Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Error Bounds and Normalizing Constants for Sequential Monte Carlo in
  High Dimensions   In a recent paper Beskos et al (2011), the Sequential Monte Carlo (SMC)
sampler introduced in Del Moral et al (2006), Neal (2001) has been shown to be
asymptotically stable in the dimension of the state space d at a cost that is
only polynomial in d, when N the number of Monte Carlo samples, is fixed. More
precisely, it has been established that the effective sample size (ESS) of the
ensuing (approximate) sample and the Monte Carlo error of fixed dimensional
marginals will converge as $d$ grows, with a computational cost of
$\mathcal{O}(Nd^2)$. In the present work, further results on SMC methods in
high dimensions are provided as $d\to\infty$ and with $N$ fixed. We deduce an
explicit bound on the Monte-Carlo error for estimates derived using the SMC
sampler and the exact asymptotic relative $\mathbb{L}_2$-error of the estimate
of the normalizing constant. We also establish marginal propagation of chaos
properties of the algorithm. The accuracy in high-dimensions of some
approximate SMC-based filtering schemes is also discussed.

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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: q-fin