Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast Gibbs sampling for high-dimensional Bayesian inversion   Solving ill-posed inverse problems by Bayesian inference has recently
attracted considerable attention. Compared to deterministic approaches, the
probabilistic representation of the solution by the posterior distribution can
be exploited to explore and quantify its uncertainties. In applications where
the inverse solution is subject to further analysis procedures, this can be a
significant advantage. Alongside theoretical progress, various new
computational techniques allow to sample very high dimensional posterior
distributions: In [Lucka2012], a Markov chain Monte Carlo (MCMC) posterior
sampler was developed for linear inverse problems with $\ell_1$-type priors. In
this article, we extend this single component Gibbs-type sampler to a wide
range of priors used in Bayesian inversion, such as general $\ell_p^q$ priors
with additional hard constraints. Besides a fast computation of the
conditional, single component densities in an explicit, parameterized form, a
fast, robust and exact sampling from these one-dimensional densities is key to
obtain an efficient algorithm. We demonstrate that a generalization of slice
sampling can utilize their specific structure for this task and illustrate the
performance of the resulting slice-within-Gibbs samplers by different computed
examples. These new samplers allow us to perform sample-based Bayesian
inference in high-dimensional scenarios with certain priors for the first time,
including the inversion of computed tomography (CT) data with the popular
isotropic total variation (TV) prior.

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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph