  We cast the problem of combinatorial auction design in a Bayesian framework
in order to incorporate prior information into the auction process and minimize
the number of rounds to convergence. We first develop a generative model of
agent valuations and market prices such that clearing prices become maximum a
posteriori estimates given observed agent valuations. This generative model
then forms the basis of an auction process which alternates between refining
estimates of agent valuations and computing candidate clearing prices. We
provide an implementation of the auction using assumed density filtering to
estimate valuations and expectation maximization to compute prices. An
empirical evaluation over a range of valuation domains demonstrates that our
Bayesian auction mechanism is highly competitive against the combinatorial
clock auction in terms of rounds to convergence, even under the most favorable
choices of price increment for this baseline.
