At the heart of Bayesian model comparison lies the so-called prior-predictive value. In the important class of Quantified-MaxEnt applications analytic approximations are routinely used which often give rise to noise-fitting and ringing. We present an improved analytic expression which overcomes these shortcomings. In most interesting real-world problems, however, standard approximations and straight forward application of Markov-Chain Monte Carlo are hampered by the complicated structure of the likelihood in parameter space. At the Maxent workshop 1997 in Boise John Skilling suggested to employ a formalism, borrowed from Statistical physics, to compute the prior-predictive value. We have scrutinized his suggestion: IT WORKS!
|Title of host publication||Maximum Entropy and Bayesian Methods Garching, Germany 1998|
|Editors||Wolfgang von der Linden, Volker Dose, Rainer Fischer, Roland Preuss|
|Number of pages||8|
|ISBN (Print)||978-94-010-5982-4 978-94-011-4710-1|
|Publication status||Published - 1999|
|Name||Fundamental Theories of Physics|
- Artificial Intelligence (incl. Robotics), Bayes factor, Coding and Information Theory, Discrete Mathematics in Computer Science, MCMC, model comparison, Prior-predictive value, Probability Theory and Stochastic Processes, Statistics, general