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On Some Problems in Bayesian Model Choice in Hydrology

L. R. Pericchi and I. Rodriguez-Iturbe
Journal of the Royal Statistical Society. Series D (The Statistician)
Vol. 32, No. 1/2, Proceedings of the 1982 I.O.S. Annual Conference on Practical Bayesian Statistics (Mar. - Jun., 1983), pp. 273-278
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2987625
Stable URL: http://www.jstor.org/stable/2987625
Page Count: 6
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On Some Problems in Bayesian Model Choice in Hydrology
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Abstract

Described is the Standard Bayesian Procedure (SBP) for model choice between K competing models as used in standard practice. The first problem which is discussed is the tendency of the SBP to yield lower posterior model probabilities for some correct sampling models, for low to moderate sample sizes, even when both models have equal numbers of adjustable parameters. This problem is exhibited in a case of model selection for hydrological extremes between Normal and Lognormal models. It is claimed in Pericchi (1981b), that the reason behind the problem is that the SBP tends to inflate the posterior probability of the model that has the smallest expected increase in information about its parameters. He then proposed to modify the SBP using an information criterion, that we adopt here. Finally, the discrimination between realistic models for hydrological extremes as Log-Pearson III, Gumbel, etc., is discussed. Previous approaches to incorporate prior information are analysed, and a tentative alternative procedure is described.

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