I can read this output well, thanks to everyone :)

Answer 1

Unfortunately, it does not look as if you can confirm convergence from the figure that you are showing (EDIT: There is at least some information, see below). The left hand side of the figure is just a caterpillar plot, which effectively just shows the 95% intervals of the distribution for each parameter.

Assessing convergence is a much more nuanced process, as there are multiple ways to decide if your model has converged. What you will want to determine is that your model has appropriately explored the parameter space for each parameter (through trace plots, traceplot function in the coda library), between and within chain variance (the gelman-rubin diagnostic, gelman.diag in the coda library), and auto-correlation in your chains (autocorr.plot in coda). There are a variety of other measures that others have suggested to assess if your model has converged, and looking through the rest of the coda package will illustrate this.

I highly suggest that you go through the WINBUGS tutorial in their user manual (link to pdf), it has a section that addresses checking model convergence. You want to ensure that the traceplots are well-mixed (look to tutorial to see what that means), that your Gelman Rubin diagnostic is < 1.10 for each parameter (general rule), and that your chains are not too correlated (this will reduce your effective sample size in your chains).

Good luck, and read up a bit on the subject, it will greatly benefit you if you are interested in Bayesian inference!

Edit

As @jacobsocolar pointed out, and I completely missed, the plots that are available in this question do at least have some information that indicates the model did converge. I did not see the R-hat plot on the right side of the left plot. These values should be less than 1.1 for each parameter if the model did indeed converge. Eyeballing the above plot does hint that the model converged, but this would be far easier to see if there was a vertical line at the 1.1 mark on the plot, which there is not.

Answer 2

Your output figure is indeed enough to (begin to) assess convergence, contra M_Fidino's answer. Next to the caterpillar plot, there is a plot of 'r-hat' values. These are the Gelman-Rubin statistic--the ratio of between-chain variance to within-chain variance, and they are all < 1.10 This is an encouraging first sign that the model has converged, assuming that the initial values were chosen to be nicely overdispersed. Otherwise, I agree with everything in M_Fidino's answer.