A new, general approach is described for approximate inference in first-order probabilistic languages, using Markov chain Monte Carlo (MCMC) techniques in the space of concrete possible worlds underlying any given knowledge base. The simplicity of the approach and its lazy construction of possible worlds make it possible to consider quite expressive languages. In particular, we consider two extensions to the basic relational probability models (RPMs) defined by Koller and Pfeffer, both of which have caused difficulties for exact algorithms. The first extension deals with uncertainty about relations among objects, where MCMC samples over relational structures. The second extension deals with uncertainty about the identity of individuals, where MCMC samples over sets of equivalence classes of objects. In both cases, we identify types of probability distributions that allow local decomposition of inference while encoding possible domains in a plausible way. We apply our algorithms to simple examples and show that the MCMC approach scales well.
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