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Bayesian Posterior Comprehension via Message from Monte Carlo

Summary: Bayesian Posterior Comprehension via
Message from Monte Carlo
Leigh J. Fitzgibbon, David L. Dowe and Lloyd Allison
School of Computer Science and Software Engineering
Monash University, Clayton, VIC 3800, Australia
We discuss the problem of producing an epitome, or brief summary, of a Bayesian
posterior distribution - and then investigate a general solution based on the Mini-
mum Message Length (MML) principle. Clearly, the optimal criterion for choosing
such an epitome is determined by the epitome's intended use. The interesting gen-
eral case is where this use is unknown since, in order to be practical, the choice of
epitome criterion becomes subjective. We identify a number of desirable properties
that an epitome could have - facilitation of point estimation, human comprehension,
and fast approximation of posterior expectations. We call these the properties of
Bayesian Posterior Comprehension and show that the Minimum Message Length
principle can be viewed as an epitome criterion that produces epitomes having
these properties. We then present and extend Message from Monte Carlo as a
means for constructing instantaneous Minimum Message Length codebooks (and
epitomes) using Markov Chain Monte Carlo methods. The Message from Monte


Source: Allison, Lloyd - Caulfield School of Information Technology, Monash University


Collections: Computer Technologies and Information Sciences