Sequential quasi Monte Carlo

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2015 · Volume 77 · Issue 3

Abstract

We derive and study sequential quasi Monte Carlo (SQMC), a class of algorithms obtained by introducing QMC point sets in particle filtering. SQMC is related to, and may be seen as an extension of, the array-RQMC algorithm of L'Ecuyer and his colleagues. The complexity of SQMC is, whereNis the number of simulations at each iteration, and its error rate is smaller than the Monte Carlo rate. The only requirement to implement SQMC algorithms is the ability to write the simulation of particlegivenas a deterministic function ofand a fixed number of uniform variates. We show that SQMC is amenable to the same extensions as standard SMC, such as forward smoothing, backward smoothing and unbiased likelihood evaluation. In particular, SQMC may replace SMC within a particle Markov chain Monte Carlo algorithm. We establish several convergence results. We provide numerical evidence that SQMC may significantly outperform SMC in practical scenarios.

Keywords

Array-randomized quasi Monte Carlo, Low discrepancy, Particle filtering, Quasi Monte Carlo; Randomized quasi Monte Carlo; Sequential Monte Carlo

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