Functional central limit theorems for the Gibbs sampler (Q2717130)
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scientific article; zbMATH DE number 1604569
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Functional central limit theorems for the Gibbs sampler |
scientific article; zbMATH DE number 1604569 |
Statements
14 June 2001
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Gibbs sampler
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Markov chain
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geometric ergodicity
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central limit theorem
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Functional central limit theorems for the Gibbs sampler (English)
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Let \(\pi\) be a probability distribution having a density on \(\mathbb R^d\) which is proprotional to \(\exp(-V(x))\). If \(V\) is smooth, strictly concave and if \(V\) has a uniformly bounded second derivative which is uniformly bounded away from \(0\), then the Markov chain induced by the method of Gibbs sampling having \(\pi\) as its invariant distribution is geometrically ergodic.
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