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Gibbs sampling, exponential families and orthogonal polynomials
 Statistical Sciences
, 2008
"... Abstract. We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate priors. In each case, the transition operator is explicitly diagonalizable with classical ort ..."
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Abstract. We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate priors. In each case, the transition operator is explicitly diagonalizable with classical orthogonal polynomials as eigenfunctions. Key words and phrases: Gibbs sampler, running time analyses, exponential families, conjugate priors, location families, orthogonal polynomials, singular value decomposition. 1.
Analysis of systematic scan Metropolis algorithms using Iwahori–Hecke algebra techniques
, 2004
"... We give the first analysis of a systematic scan version of the Metropolis algorithm. Our examples include generating random elements of a Coxeter group with probability determined by the length function. The analysis is based on interpreting Metropolis walks in terms of the multiplication in the Iwa ..."
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Cited by 34 (8 self)
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We give the first analysis of a systematic scan version of the Metropolis algorithm. Our examples include generating random elements of a Coxeter group with probability determined by the length function. The analysis is based on interpreting Metropolis walks in terms of the multiplication in the IwahoriHecke algebra.
Trouve, A.: Construction of Bayesian deformable models via stochastic approximation algorithm: a convergence study. arXiv.org
, 2009
"... Abstract. The problem of the definition and the estimation of generative models based on deformable templates from raw data is of particular importance for modeling nonaligned data affected by various types of geometrical variability. This is especially true in shape modeling in the computer vision ..."
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Cited by 17 (1 self)
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Abstract. The problem of the definition and the estimation of generative models based on deformable templates from raw data is of particular importance for modeling nonaligned data affected by various types of geometrical variability. This is especially true in shape modeling in the computer vision community or in probabilistic atlas building in Computational Anatomy. A first coherent statistical framework modeling the geometrical variability as hidden variables was described by Allassonnière, Amit and Trouvé in [2]. The present paper gives a theoretical proof of convergence of effective stochastic approximation expectation strategies to estimate such models and shows the robustness of this approach against noise through numerical experiments in the context of handwritten digit modeling.
Matrix Norms and Rapid Mixing for Spin Systems
, 2007
"... We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm of the associated dependency matrix is less than 1. We give improved an ..."
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Cited by 5 (0 self)
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We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm of the associated dependency matrix is less than 1. We give improved analysis for the case in which the diagonal of the dependency matrix is 0 (as in heat bath dynamics). We apply the matrix norm methods to random update and systematic scan Glauber dynamics for colouring various classes of graphs. We give a general method for estimating a norm of a symmetric nonregular matrix. This leads to improved mixing times for any class of graphs which is hereditary and sufficiently sparse including several classes of degreebounded graphs such as nonregular graphs, trees, planar graphs and graphs with given treewidth and genus. 1
Rate of Convergence of the Gibbs Sampler by Gaussian Approximation
, 1997
"... this article we approximate the rate of convergence of the Gibbs sampler by a normal approximation of the target distribution. Based on this approximation, we consider many implementational issues for the Gibbs sampler, e.g., updating strategy, parameterization and blocking. We give theoretical resu ..."
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Cited by 5 (3 self)
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this article we approximate the rate of convergence of the Gibbs sampler by a normal approximation of the target distribution. Based on this approximation, we consider many implementational issues for the Gibbs sampler, e.g., updating strategy, parameterization and blocking. We give theoretical results to justify our approximation and illustrate our methods in a number of realistic examples. Key words: Correlation Structure; Gaussian distribution; Generalized linear models; Gibbs sampler; Markov chain Monte Carlo; Parameterization; Random scan; Rates of convergence.
Comment: On Random Scan Gibbs Samplers
, 808
"... We congratulate the authors on a review of convergence rates for Gibbs sampling routines. Their combined work on studying convergence rates via orthogonal polynomials in the present paper under ..."
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Cited by 2 (0 self)
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We congratulate the authors on a review of convergence rates for Gibbs sampling routines. Their combined work on studying convergence rates via orthogonal polynomials in the present paper under
Efficient Markov chain Monte Carlo with incomplete multinomial data, Technical report 382, The University of Iowa See Also part, partition, and rdirichlet Examples complete<c(20,655,17,15,11,8,5,10,4) # so k=9, and # there are 20 observed counts of 1’s,
 Author(s) Kwang Woo Ahn and KungSik Chan See Also setdiff, intersect, and partition Examples ms1<c(1,3,7,9,10) ms2<c(7,9,10,12,13) part(ms1,ms2) 5 partition The Coarsest Partition of a Finite Sequence of Sets for Which Only Consecutive Sets
, 2007
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