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SUMMARY:Uniform Ergodicity of the Iterated Conditional SMC and Geometric E
 rgodicity of Particle Gibbs samplers - Anthony Lee\, University of Warwick
DTSTART:20140124T160000Z
DTEND:20140124T170000Z
UID:TALK49563@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:Particle MCMC is an increasingly popular methodology for perfo
 rming static parameter inference for hidden Markov models on general state
  spaces\, of which one method is the particle Gibbs algorithm. We establis
 h quantitative bounds for rates of convergence and asymptotic variances fo
 r iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and a
 ssociated particle Gibbs samplers. Our main findings are that the essentia
 l boundedness of potential functions associated with the i-cSMC algorithm 
 provide necessary and sufficient conditions for the uniform ergodicity of 
 the i-cSMC Markov chain\, as well as quantitative bounds on its (uniformly
  geometric) rate of convergence. This complements more straightforward res
 ults for the particle independent Metropolis--Hastings (PIMH) algorithm. O
 ur results for i-cSMC imply that the rate of convergence can be improved a
 rbitrarily 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 increasing N linearly with the time horizon. Neither 
 of these phenomena are observed for the PIMH algorithm. We translate the s
 ufficiency of the boundedness condition for i-cSMC into sufficient conditi
 ons for the particle Gibbs Markov chain to be geometrically ergodic and qu
 antitative bounds on its geometric rate of convergence. These results comp
 lement recently discovered\, and related\, conditions for the particle mar
 ginal Metropolis--Hastings (PMMH) Markov chain. This is joint work with Ch
 ristophe Andrieu and Matti Vihola.
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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