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Recent efforts in data cleaning of structured data have focused exclusively on problems like data deduplication, record matching, and data standardization; none of the approaches addressing these problems focus on fixing incorrect attribute values in tuples. Correcting values in tuples is typically performed by a minimum cost repair of tuples that violate static constraints like Conditional Functional Dependencies (which have to be provided by domain experts or learned from a clean sample of the database). In this article, we provide a method for correcting individual attribute values in a structured database using a Bayesian generative model and a statistical error model learned from the noisy database directly. We thus avoid the necessity for a domain expert or clean master data. We also show how to efficiently perform consistent query answering using this model over a dirty database, in case write permissions to the database are unavailable. We evaluate our methods over both synthetic and real data.