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We present a framework for information retrieval that combines document models and query models using a probabilistic ranking function based on Bayesian decision theory. The framework suggests an operational retrieval model that extends recent developments in the language modeling approach to information retrieval. A language model for each document is estimated, as well as a language model for each query, and the retrieval problem is cast in terms of risk minimization. The query language model can be exploited to model user preferences, the context of a query, synonomy and word senses. While recent work has incorporated word translation models for this purpose, we introduce a new method using Markov chains defined on a set of documents to estimate the query models. The Markov chain method has connections to algorithms from link analysis and social networks. The new approach is …