Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions
نویسندگان
چکیده
منابع مشابه
Rates of Convergence of Some Multivariate Markov Chains with Polynomial Eigenfunctions by Kshitij Khare
We provide a sharp nonasymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate orthogonal polynomial as eigenfunctions. Our examples include the Moran model in population genetics and its variants in community ecology, the Dirichlet-multinomial Gibbs sampler, a class of generalized Be...
متن کاملRates of Convergence of Some Multivariate Markov Chains with Polynomial Eigenfunctions
We provide a sharp non-asymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate orthogonal polynomial as eigenfunctions. Our examples include the Moran’s model in population genetics and its variants in community ecology, the Dirichlet-Multinomial Gibbs sampler, a class of generalized...
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This is an expository paper which presents various ideas related to nonasymptotic rates of convergence for Markov chains. Such rates are of great importance for stochastic algorithms which are widely used in statistics and in computer science. They also have applications to analysis of card shuffling and other areas. In this paper, we attempt to describe various mathematical techniques which ha...
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1. Orientation 1 1.1. Example 1: Random-to-Top Card Shuffling 1 1.2. Example 2: The Ehrenfest Urn Model of Diffusion 2 1.3. Example 3: Metropolis-Hastings Algorithm 4 1.4. Reversible Markov Chains 5 1.5. Exercises: Reversiblity, Symmetries and Stationary Distributions 8 2. Coupling 9 2.1. Coupling and Total Variation Distance 9 2.2. Coupling Constructions and Convergence of Markov Chains 10 2.3...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2009
ISSN: 1050-5164
DOI: 10.1214/08-aap562