A crucial prerequisite to data fusion is data association: i.e., the specification of which data arise from the same source. The Bayesian approach to association pioneered by Mori and Chong is based on principled probability formulas, which thus provide re-liable confidence estimates for association hypotheses, in contrast to approaches that rely on costs which can only be heuristically transformed into probabilities. This paper extends the Bayesian approach in several ways. It presents a general derivation of association probability between any number of sensors for arbitrary data types, then derives specific results for kinematic and non-kinematic cases. The kinematic case includes bias and is novel in three ways. First, it is a proper Bayesian approach to bias which integrates over all bias hypotheses rather than selecting one. Second, it handles bias on an arbitrary number of sensors. Third, the formula is exact: previous treatments of even the unbiased case involve an integral approximation which is not needed here. The treatment of features allows for several complex phenomena, including feature behavior which depends on object type, and noisy and/or missing feature data. A rigorous verification procedure is used to demonstrate that the implementation of these formulas produces correct probabilities.