Abstract

Co-authors: Hongsheng Dai (Essex), Paul Fearnhead (Lancaster), Adam Johansen (Warwick), Divakar Kumar (Warwick), Gareth Roberts (Warwick)

This talk will introduce novel methodologies for exploring posterior distributions by modifying methodology for exactly (without error) simulating diffusion sample paths. The methodologies discussed have found particular applicability to “Big Data” problems. We begin by presenting the Scalable Langevin Exact Algorithm (ScaLE) and recent methodological extensions (including Re-ScaLE, which avoids the need for particle approximation in ScaLE), which has remarkably good scalability properties as the size of the data set increases (it has sub-linear cost, and potentially no cost as a function of data size). ScaLE has particular applicability in the “single-core” big data setting – in which inference is conducted on a single computer. In the second half of the talk we will present methodology to exactly recombine inferences on separate data sets computed on separate cores – an exact version of “divide and conquer”. As such this approach has particu lar applicability in the “multi-core” big data setting. We conclude by commenting on future work on the confluence of these approaches. Joint work with Hongsheng Dai, Paul Fearnhead, Adam Johansen, Divakar Kumar, Gareth Roberts.