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(Hands-on + discussion) Scaling limits for modern MCMC algorithms

Banff International Research Station for Mathematical Innovation and Discovery

The presentation will review results on infinite dimensional limits for some modern MCMC algorithms with a particular focus on Piecewise Deterministic Markov Processes PDMPs. The talk will also discuss the methodological consequences of these results for MCMC implementation. For certain stylised sequences of target density and particular MCMC algorithms, limit results can be obtained as the dimension of the target diverges. For traditional (Metropolis-Hastings type) MCMC algorithms, such limits are typically (but not always) diffusions. For non-reversible alternatives such as PDMPs similar results can be obtained, although often not of diffusion form and not even Markov. The two simplest PDMP strategies, Zig-Zag and the Bouncy Particle Sampler (BPS) can be readily analysed with some surprising conclusions; not least that the BPS has some undesirable asymptotic reducibility properties as dimension diverges. Most of the results in this area assume stationarity, but work on the transient phase will also be at least briefly described.

Mathematics; Statistics; Statistical mechanics, structure of matter; Statistical mechanics

video/mp4

Author affiliation: University of Warwick

2019-05-13

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/70146

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/