BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Scaling of Piecewise Deterministic Monte Carlo for Anisotropic Tar
 gets - Kengo Kamatani (The Institute of Statistical Mathematics (ISM))
DTSTART:20241129T091500Z
DTEND:20241129T100500Z
UID:TALK221566@talks.cam.ac.uk
DESCRIPTION:Piecewise deterministic Markov processes (PDMPs) are a type of
  continuous-time Markov process that combine deterministic flows with jump
 s. Recently\, PDMPs have garnered attention within the Monte Carlo communi
 ty as a potential alternative to traditional Markov chain Monte Carlo (MCM
 C) methods. The Zig-Zag sampler and the Bouncy Particle Sampler are common
 ly used examples of the PDMP methodology which have also yielded impressiv
 e theoretical properties\, but little is known about their robustness to e
 xtreme dependence or anisotropy of the target density. It turns out that P
 DMPs may suffer from poor mixing due to anisotropy and this paper investig
 ates this effect in detail in the stylised but important Gaussian case. To
  this end\, we employ a multi-scale analysis framework in this paper. Our 
 results show that when the Gaussian target distribution has two scales\, o
 f order 1 and \\epsilon\, the computational cost of the Bouncy Particle Sa
 mpler is of order \\epsilon^&minus\;1\, and the computational cost of the 
 Zig-Zag sampler is \\epsilon^&minus\;2. In comparison\, the cost of the tr
 aditional MCMC methods such as RWM is of order \\epsilon^&minus\;2\, at le
 ast when the dimensionality of the small component is more than 1. Therefo
 re\, there is a robustness advantage to using PDMPs in this context.\nThis
  is joint work with Joris Bierkens (TU Delft) and Gareth O. Roberts (Warwi
 ck)
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR