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SUMMARY:The Discrete Bouncy Particle Sampler - Chris Sherlock (Lancaster U
 niversity)
DTSTART:20170706T151500Z
DTEND:20170706T160000Z
UID:TALK73210@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The Bouncy Particle Sampler (BPS) is a continuous-time\, non-r
 eversible  MCMC algorithm that shows great promise in efficiently sampling
  from  certain high-dimensional distributions\; a particle moves with a fi
 xed  velocity except that occasionally it "bounces" off the hyperplane  pe
 rpendicular to the gradient of the target density. One practical  difficul
 ty is that for each specific target distribution\, a  locally-valid upper 
 bound on the component of the gradient in the  direction of movement must 
 be found so as to allow for simulation of the  bounce times via Poisson th
 inning\; for efficient implementation this  bound should also be tight. In
  dimension $d=1$\, the discrete-time  version of the Bouncy Particle Sampl
 er (and\, equivalently\, of the  Zig-Zag sampler\, another continuous-time
 \, non-reversible algorithm) is  known to consist of fixing a time step\, 
 $\\Delta t$\, and proposing a  shift of $v \\Delta t$ which is accepted wi
 th a probability dependent on  the ratio of target evaluated at the propos
 ed and current positions\; on  rejection the velocity is reversed. We pres
 ent a discrete-time version  of the BPS that is valid in any dimension $d\
 \ge 1$ and the limit of  which (as $\\Delta t\\downarrow 0$) is the BPS\, 
 which is rejection free.  The Discrete BPS has the advantages of non-rever
 sible algorithms in  terms of mixing\, but does not require an upper bound
  on a Poisson  intensity and so is straightforward to apply to complex tar
 gets\, such as  those which can be evaluated pointwise but for which gener
 al  properties\, such as local or global Lipshitz bounds on derivatives\, 
  cannot be obtained. [Joint work with Dr. Alex Thiery].
LOCATION:Seminar Room 1\, Newton Institute
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