Post date: 20-Dec-2013 14:06:29
* 15h, Christophe Andrieu, Bristol University
Establishing some order amongst exact approximation MCMCs
Abstract Exact approximation Markov chain Monte Carlo (MCMC) algorithms are a general class of algorithms for Bayesian inference in complex models. We discover a general sufficient condition which allows to order two implementations of such algorithms in terms of mean acceptance probability and asymptotic variance. The key condition is convex order between the `weight' distributions, which emerges naturally when the weight distributins stem from importance sampling approximations with different number of samples. We also discuss also the implications to the spectrum of the algorithms. We develop a general theory that allows us to order pseudo-marginal algorithms in terms of their spectral gaps and asymptotic performance.
* 16h15, Mathieu Gerber, CREST-ENSAE & Université de Lausanne
Sequential Quasi Monte Carlo
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(N log N) where N is the number of simulations at each iteration, and its error rate is smaller than the Monte Carlo rate O(N^{-1/2}). The only requirement to implement SQMC is the ability to write the simulation of particle x_t^n given x_{t-1}^n as a deterministic function of x_{t-1}^n 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.
(joint work with N. Chopin)