Ensemble Rejection Sampling

George Deligiannidis; Arnaud Doucet; Sylvain Rubenthaler

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arXiv · 2001.09188

Ensemble Rejection Sampling

George Deligiannidis·Arnaud Doucet·Sylvain Rubenthaler

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Abstract

We introduce Ensemble Rejection Sampling, a scheme for exact simulation from the posterior distribution of the latent states of a class of non-linear non-Gaussian state-space models. Ensemble Rejection Sampling relies on a proposal for the high-dimensional state sequence built using ensembles of state samples. Although this algorithm can be interpreted as a rejection sampling scheme acting on an extended space, we show 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. We demonstrate this methodology by sampling exactly state sequences according to the posterior distribution of a stochastic volatility model and a non-linear autoregressive process. We also present an application to rare event simulation.

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George Deligiannidis, Arnaud Doucet, Sylvain Rubenthaler. 2020-01-24. Ensemble Rejection Sampling. https://arxiv.org/abs/2001.09188

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