  Testing between hypotheses, when independent sampling is possible, is a well
developed subject. In this paper, we propose hypothesis tests that are
applicable when the samples are obtained using Markov chain Monte Carlo. These
tests are useful when one is interested in deciding whether the expected value
of a certain quantity is above or below a given threshold. We show
non-asymptotic error bounds and bounds on the expected number of samples for
three types of tests, a fixed sample size test, a sequential test with
indifference region, and a sequential test without indifference region. Our
tests can lead to significant savings in sample size. We illustrate our results
on an example of Bayesian parameter inference involving an ODE model of a
biochemical pathway.
