Abstract
Computations involved in Bayesian approach to practical model selection problems are usually very difficult. Computational 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 solutions. First, connections between the Bayesian approach and MDL are theoretically explored; thereafter a few illustrations are provided to describe how MDL can give useful computational simplifications.
Highlights
Bayesian computations can be difficult, in particular those in model selection problems
Computations involved in Bayesian approach to practical model selection problems are usually very difficult
There is a large literature available on a methodology based on information theory called Minimum Description Length (MDL)
Summary
Bayesian computations can be difficult, in particular those in model selection problems. We discuss some aspects of Minimum Description Length (MDL) methods with this point of view. Another important reason for exploring these methods is that there is a substantial literature on this topic available in engineering and computer science with potential applications in statistics. Explore certain other aspects of MDL such as the “Normalized Maximum Likelihood (NML)” introduced by [4] which do not seem to be in the spirit of the Bayesian approach that we have taken here. It is shown how a different version of MDL can provide such an approximation. MDL approach to step-wise regression in Section 5.1, wavelet thresholding in 5.2 and a change-point problem in 5.3 are described
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