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Bayesian posterior comprehension via message from monte carlo (2003).
| Content Provider | CiteSeerX |
|---|---|
| Author | Dowe, David L. Allison, Lloyd Fitzgibbon, Leigh J. |
| Abstract | 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 Minimum Message Length (MML) principle. Clearly, the optimal criterion for choosing such an epitome is determined by the epitome's intended use. The interesting general 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 Carlo methodology is illustrated for binary regression, generalised linear model, and multiple change-point problems. |
| File Format | |
| Publisher Date | 2003-01-01 |
| Access Restriction | Open |
| Subject Keyword | Bayesian Posterior Comprehension Point Estimation Interesting General Case Markov Chain Monte Carlo Method Fast Approximation Linear Model Monte Carlo Posterior Expectation Minimum Message Length Bayesian Posterior Distribution Desirable Property Binary Regression Monte Carlo Methodology Multiple Change-point Problem Instantaneous Minimum Message Length Codebooks Human Comprehension General Solution Optimal Criterion Epitome Criterion Minimum Message Length Principle Extend Message |
| Content Type | Text |
