  Tasks such as record linkage and multi-target tracking, which involve
reconstructing the set of objects that underlie some observed data, are
particularly challenging for probabilistic inference. Recent work has achieved
efficient and accurate inference on such problems using Markov chain Monte
Carlo (MCMC) techniques with customized proposal distributions. Currently,
implementing such a system requires coding MCMC state representations and
acceptance probability calculations that are specific to a particular
application. An alternative approach, which we pursue in this paper, is to use
a general-purpose probabilistic modeling language (such as BLOG) and a generic
Metropolis-Hastings MCMC algorithm that supports user-supplied proposal
distributions. Our algorithm gains flexibility by using MCMC states that are
only partial descriptions of possible worlds; we provide conditions under which
MCMC over partial worlds yields correct answers to queries. We also show how to
use a context-specific Bayes net to identify the factors in the acceptance
probability that need to be computed for a given proposed move. Experimental
results on a citation matching task show that our general-purpose MCMC engine
compares favorably with an application-specific system.
