10.7 Convergence
Theoretically, MCMC methods are guaranteed to converge once we take infinite samples. In practice, we need to check that we have reasonable finite samples. Usually, we say the sampler has converged once we have collected evidence showing that samples are stable in some sense. A simple test to do is to run the same MCMC simulation multiple times and check whether we get the same result every time. This is the reason why PyMC runs more by default than on chain. For modern computers, this is virtually free as we have multiple cores. Also, they do not create any waste, as we can combine samples from different chains to compute summaries, plots, etc.
There are many ways to check that different chains are practically equivalent, both visually and with formal tests. We are not going to get too technical here; we are just going to show a few examples and hope they are enough for you to develop an intuition for interpreting diagnostics.
10.7.1 Trace plot
One way to check...
