Brazilian Journal of Probability and Statistics

Subjective Bayesian testing using calibrated prior probabilities

Dan J. Spitzner

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Abstract

This article proposes a calibration scheme for Bayesian testing that coordinates analytically-derived statistical performance considerations with expert opinion. In other words, the scheme is effective and meaningful for incorporating objective elements into subjective Bayesian inference. It explores a novel role for default priors as anchors for calibration rather than substitutes for prior knowledge. Ideas are developed for use with multiplicity adjustments in multiple-model contexts, and to address the issue of prior sensitivity of Bayes factors. Along the way, the performance properties of an existing multiplicity adjustment related to the Poisson distribution are clarified theoretically. Connections of the overall calibration scheme to the Schwarz criterion are also explored. The proposed framework is examined and illustrated on a number of existing data sets related to problems in clinical trials, forensic pattern matching, and log-linear models methodology.

Article information

Source
Braz. J. Probab. Stat., Volume 33, Number 4 (2019), 861-893.

Dates
Received: March 2018
Accepted: November 2018
First available in Project Euclid: 26 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1566806436

Digital Object Identifier
doi:10.1214/18-BJPS424

Mathematical Reviews number (MathSciNet)
MR3996320

Keywords
Subjective Bayes Bayesian testing Bayes factors default priors high-dimensional statistics multiplicity variable selection Schwarz criterion

Citation

Spitzner, Dan J. Subjective Bayesian testing using calibrated prior probabilities. Braz. J. Probab. Stat. 33 (2019), no. 4, 861--893. doi:10.1214/18-BJPS424. https://projecteuclid.org/euclid.bjps/1566806436


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