Efficient Use of Derivative Information within SMC Methods for Static Bayesian Models

Sequential Monte Carlo (SMC) is a powerful method for sampling from the posterior distribution of static Bayesian models and estimating the evidence for model choice. SMC applies reweighting, resampling and mutation steps to transition a population of particles through a sequence of distributions. The mutation step has the most impact on the computational and statistical efficiency of SMC and is often performed via several iterations of a Markov chain Monte Carlo (MCMC) kernel. We propose to make efficient use of the derivatives of the log posterior with respect to the parameters, which are available either in closed form or can be unbiasedly estimated for a large class of problems. We explore the use of Metropolis adjusted Langevin algorithm (MALA) moves, which requires derivative information, in the mutation step. As a by-product of our research, we also develop a new approach to adapt the tuning parameters of the mutation proposal density, using neural networks and the information from the population of particles. We apply post-processing steps using zero-variance control variates to lower the variance of expectations with respect to the posterior and of two alternative evidence estimators. The improvements when compared to a more standard implementation of SMC are demonstrated through an example. This is a working paper to which additional examples and ideas will be added