Unbiased Bayes for Big Data: Paths of Partial Posteriors

Understand

A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution.

• Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn from an approximate posterior.
• However, its feasibility is being challenged in the era of so called Big Data as all data needs to be processed in every iteration.
• Realising that such simulation is an unnecessarily hard problem if the goal is estimation, we construct a computationally scalable methodology that allows unbiased estimation of the required expectations -- without explicit simulation from the full posterior.