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Abstract:
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Bayesian inference is known to provide misleading uncertainty estimation when the considered model is misspecified. This talk will explore alternatives to standard Bayesian inference under model misspecification, based on extensions of the Weighted Likelihood Bootstrap (Newton & Raftery, 1994).
We will talk about Posterior Bootstrap, which is an extension of Weighted Likelihood Bootstrap, allowing the user to properly incorporate the prior. We consider two approaches to incorporating prior knowledge: the first is based on penalization of the Weighted Likelihood Bootstrap objective function, and the second uses pseudo-samples from the prior predictive distribution. We will see how Edgeworth expansions can be used to understand the impact of the prior and guide the choice of hyperparameters. We will also discuss extending Posterior Bootstrap to hierarchical models, and illustrate it with real-data examples.
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