Conclusion

We have discussed the problem of producing a special kind of epitome of a posterior distribution with properties that we call Bayesian Posterior Comprehension (BPC). The epitome breaks down a posterior distribution into a small weighted subset of models from the parameter space. Such a set can be used as point estimates, for human comprehension and for fast approximation of posterior expectations. The Minimum Message Length (MML) instantaneous codebook corresponds to an epitome with BPC properties. A general methodology called Message from Monte Carlo, for constructing instantaneous MML codebooks, was extended and demonstrated on several problems with positive results.

2003-04-23