Gather around so we can talk briefly about assessing your MCMC samples.

As you may know, MCMC sampling is often used in Bayesian statistics. However, you can use MCMC to approximate any "target" distribution, not just a posterior distribution.

(1/big number?)

When you're doing MCMC, an important question is "when do we stop sampling?" In other words, what "Monte Carlo" sample size is big enough?

Note: The Monte Carlo sample size is the number of MCMC samples or ordinary Monte Carlo samples (OMC is just dependent draws). (2/)

There are a couple questions to ask when you look at your MCMC samples:
1. Have we started sampling from the target distribution?
2. Do we have enough samples to accurately approximate the target distribution?

(3/)

You may have heard of "burn in," which addresses the first question. The basic idea: it takes awhile for the sampling distribution to converge to the target distribution.

Some Bayesians throw away the first few samples while others retain all the samples. (4/)

Argument for throwing them out: they were taken during the "burn in" period (the time needed to converge to the target). This will oversample (and thus overemphasize) part of the target distribution. (eg disproportionately many samples in the lower tail would pull mean down) (5/)

There are a couple questions to ask when you look at your MCMC samples:
1. Have we started sampling from the target distribution?
2. Do we have enough samples to accurately approximate the target distribution? (3/)