A Metropolis-Hastings algorithm for posterior measures with self-decomposable priors
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We introduce a new class of Metropolis-Hastings algorithms for sampling target measures that are absolutely continuous with respect to an underlying self-decomposable prior measure on infinite-dimensional Hilbert spaces. We particularly focus on measures that are highly non-Gaussian and cannot be sampled effectively using conventional algorithms. We utilize the self-decomposability of the prior to construct an autoregressive proposal kernel that preserves the prior measure and satisfies detailed balance. We then introduce an entirely new class of self-decomposable prior measures, called the Bessel-K prior, as a generalization of the gamma density to infinite dimensions. The Bessel-K priors interpolate between well-known priors such as the gamma distribution and Besov priors and can model sparse or compressible parameters. We present example applications of our algorithm in inverse problems ranging from finite-dimensioanl denoising to deconvolution on L^2 .
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