Abstract
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!
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Von Der Linden, W., Preuss, R., Dose, V. (1999). The Prior-Predictive Value: A Paradigm of Nasty Multi-Dimensional Integrals. In: von der Linden, W., Dose, V., Fischer, R., Preuss, R. (eds) Maximum Entropy and Bayesian Methods Garching, Germany 1998. Fundamental Theories of Physics, vol 105. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4710-1_31
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DOI: https://doi.org/10.1007/978-94-011-4710-1_31
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