Statistics and Its Interface

Volume 16 (2023)

Number 3

Weakly informative priors and prior-data conflict checking for likelihood-free inference

Pages: 445 – 457



Atlanta Chakraborty (Institute of Operations Research and Analytics, National University of Singapore)

David J. Nott (Institute of Operations Research and Analytics, National University of Singapore; and Department of Statistics and Data Science, National University of Singapore)

Michael Evans (Department of Statistics, University of Toronto, Ontario, Canada)


Bayesian likelihood-free inference, which is used to perform Bayesian inference when the likelihood is intractable, enjoys an increasing number of important scientific applications. However, many aspects of a Bayesian analysis become more challenging in the likelihood-free setting. One example of this is prior-data conflict checking, where the goal is to assess whether the information in the data and the prior are inconsistent. Conflicts of this kind are important to detect, since they may reveal problems in an investigator’s understanding of what are relevant values of the parameters, and can result in sensitivity of Bayesian inferences to the prior. Here we consider methods for prior-data conflict checking which are applicable regardless of whether the likelihood is tractable or not. In constructing our checks, we consider checking statistics based on prior-to-posterior Kullback–Leibler divergences. The checks are implemented using mixture approximations to the posterior distribution and closed-form approximations to Kullback–Leibler divergences for mixtures, which make Monte Carlo approximation of reference distributions for calibration computationally feasible. When prior-data conflicts occur, it is useful to consider weakly informative prior specifications in alternative analyses as part of a sensitivity analysis. As a main application of our methodology, we develop a technique for searching for weakly informative priors in likelihood-free inference, where the notion of a weakly informative prior is formalized using prior-data conflict checks. The methods are demonstrated in three examples.


approximate Bayesian computation, Bayesian inference, mixture model, prior-data conflict

2010 Mathematics Subject Classification

Primary 62C10, 62F15. Secondary 65C05.

Received 4 August 2021

Accepted 26 March 2022

Published 14 April 2023