Bayesian Analysis

Prior Effective Sample Size in Conditionally Independent Hierarchical Models

Satoshi Morita, Peter F. Thall, and Peter Müller

Full-text: Open access

Abstract

Prior effective sample size (ESS) of a Bayesian parametric model was defined by Morita, et al. (2008, Biometrics, 64, 595-602). Starting with an ɛ-information prior defined to have the same means and correlations as the prior but to be vague in a suitable sense, the ESS is the required sample size to obtain a hypothetical posterior very close to the prior. In this paper, we present two alternative definitions for the prior ESS that are suitable for a conditionally independent hierarchical model. The two definitions focus on either the first level prior or second level prior. The proposed methods are applied to important examples to verify that each of the two types of prior ESS matches the intuitively obvious answer where it exists. We illustrate the method with applications to several motivating examples, including a single-arm clinical trial to evaluate treatment response probabilities across different disease subtypes, a dose-finding trial based on toxicity in this setting, and a multicenter randomized trial of treatments for affective disorders.

Article information

Source
Bayesian Anal. Volume 7, Number 3 (2012), 591-614.

Dates
First available in Project Euclid: 28 August 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1346158777

Digital Object Identifier
doi:10.1214/12-BA720

Mathematical Reviews number (MathSciNet)
MR2981629

Zentralblatt MATH identifier
1330.62147

Keywords
Bayesian hierarchical model Conditionally independent hierarchical model Computationally intensive methods Effective sample size Epsilon-information prior

Citation

Morita, Satoshi; Thall, Peter F.; Müller, Peter. Prior Effective Sample Size in Conditionally Independent Hierarchical Models. Bayesian Anal. 7 (2012), no. 3, 591--614. doi:10.1214/12-BA720. https://projecteuclid.org/euclid.ba/1346158777


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