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SUMMARY:Comparison of Markov chains via weak Poincaré inequalities\, with
  application to pseudo-marginal MCMC - Sam Power (University of Bristol)
DTSTART:20221014T130000Z
DTEND:20221014T140000Z
UID:TALK182717@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:We investigate the use of a certain class of functional inequa
 lities known as weak Poincaré inequalities to bound the convergence of Ma
 rkov chains to equilibrium. We show that this enables the straightforward 
 and transparent derivation of subgeometric convergence bounds for several 
 'pseudo-marginal' sampling algorithms which are popular for carrying out B
 ayesian inference in the setting of intractable likelihoods\, which are ne
 cessarily subgeometric in many practical settings. These results rely on n
 ovel quantitative comparison theorems between Markov chains. Associated pr
 oofs are simpler than those relying on drift / minorization conditions\, a
 nd the tools developed allow us to recover and further extend known result
 s as particular cases. As a consequence of our results\, we are then able 
 to provide new insights into the practical use of pseudo-marginal algorith
 ms\, analysing the effect of averaging in Approximate Bayesian Computation
  (ABC)\, the use of products of independent averages\, and the complexity 
 trade-offs which arise for particle marginal Metropolis-Hastings (PMMH).\n
 \n(https://arxiv.org/abs/2112.05605\, joint work with Christophe Andrieu\,
  Anthony Lee\, and Andi Q. Wang)
LOCATION:MR12\, Centre for Mathematical Sciences
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