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Accelerated Gibbs sampling of normal distributions using matrix splittings and
Colin Fox,Albert E. Parker +1 more
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The article was published on 2015-01-01 and is currently open access. It has received 19 citations till now. The article focuses on the topics: Matrix (mathematics) & Gibbs sampling.read more
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Approximation and sampling of multivariate probability distributions in the tensor train decomposition
TL;DR: A sampler for arbitrary continuous multivariate distributions that is based on low-rank surrogates in the tensor train format, a methodology that has been exploited for many years for scalable, high-dimensional density function approximation in quantum physics and chemistry.
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MALA-within-Gibbs Samplers for High-Dimensional Distributions with Sparse Conditional Structure
TL;DR: It is shown that the acceptance ratio and step size of this MCMC sampler are independent of the overall problem dimension when (i) the target distribution has sparse conditional structure, and (ii) this structure is reflected in the partial updating strategy of MALA-within-Gibbs.
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Localization for MCMC: sampling high-dimensional posterior distributions with local structure
TL;DR: Morzfeld et al. as discussed by the authors used covariance localization in numerical weather prediction to sample high-dimensional posterior distributions arising in Bayesian inverse problems, and showed that the convergence rate is independent of dimension for localized linear problems.
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Convergence in Variance of Chebyshev Accelerated Gibbs Samplers
Colin Fox,Albert E. Parker +1 more
TL;DR: An algorithm for the stochastic version of the second-order Chebyshev accelerated SSOR (symmetric successive overrelaxation) iteration is given and numerical examples of sampling from multivariate Gaussian distributions are provided to confirm that the desired convergence properties are achieved in finite precision.
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High-dimensional Gaussian sampling: a review and a unifying approach based on a stochastic proximal point algorithm
TL;DR: This paper proposes a unifying Gaussian simulation framework by deriving a stochastic counterpart of the celebrated proximal point algorithm in optimization and offers a novel and unifying revisit of most of the existing MCMC approaches while extending them.
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Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
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An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
Book
Bayesian Data Analysis
TL;DR: Detailed notes on Bayesian Computation Basics of Markov Chain Simulation, Regression Models, and Asymptotic Theorems are provided.
Book
Iterative Methods for Sparse Linear Systems
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.