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Bayesian likelihood-free inference, which is used to perform Bayesianinference when the likelihood is intractable, enjoys an increasing number ofimportant scientific applications. However, many aspects of a Bayesian analysisbecome more challenging in the likelihood-free setting. One example of this isprior-data conflict checking, where the goal is to assess whether theinformation in the data and the prior are inconsistent. Conflicts of this kindare important to detect, since they may reveal problems in an investigator'sunderstanding of what are relevant values of the parameters, and can result insensitivity of Bayesian inferences to the prior. Here we consider methods forprior-data conflict checking which are applicable regardless of whether thelikelihood is tractable or not. In constructing our checks, we considerchecking statistics based on prior-to-posterior Kullback-Leibler divergences.The checks are implemented using mixture approximations to the posteriordistribution and closed-form approximations to Kullback-Leibler divergences formixtures, which make Monte Carlo approximation of reference distributions forcalibration computationally feasible. When prior-data conflicts occur, it isuseful to consider weakly informative prior specifications in alternativeanalyses as part of a sensitivity analysis. As a main application of ourmethodology, we develop a technique for searching for weakly informative priorsin likelihood-free inference, where the notion of a weakly informative prior isformalized using prior-data conflict checks. The methods are demonstrated inthree examples.

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