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Determining the Effective Sample Size of a Parametric Prior
Author(s) -
Morita Satoshi,
Thall Peter F.,
Müller Peter
Publication year - 2008
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2007.00888.x
Subject(s) - sample size determination , range (aeronautics) , parametric statistics , prior probability , monte carlo method , logarithm , bayesian probability , computer science , mathematics , sample (material) , curvature , posterior probability , algorithm , mathematical optimization , statistical physics , statistics , mathematical analysis , geometry , materials science , chemistry , chromatography , composite material , physics
Summary We present a definition for the effective sample size of a parametric prior distribution in a Bayesian model, and propose methods for computing the effective sample size in a variety of settings. Our approach first constructs a prior chosen to be vague in a suitable sense, and updates this prior to obtain a sequence of posteriors corresponding to each of a range of sample sizes. We then compute a distance between each posterior and the parametric prior, defined in terms of the curvature of the logarithm of each distribution, and the posterior minimizing the distance defines the effective sample size of the prior. For cases where the distance cannot be computed analytically, we provide a numerical approximation based on Monte Carlo simulation. We provide general guidelines for application, illustrate the method in several standard cases where the answer seems obvious, and then apply it to some nonstandard settings.