Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform Ergodicity of the Iterated Conditional SMC and Geometric
  Ergodicity of Particle Gibbs samplers   We establish quantitative bounds for rates of convergence and asymptotic
variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov
chains and associated particle Gibbs samplers. Our main findings are that the
essential 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. Furthermore, we show that the i-cSMC
Markov chain cannot even be geometrically ergodic if this essential boundedness
does not hold in many applications of interest. Our sufficiency and
quantitative bounds rely on a novel non-asymptotic analysis of the expectation
of a standard normalizing constant estimate with respect to a "doubly
conditional" SMC algorithm. In addition, our results for i-cSMC imply that the
rate of convergence can be improved arbitrarily by increasing N, the number of
particles in the algorithm, and that in the presence of mixing assumptions, the
rate of convergence can be kept constant by increasing N linearly with the time
horizon. We translate the sufficiency of the boundedness condition for i-cSMC
into sufficient conditions for the particle Gibbs Markov chain to be
geometrically ergodic and quantitative bounds on its geometric rate of
convergence, which imply convergence of properties of the particle Gibbs Markov
chain to those of its corresponding Gibbs sampler. These results complement
recently discovered, and related, conditions for the particle marginal
Metropolis-Hastings (PMMH) Markov chain.

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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph