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Sequential Quasi-Monte Carlo

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Advanced Monte Carlo Methods for Complex Inference Problems

Co-author: Mathieu Gerber (Universit de Lausanne and CREST )

We develop a new class of algorithms, SQMC (Sequential Quasi-Monte Carlo), as a variant of SMC (Sequential Monte Carlo) based on low-discrepancy points. The complexity of SQMC is O(Nlog N), where N is the number of simulations at each iteration, and its error rate is smaller than the Monte Carlo rate O(N). The only requirement to implement SQMC is the ability to write the simulation of particle xn_t given xn_{t-1} as a deterministic function of xn_{t-1} and uniform variates. We show that SQMC is amenable to the same extensions as standard SMC , such as forward smoothing, backward smoothing, unbiased likelihood evaluation, and so on. In particular, SQMC may replace SMC within a PMCMC (particle Markov chain Monte Carlo) algorithm. We establish several convergence results. We provide numerical evidence in several difficult scenarios than SQMC significantly outperforms SMC in terms of approximation error.

This talk is part of the Isaac Newton Institute Seminar Series series.

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