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June 2006 Closed form expressions for Bayesian sample size
B. Clarke, Ao Yuan
Ann. Statist. 34(3): 1293-1330 (June 2006). DOI: 10.1214/009053606000000308


Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the data. Thus, when a sample size criterion is formalized in terms of a functional of the posterior, its value is a random variable. Generally, such functionals have means under the true distribution.

We give asymptotic expressions for the expected value, under a fixed parameter, for certain types of functionals of the posterior density in a Bayesian analysis. The generality of our treatment permits us to choose functionals that encapsulate a variety of inference criteria and large ranges of error bounds. Consequently, we get simple inequalities which can be solved to give minimal sample sizes needed for various estimation goals. In several parametric examples, we verify that our asymptotic bounds give good approximations to the expected values of the functionals they approximate. Also, our numerical computations suggest our treatment gives reasonable results.


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B. Clarke. Ao Yuan. "Closed form expressions for Bayesian sample size." Ann. Statist. 34 (3) 1293 - 1330, June 2006.


Published: June 2006
First available in Project Euclid: 10 July 2006

zbMATH: 1113.62029
MathSciNet: MR2278359
Digital Object Identifier: 10.1214/009053606000000308

Primary: 62F15
Secondary: 62F12

Keywords: asymptotic , Bayesian inference , Edgeworth expansion , posterior distribution , sample size

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 3 • June 2006
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