Computations involved in Bayesian approach to practical model selection problems are usually very difficult. Computa tional simplifications are sometimes possible, but are not generally applicable. There is a large literature available on a methodology based on information theory called Minimum Description Length (MDL). It is described here how many of these techniques are either directly Bayesian in nature, or are very good objective approximations to Bayesian solu tions. First, connections between the Bayesian approach and MDL are theoretically explored; thereafter a few illustra tions are provided to describe how MDL can give useful computational simplifications.
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