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CATEGORIES:Statistics
SUMMARY:Uniform Ergodicity of the Iterated Conditional SMC
and Geometric Ergodicity of Particle Gibbs sample
rs - Anthony Lee\, University of Warwick
DTSTART;TZID=Europe/London:20140124T160000
DTEND;TZID=Europe/London:20140124T170000
UID:TALK49563AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/49563
DESCRIPTION:Particle MCMC is an increasingly popular methodolo
gy for performing static parameter inference for h
idden Markov models on general state spaces\, of w
hich one method is the particle Gibbs algorithm. W
e establish quantitative bounds for rates of conve
rgence and asymptotic variances for iterated condi
tional sequential Monte Carlo (i-cSMC) Markov chai
ns and associated particle Gibbs samplers. Our mai
n findings are that the essential boundedness of p
otential functions associated with the i-cSMC algo
rithm provide necessary and sufficient conditions
for the uniform ergodicity of the i-cSMC Markov ch
ain\, as well as quantitative bounds on its (unifo
rmly geometric) rate of convergence. This compleme
nts more straightforward results for the particle
independent Metropolis--Hastings (PIMH) algorithm.
Our results for i-cSMC imply that the rate of con
vergence can be improved arbitrarily by increasing
N\, the number of particles in the algorithm\, an
d that in the presence of mixing assumptions\, the
rate of convergence can be kept constant by incre
asing N linearly with the time horizon. Neither of
these phenomena are observed for the PIMH algorit
hm. We translate the sufficiency of the boundednes
s condition for i-cSMC into sufficient conditions
for the particle Gibbs Markov chain to be geometri
cally ergodic and quantitative bounds on its geome
tric rate of convergence. These results complement
recently discovered\, and related\, conditions fo
r the particle marginal Metropolis--Hastings (PMMH
) Markov chain. This is joint work with Christophe
Andrieu and Matti Vihola.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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