Perfect Simulation for Feynman-Kac Models using Ensemble Rejection Sampling

Abstract: I will introduce Ensemble Rejection Sampling, a scheme for perfect simulation of a class of Feynmac-Kac models. In particular, this scheme allows us to sample exactly from the posterior distribution of the latent states of a class of non-linear non-Gaussian state-space models and from the distribution of a class of conditioned random walks. Ensemble Rejection Sampling relies on a high-dimensional proposal distribution built using ensembles of state samples and dynamic programming. Although this algorithm can be interpreted as a rejection sampling scheme acting on an extended space, it can be shown under regularity conditions that the expected computational cost to obtain an exact sample increases cubically with the length of the state sequence instead of exponentially for standard rejection sampling.

This is joint work with George Deligiannidis & Sylvain Rubenthaler.

–

Bio: Arnaud Doucet obtained his PhD from University Paris-XI (Orsay) in 1997. He has held faculty positions in Melbourne University, Cambridge University, the University of British Columbia and the Institute of Statistical Mathematics in Tokyo. He joined the department of Statistics of Oxford University in 2011 where he is now a Statutory Professor (Oxford speak for chair). Since 2019, he is also a senior research scientist at Google DeepMind. He was an IMS Medallion Lecturer in 2016, was elected an IMS fellow in 2017 and has been awarded the Guy Silver medal of the Royal Statistical Society in 2020.