Gibbs sampling, exponential families and orthogonal polynomials

DOI10.1214/07-STS252zbMath1327.62058arXiv0808.3852MaRDI QIDQ900452

Persi Diaconis, Kshitij Khare, Laurent Saloff-Coste

Publication date: 22 December 2015

Published in: Statistical Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.3852

zbMATH Keywords

orthogonal polynomials exponential families singular value decomposition Gibbs sampler conjugate priors location families running time analyses

Mathematics Subject Classification ID

Sampling theory, sample surveys (62D05) Probability distributions: general theory (60E05) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20)

Related Items

The `life machine': a quantum metaphor for living matter, Sandwich algorithms for Bayesian variable selection, Dimension free convergence rates for Gibbs samplers for Bayesian linear mixed models, Entropy decay in the Swendsen-Wang dynamics on \(\mathbb{Z}^d\), Geometric ergodicity of Gibbs samplers for the horseshoe and its regularized variants, Convergence rates of two-component MCMC samplers, Exact convergence analysis of the independent Metropolis-Hastings algorithms, A Fresh Look at the Running Time Analysis for the Gibbs Sampler, On the convergence rate of the ``out-of-order block Gibbs sampler, On the mixing time of Kac's walk and other high-dimensional Gibbs samplers with constraints, A QUADRATIC REGRESSION PROBLEM FOR TWO-STATE ALGEBRAS WITH AN APPLICATION TO THE CENTRAL LIMIT THEOREM, Stochastic alternating projections, Semigroups of distributions with linear Jacobi parameters, Geometric ergodicity and the spectral gap of non-reversible Markov chains, Rigorous confidence bounds for MCMC under a geometric drift condition, Rates of convergence for Gibbs sampling in the analysis of almost exchangeable data, Hahn polynomials and the Burnside process, Spectral telescope: convergence rate bounds for random-scan Gibbs samplers based on a hierarchical structure, Continuous-time Markov processes, orthogonal polynomials and Lancaster probabilities, Gibbs sampling, exponential families and orthogonal polynomials, Comment: On random scan Gibbs samplers, Polynomial moments with a weighted zeta square measure on the critical line, Hit and run as a unifying device, Convergence rate of multiple-try Metropolis independent sampler, On the stability of positive semigroups, Gibbs sampling, conjugate priors and coupling, Adaptive Gibbs samplers and related MCMC methods, Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials, Orthogonal polynomial kernels and canonical correlations for Dirichlet measures, On a class of polynomial sets generated by F(xt−R(t)), Improving the convergence properties of the data augmentation algorithm with an application to Bayesian mixture modeling, The mathematics of mixing things up, Unnamed Item, An introduction to multivariate Krawtchouk polynomials and their applications, Analysis of convergence rates of some Gibbs samplers on continuous state spaces, Spectral analytic comparisons for data augmentation, Convergence rate and concentration inequalities for Gibbs sampling in high dimension, On reparametrization and the Gibbs sampler, A spectral analytic comparison of trace-class data augmentation algorithms and their sandwich variants, Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models, Combinatorial and analytic properties of the \(n\)-dimensional Hermite polynomials, Mixing of Hamiltonian Monte Carlo on strongly log-concave distributions: continuous dynamics, Fast mixing of Metropolis-Hastings with unimodal targets, Bochner-Pearson-type characterization of the free Meixner class, Estimating the spectral gap of a trace-class Markov operator, One-sided Cauchy-Stieltjes kernel families, Unnamed Item, Geometric Ergodicity and Scanning Strategies for Two-Component Gibbs Samplers, Distance correlation coefficients for Lancaster distributions, Computable upper bounds on the distance to stationarity for Jovanovski and Madras's Gibbs sampler, Component-wise Markov chain Monte Carlo: uniform and geometric ergodicity under mixing and composition, EXCHANGEABLE PAIRS OF BERNOULLI RANDOM VARIABLES, KRAWTCHOUCK POLYNOMIALS, AND EHRENFEST URNS, On the Letac-Massam conjecture and existence of high dimensional Bayes estimators for graphical models, Trivial intersection of \(\sigma \)-fields and Gibbs sampling, The Markov chain Monte Carlo revolution, Convergence analysis of the Gibbs sampler for Bayesian general linear mixed models with improper priors, Composition Markov chains of multinomial type, A characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind, Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions, Convergence complexity analysis of Albert and Chib's algorithm for Bayesian probit regression, On the convergence complexity of Gibbs samplers for a family of simple Bayesian random effects models, Carries, shuffling, and symmetric functions, Limit profiles for reversible Markov chains, Stochastic processes with orthogonal polynomial eigenfunctions, Dual and triple equations andq-orthogonal polynomials, Analysis of non-reversible Markov chains via similarity orbits, Random doubly stochastic tridiagonal matrices, Consistent estimation of the spectrum of trace class data augmentation algorithms, MCMC for Imbalanced Categorical Data, Geometric ergodicity of Gibbs samplers for Bayesian general linear mixed models with proper priors

Uses Software

BaM

Cites Work