  The Eigenvector Method for Umbrella Sampling (EMUS) belongs to a popular
class of methods in statistical mechanics which adapt the principle of
stratified survey sampling to the computation of free energies. We develop a
detailed theoretical analysis of EMUS. Based on this analysis, we show that
EMUS is an efficient general method for computing averages over arbitrary
target distributions. In particular, we show that EMUS can be dramatically more
efficient than direct MCMC when the target distribution is multimodal or when
the goal is to compute tail probabilities. To illustrate these theoretical
results, we present a tutorial application of the method to a problem from
Bayesian statistics.
