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December 2019 Calibration Procedures for Approximate Bayesian Credible Sets
Jeong Eun Lee, Geoff K. Nicholls, Robin J. Ryder
Bayesian Anal. 14(4): 1245-1269 (December 2019). DOI: 10.1214/19-BA1175

Abstract

We develop and apply two calibration procedures for checking the coverage of approximate Bayesian credible sets, including intervals estimated using Monte Carlo methods. The user has an ideal prior and likelihood, but generates a credible set for an approximate posterior based on some approximate prior and likelihood. We estimate the realised posterior coverage achieved by the approximate credible set. This is the coverage of the unknown “true” parameter if the data are a realisation of the user’s ideal observation model conditioned on the parameter, and the parameter is a draw from the user’s ideal prior. In one approach we estimate the posterior coverage at the data by making a semi-parametric logistic regression of binary coverage outcomes on simulated data against summary statistics evaluated on simulated data. In another we use Importance Sampling from the approximate posterior, windowing simulated data to fall close to the observed data. We illustrate our methods on four examples.

Citation

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Jeong Eun Lee. Geoff K. Nicholls. Robin J. Ryder. "Calibration Procedures for Approximate Bayesian Credible Sets." Bayesian Anal. 14 (4) 1245 - 1269, December 2019. https://doi.org/10.1214/19-BA1175

Information

Published: December 2019
First available in Project Euclid: 3 October 2019

zbMATH: 07159875
MathSciNet: MR4044852
Digital Object Identifier: 10.1214/19-BA1175

Subjects:
Primary: 62F15, 65C05, 68W25

JOURNAL ARTICLE
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Vol.14 • No. 4 • December 2019
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