Abstract: Bayesian inference has many attractive features, but a major challenge is its potentially very high computational cost. While sampling from the prior distribution is often straightforward, the most expensive part is typically conditioning on the data. In many problems, a single data set data may not be informative enough to enable reliable inference for a given quantity of interest. This can be difficult to assess in advance and may require a considerable amount of computation to discover, resulting in a weakly informative posterior distribution “gone to waste”. On the other hand, borrowing strength across multiple related data sets using a hierarchical model may for very costly models be computationally infeasible.

As an alternative approach to traditional hierarchical models, we develop in this work a framework which reuses and combines posterior distributions computed on individual data sets to achieve post-hoc borrowing of strength, without the need to re-do expensive computations on the data. As a by-product, we also obtain a notion of meta-analysis for posterior distributions. By adopting the view that posterior distributions are beliefs which reflect the uncertainty about the value of some quantity, we formulate our approach as Bayesian inference with uncertain observations. We further show that this formulation is closely related to belief propagation. Finally, we illustrate the framework with post-hoc analyses of likelihood-free Bayesian inferences.

Speaker: Paul Blomstedt

Affiliation: Department of Computer Science, Aalto University

Place of Seminar: Aalto University