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. 2008 Jun;64(2):595-602.
doi: 10.1111/j.1541-0420.2007.00888.x. Epub 2007 Aug 30.

Determining the effective sample size of a parametric prior

Satoshi Morita  1 , Peter F Thall, Peter Müller
Affiliations

Determining the effective sample size of a parametric prior

Satoshi Morita et al. Biometrics. 2008 Jun.

Abstract

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.

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Figures

Figure 1
Figure 1
Plot of δ(m, θ̄, p, q0) against m for the beta/binomial model with θ̃ = (α̃, β̃) = (3, 7).
See this image and copyright information in PMC

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