BAYESIAN LIKELIHOOD-FREE INFERENCE

Abstract

Likelihood-free inference approaches are used when the likelihood is intractable or unavailable in closed form.They are challenging to implement when the model parameter is high-dimensional. These situations arise in a variety of real-world applications ranging from genetics to financial modeling, thus making it crucial to address these challenges. As the first contribution of the thesis, we consider a post-processing adjustment for likelihood-free inference using an optimization based approach. The essence of the approach is to combine estimates from many low- dimensional problems to improve the particle estimate of the posterior in the original high-dimensional problem. Secondly, we develop some new methods for assessing whether the information in the data and the prior are consistent or not in Bayesian inference. We also consider specifying a “weakly-informative” prior for likelihood-free inferences, in situations where a prior-data conflict occurs. Finally, we consider “cutting feedback” approaches which aim to modify Bayesian inference for a model consisting of a number of coupled modules and with a misspecification in any of the modules.