  Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for
estimating properties of complicated distributions. While their use has become
commonplace and there is a large literature on MCMC theory and practice, MCMC
users still have to contend with several challenges with each implementation of
the algorithm. These challenges include determining how to construct an
efficient algorithm, finding reasonable starting values, deciding whether the
sample-based estimates are accurate, and determining an appropriate length
(stopping rule) for the Markov chain. We describe an approach for resolving
these issues in a theoretically sound fashion in the context of spatial
generalized linear models, an important class of models that result in
challenging posterior distributions. Our approach combines analytical
approximations for constructing provably fast mixing MCMC algorithms, and takes
advantage of recent developments in MCMC theory. We apply our methods to real
data examples, and find that our MCMC algorithm is automated and efficient.
Furthermore, since starting values, rigorous error estimates and theoretically
justified stopping rules for the sampling algorithm are all easily obtained for
our examples, our MCMC-based estimation is practically as easy to perform as
Monte Carlo estimation based on independent and identically distributed draws.
