Bayes Reading Group: Nicolas Chopin (ENSAE, polytechnique Paris)

Discussion Lead: Nicolas Chopin (ENSAE, polytechnique Paris)

Topic: Waste-free Sequential Monte Carlo (joint work with Hai-Dang Dau)

Abstract: A standard way to move particles in a SMC sampler is to apply several

steps of a MCMC (Markov chain Monte Carlo) kernel. Unfortunately, it
is not clear how many steps need to be performed for optimal
performance. In addition, the output of the intermediate steps are
discarded and thus wasted somehow. We propose a new, waste-free SMC
algorithm which uses the outputs of all these intermediate MCMC steps
as particles. We establish that its output is consistent and
asymptotically normal. We use the expression of the asymptotic
variance to develop various insights on how to implement the algorithm
in practice. We develop in particular a method to estimate, from a
single run of the algorithm, the asymptotic variance of any particle
estimate. We show empirically, through a range of numerical examples,
that waste-free SMC tends to outperform standard SMC samplers, and
especially so in situations where the mixing of the considered MCMC
kernels decreases across iterations (as in tempering or rare event
problems)