The Annals of Statistics

Closed form expressions for Bayesian sample size

B. Clarke and Ao Yuan

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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.

Article information

Ann. Statist., Volume 34, Number 3 (2006), 1293-1330.

First available in Project Euclid: 10 July 2006

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15: Bayesian inference
Secondary: 62F12: Asymptotic properties of estimators

Sample size Bayesian inference Edgeworth expansion asymptotic posterior distribution


Clarke, B.; Yuan, Ao. Closed form expressions for Bayesian sample size. Ann. Statist. 34 (2006), no. 3, 1293--1330. doi:10.1214/009053606000000308.

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