Title: Unbiased and consistent nested sampling via sequential Monte Carlo
Authors: Robert Salomone - University of New South Wales (Australia)
Leah South - Lancaster University (United Kingdom) [presenting]
Adam Johansen - University of Warwick (United Kingdom)
Christopher Drovandi - Queensland University of Technology (Australia)
Dirk Kroese - University of Queensland (Australia)
Abstract: A new class of sequential Monte Carlo methods is introduced which is called Nested Sampling via Sequential Monte Carlo (NS-SMC), and which reframes the Nested Sampling method of Skilling in terms of sequential Monte Carlo techniques. This new framework allows one to obtain provably consistent estimates of the marginal likelihood and posterior inferences when Markov chain Monte Carlo (MCMC) is used to produce new samples. An additional benefit is that marginal likelihood estimates are also unbiased. For applications of NS--SMC, we give advice on tuning MCMC kernels in an automated manner via a preliminary pilot run, and present a new method for appropriately choosing the number of MCMC repeats at each iteration. A numerical study is conducted where the performance of NS--SMC and temperature--annealed SMC is compared on several challenging and realistic problems.