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      On Markov chain Monte Carlo for sparse and filamentary distributions

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          Abstract

          A novel strategy that combines a given collection of reversible Markov kernels is proposed. It consists in a Markov chain that moves, at each iteration, according to one of the available Markov kernels selected via a state-dependent probability distribution which is thus dubbed locally informed. In contrast to random-scan approaches that assume a constant selection probability distribution, the state-dependent distribution is typically specified so as to privilege moving according to a kernel which is relevant for the local topology of the target distribution. The second contribution is to characterize situations where a locally informed strategy should be preferred to its random-scan counterpart. We find that for a specific class of target distribution, referred to as sparse and filamentary, that exhibits a strong correlation between some variables and/or which concentrates its probability mass on some low dimensional linear subspaces or on thinned curved manifolds, a locally informed strategy converges substantially faster and yields smaller asymptotic variances than an equivalent random-scan algorithm. The research is at this stage essentially speculative: this paper combines a series of observations on this topic, both theoretical and empirical, that could serve as a groundwork for further investigations.

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          A note on Metropolis-Hastings kernels for general state spaces

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            Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo

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              Asymptotic Variance and Convergence Rates of Nearly-Periodic Markov Chain Monte Carlo Algorithms

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                Author and article information

                Journal
                23 June 2018
                Article
                1806.09000
                43bf9674-7e8f-46eb-ac66-ff38d57cb43d

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                60J10, 60J20, 60J22, 65C40, 65C05
                stat.ME

                Methodology
                Methodology

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