Markov Chains and De‐initializing Processes

By Gareth O. Roberts, Jeffrey S. Rosenthal. 2001

87 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3654e9af73f0b1e7b81cd5ac8f7ad999794ab95c

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Citations in the corpus

Component-Wise Markov Chain Monte Carlo: Uniform and Geometric Ergodicity under Mixing and Composition (2009, background): “(19) Then PY and PHC are geometrically ergodic.”
On the Markov chain central limit theorem (2004, methodology): “given by Roberts and Rosenthal (1997) whose Theorem 2.1 shows that if X is geometrically ergodic and (8) holds then there exists a c Roberts and Rosenthal, 1997 ) Let X be a geometrically ergodic Markov chain with stationary distribution π. Suppose X satisfies (8) and that E�f 2(x) Roberts and R”
General state space Markov chains and MCMC algorithms (2004, result): “ the d-step chain deﬁned on X 1 ×...×Xd, and h(x 0,...,xd−1) = h(x 0)+...+h(xd−1). Then P inherits the irreducibility and ergodicity properties of P′ (formally, since P′ is de-initialising for P; see [73]). Then, Theorem 23 or 24 establishes a CLT for P and h. However, this is easily seen to be equi”
Stability of the Gibbs sampler for Bayesian hierarchical models (2007, background): “Moreover, it can be shown [25] that the convergence rate of the joint chain coincides with the convergence rate of the marginal chain, { n}.”
Uniform ergodicity of the iterated conditional SMC and geometric ergodicity of particle Gibbs samplers (2013, result): “In the context of the PGibbs sampler the latter result parallels what is known for pseudo-marginal algorithms [5], (d) we note that from [22], Theorem 1; Proposition 1, is geometrically ergodic as soon as x is geometrically ergodic.”
Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression (2007, background): “The Convergence Rates and Standard Errors for Markov Chain Monte Carlo Algorithms 613 deinitializing arguments of Roberts and Rosenthal (2001) can be used to show that this chain inherits geometric ergodicity from its marginal chain {βj}∞j=0, whose Markov transition density is k.β′|β/.”
On the applicability of regenerative simulation in Markov chain Monte Carlo (2002, background): “Fortunately, Mykland, Tierney, and Yu [1995] and Rosenthal [1995] have given recipes for establishing (5) for many of the Gibbs samplers and Metropolis–Hastings algorithms that arise in MCMC.”