  Markov Chain Monte Carlo (MCMC) methods for sampling probability density
functions (combined with abundant computational resources) have transformed the
sciences, especially in performing probabilistic inferences, or fitting models
to data. In this primarily pedagogical contribution, we give a brief overview
of the most basic MCMC method and some practical advice for the use of MCMC in
real inference problems. We give advice on method choice, tuning for
performance, methods for initialization, tests of convergence, troubleshooting,
and use of the chain output to produce or report parameter estimates with
associated uncertainties. We argue that autocorrelation time is the most
important test for convergence, as it directly connects to the uncertainty on
the sampling estimate of any quantity of interest. We emphasize that sampling
is a method for doing integrals; this guides our thinking about how MCMC output
is best used.
