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SUMMARY:Convergence Bounds for the Random Walk Metropolis Algorithm - Pers
 pectives from Isoperimetry - Sam Power (University of Bristol)
DTSTART:20241125T133000Z
DTEND:20241125T142000Z
UID:TALK221473@talks.cam.ac.uk
DESCRIPTION:The Random Walk&nbsp\;Metropolis&nbsp\;(RWM) is a simple and e
 nduring Markov chain-based algorithm for approximate simulation from an in
 tractable &lsquo\;target&rsquo\; probability distribution. In a pair of re
 cent works\, we have undertaken a detailed study of the quantitative conve
 rgence of this algorithm to its equilibrium distribution\, establishing no
 n-asymptotic estimates on mixing times\, with explicit dependence on dimen
 sion and other relevant problem parameters. The results hold at a reasonab
 le level of generality\, and are often sharp in a suitable sense.\nThe foc
 us of the talk will be conceptual rather than technical\, with an eye towa
 rds enabling intuition for i) which high-level aspects of the target distr
 ibution influence the convergence behaviour of RWM\, and ii) which concret
 e properties must be verified in order to obtain a rigorous proof. A key e
 lement will be the impact of tail behaviour and measure concentration on t
 he convergence profile of the algorithm across different time-scales.&nbsp
 \;\nNo prior knowledge of the RWM is required from the audience.\n(joint w
 ork with C. Andrieu\, A. Lee and A. Wang)
LOCATION:Seminar Room 1\, Newton Institute
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