Markov chain Monte Carlo (MCMC) is a class of algorithms for sampling from probability distributions. In the end, given a parametric model explaining the data, MCMC could also be used for parameter estimation, in which case I wonder what the different options for processing MCMC samples are. For monomodal distributions for instance, I can think of averaging the $n$ last samples of a run, averaging the last sample of different MCMC runs. What are the options for estimating posterior of parameters?


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Are you looking for techniques, or might you be looking for packages, such as R's coda?

As you note, you'd ignore the first N data points in each chain, which are called "burn-in". How large N is depends on how quickly your model converged and there are a whole host of methods that you can use to give an idea of convergence. (Some of these methods require multiple chains.) If you're not sure your run has become well-mixed (converged), any calculations you do with your results will be meaningless.

I would run M chains, drop the first N points from each chain, then pool the rest of the points together. Then do a density plot to see what kind of distribution you have. As you suggest, you can take the mean value. (Especially if you can see that the distribution is reasonably normal.)

I wouldn't average the last sample from different runs.


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