Overall Objective Priors

Abstract

In multi-parameter models, reference priors typically depend on the parameter or quantity of interest, and it is well known that this is necessary to produce objective posterior distributions with optimal properties. There are, however, many situations where one is simultaneously interested in all the parameters of the model or, more realistically, in functions of them that include aspects such as prediction, and it would then be useful to have a single objective prior that could safely be used to produce reasonable posterior inferences for all the quantities of interest. In this paper, we consider three methods for selecting a single objective prior and study, in a variety of problems including the multinomial problem, whether or not the resulting prior is a reasonable overall prior.

Published at http://dx.doi.org/10.1214/14-BA915 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/)

References in corpus (5)

• Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
• The formal definition of reference priors
• Objective Priors: An Introduction for Frequentists
• Objective priors for the bivariate normal model
• Posterior propriety and admissibility of hyperpriors in normal hierarchical models

Cited by in corpus (23)

• On an inferential model construction using generalized associations
• Objective Bayesian inference with proper scoring rules
• Penalising model component complexity: A principled, practical approach to constructing priors
• Bayesian Estimates of Astronomical Time Delays between Gravitationally Lensed Stochastic Light Curves
• Bayesian Neural Networks for Fast SUSY Predictions
• Automated Learning of Interpretable Models with Quantified Uncertainty
• A new Bayesian regression model for counts in medicine
• Objective Bayesian analysis of "on/off" measurements
• Objective Bayesian Analysis of a Cokriging Model for Hierarchical Multifidelity Codes
• Bridging Bayesian, frequentist and fiducial (BFF) inferences using confidence distribution
• Models of radial velocities and transit light curves
• Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging
• Organic fiducial inference
• Bayesian Adaptive Trials for Social Policy
• Maximum Probability Theorem: A Framework for Probabilistic Learning
• Integrated organic inference (IOI): A reconciliation of statistical paradigms
• Bayesian Cumulative Probability Models for Continuous and Mixed Outcomes
• Objective Bayesian Inference for Repairable System Subject to Competing Risks
• Partial exchangeability of the prior via shuffling
• Learning Approximately Objective Priors
• A Geometric Perspective on Bayesian and Generalized Fiducial Inference
• An adaptive kriging method for solving nonlinear inverse statistical problems
• Objective Bayesian analysis of counting experiments with correlated sources of background