Hamiltonian Sequential Monte Carlo with Application to Consumer Choice Behavior

Practical use of nonparametric Bayesian methods requires the availability of efficient algorithms for implementation for posterior inference. The inherently serial nature of Markov Chain Monte Carlo (MCMC) imposes limitations on its efficiency and scalability. In recent years there has been a surge of research activity devoted to developing alternative implementation methods that target parallel computing environments. Sequential Monte Carlo (SMC), also known as a particle filter, has been gaining popularity due to its desirable properties. SMC uses a genetic mutation-selection sampling approach with a set of particles representing the posterior distribution of a stochastic process. We propose to enhance the performance of SMC by utilizing Hamiltonian transition dynamics in the particle transition phase, in place of random walk used in the previous literature. We call the resulting procedure Hamiltonian Sequential Monte Carlo (HSMC). Hamiltonian transition dynamics has been shown to yield superior mixing and convergence properties relative to random walk transition dynamics in the context of MCMC procedures. The rationale behind HSMC is to translate such gains to the SMC environment. We apply both SMC and HSMC to a panel discrete choice model with a nonparametric distribution of unobserved individual heterogeneity. We contrast both methods in terms of convergence properties and show the favorable performance of HSMC.