Rates of Convergence for Gibbs Sampling for Variance Component Models
نویسندگان
چکیده
منابع مشابه
Rates of Convergence for Gibbs Sampling for Variance Component Models
This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for K location parameters, with J observations each, the number of iterations required for convergence (for large K and J) is a constant times 1 + log K log J. This is one of the rst rigorous, a priori results abo...
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This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for K location parameters, with J observations each, the number of iterations required for convergence (for large K and J) is a constant times ( 1 + logK log J ) . This is one of the first rigorous, a priori resul...
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Proof. Let x, y 2 ⌦ be two configurations. We will prove the claim for the visible conditional distributions. The proof for the hidden conditional distributions will follow symmetrically. For each visible node v i , let (X(v i ), Y (v i )) be the maximal coupling of P (v)(X(v i ) |x(h)) and P (v)(Y (v i ) | y(h)) guaranteed in Lemma 1. By doing this independently for all visible nodes, we have ...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1995
ISSN: 0090-5364
DOI: 10.1214/aos/1176324619