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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The Discrete Bouncy Particle Sampler - Chris Sherl
ock (Lancaster University)
DTSTART;TZID=Europe/London:20170706T161500
DTEND;TZID=Europe/London:20170706T170000
UID:TALK73210AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/73210
DESCRIPTION:The Bouncy Particle Sampler (BPS) is a continuous-
time\, non-reversible MCMC algorithm that shows g
reat promise in efficiently sampling from certain
high-dimensional distributions\; a particle moves
with a fixed velocity except that occasionally i
t "bounces" off the hyperplane perpendicular to t
he gradient of the target density. One practical
difficulty is that for each specific target distri
bution\, a locally-valid upper bound on the compo
nent of the gradient in the direction of movement
must be found so as to allow for simulation of th
e bounce times via Poisson thinning\; for efficie
nt implementation this bound should also be tight
. In dimension $d=1$\, the discrete-time version
of the Bouncy Particle Sampler (and\, equivalently
\, of the Zig-Zag sampler\, another continuous-ti
me\, non-reversible algorithm) is known to consis
t of fixing a time step\, $\\Delta t$\, and propos
ing a shift of $v \\Delta t$ which is accepted wi
th a probability dependent on the ratio of target
evaluated at the proposed and current positions\;
on rejection the velocity is reversed. We presen
t a discrete-time version of the BPS that is vali
d in any dimension $d\\ge 1$ and the limit of whi
ch (as $\\Delta t\\downarrow 0$) is the BPS\, whic
h is rejection free. The Discrete BPS has the adv
antages of non-reversible algorithms in terms of
mixing\, but does not require an upper bound on a
Poisson intensity and so is straightforward to ap
ply to complex targets\, such as those which can
be evaluated pointwise but for which general prop
erties\, such as local or global Lipshitz bounds o
n derivatives\, cannot be obtained. [Joint work w
ith Dr. Alex Thiery].
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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