Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Low Rank Independence Samplers in Bayesian Inverse Problems   In Bayesian inverse problems, the posterior distribution is used to quantify
uncertainty about the reconstructed solution. In practice, Markov chain Monte
Carlo algorithms often are used to draw samples from the posterior
distribution. However, implementations of such algorithms can be
computationally expensive. We present a computationally efficient scheme for
sampling high-dimensional Gaussian distributions in ill-posed Bayesian linear
inverse problems. Our approach uses Metropolis-Hastings independence sampling
with a proposal distribution based on a low-rank approximation of the
prior-preconditioned Hessian. We show the dependence of the acceptance rate on
the number of eigenvalues retained and discuss conditions under which the
acceptance rate is high. We demonstrate our proposed sampler by using it with
Metropolis-Hastings-within-Gibbs sampling in numerical experiments in image
deblurring, computerized tomography, and NMR relaxometry.

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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph