Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Markov chain Monte Carlo importance samplers for Bayesian models with
  intractable likelihoods   We consider the efficient use of an approximation within Markov chain Monte
Carlo (MCMC), with subsequent importance sampling (IS) correction of the Markov
chain inexact output, leading to asymptotically exact inference. We detail
convergence and central limit theorems for the resulting MCMC-IS estimators. We
also consider the case where the approximate Markov chain is pseudo-marginal,
requiring unbiased estimators for its approximate marginal target. Convergence
results with asymptotic variance formulae are shown for this case, and for the
case where the IS weights based on unbiased estimators are only calculated for
distinct output samples of the so-called `jump' chain, which, with a suitable
reweighting, allows for improved efficiency. As the IS type weights may assume
negative values, extended classes of unbiased estimators may be used for the IS
type correction, such as those obtained from randomised multilevel Monte Carlo.
Using Euler approximations and coupling of particle filters, we apply the
resulting estimator using randomised weights to the problem of parameter
inference for partially observed It\^{o} diffusions. Convergence of the
estimator is verified to hold under regularity assumptions which do not require
that the diffusion can be simulated exactly. In the context of approximate
Bayesian computation (ABC), we suggest an adaptive MCMC approach to deal with
the selection of a suitably large tolerance, with IS correction possible to
finer tolerance, and with provided approximate confidence intervals. A
prominent question is the efficiency of MCMC-IS compared to standard direct
MCMC, such as pseudo-marginal, delayed acceptance, and ABC-MCMC. We provide a
comparison criterion which generalises the covariance ordering to the IS
setting.

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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: math
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph