Optimising Poisson bridge constructions for variance reduction methods

Abstract

Abstract In this paper we discuss different Monte Carlo (MC) approaches to generate unit-rate Poisson processes and provide an analysis of Poisson bridge constructions, which form the discrete analogue of the well-known Brownian bridge construction for a Wiener process. One of the main advantages of these Poisson bridge constructions is that they, like the Brownian bridge, can be effectively combined with variance reduction techniques. In particular, we show here, in practice and proof, how we can achieve orders of magnitude efficiency improvement over standard MC approaches when generating unit-rate Poisson processes via a synthesis of antithetic sampling and Poisson bridge constructions. At the same time we provide practical guidance as to how to implement and tune Poisson bridge methods to achieve, in a mean sense, (near) optimal performance.