Print Email Facebook Twitter The Zig-Zag process and super-efficient sampling for Bayesian analysis of big data Title The Zig-Zag process and super-efficient sampling for Bayesian analysis of big data Author Bierkens, G.N.J.C. (TU Delft Statistics) Fearnhead, Paul (Lancaster University) Roberts, Gareth (University of Warwick) Date 2019 Abstract Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational burden, but with the drawback that these algorithms no longer target the true posterior distribution. We introduce a new family of Monte Carlo methods based upon a multidimensional version of the Zig-Zag process of [Ann. Appl. Probab. 27 (2017) 846–882], a continuous-time piecewise deterministic Markov process. While traditional MCMC methods are reversible by construction (a property which is known to inhibit rapid convergence) the Zig-Zag process offers a flexible nonreversible alternative which we observe to often have favourable convergence properties. We show how the Zig-Zag process can be simulated without discretisation error, and give conditions for the process to be ergodic. Most importantly, we introduce a sub-sampling version of the Zig-Zag process that is an example of an exact approximate scheme, that is, the resulting approximate process still has the posterior as its stationary distribution. Furthermore, if we use a control-variate idea to reduce the variance of our unbiased estimator, then the Zig-Zag process can be super-efficient: after an initial preprocessing step, essentially independent samples from the posterior distribution are obtained at a computational cost which does not depend on the size of the data. Subject MCMCnonreversible Markov processpiecewise deterministic Markov processstochastic gradient Langevin dynamicssub-samplingexact sampling To reference this document use: http://resolver.tudelft.nl/uuid:c8aa0421-e47f-48c3-8611-9bd8a55d6f2c DOI https://doi.org/10.1214/18-AOS1715 ISSN 0090-5364 Source Annals of Statistics, 47 (3), 1288-1320 Part of collection Institutional Repository Document type journal article Rights © 2019 G.N.J.C. Bierkens, Paul Fearnhead, Gareth Roberts Files PDF AOS1715.pdf 775.9 KB Close viewer /islandora/object/uuid:c8aa0421-e47f-48c3-8611-9bd8a55d6f2c/datastream/OBJ/view