On the applicability of regenerative simulation in Markov chain Monte Carlo

By James P. Hobert, Galin L. Jones, Brett Presnell, Jeffrey S. Rosenthal. 2002

139 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e0bd70a5d46915a54c1f3391b44813fa023cf3d1

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Batch means and spectral variance estimators in Markov chain Monte Carlo (2008, unknown): “(2) Received November 2008; revised April 2009.”
Variance bounding Markov chains. (2008, background): “3; see also [3], [10]) that if P is geometrically ergodic, then h satisfies a usual CLT, provided π(|h|2+δ) < ∞ for some δ > 0.”
Optimal Proposal Distributions and Adaptive MCMC (2008, methodology): “Many applications of MCMC make use of such Markov chain limit theorems as the Weak Law of Large Numbers (WLLN), Strong Law of Large Numbers (SLLN), and Central Limit Theorem (CLT), in order to guarantee good asymptotic estimates and estimate standard errors (see e.g. Tierney, 1994; Jones and Hobert,”
Component-Wise Markov Chain Monte Carlo: Uniform and Geometric Ergodicity under Mixing and Composition (2009, methodology): “Along with various moment conditions, the existence of M and t in (1) is also a key sufficient condition for using a variety of methods such as batch means, spectral methods or regenerative simulation to construct a strongly consistent estimator of σ 2 g , ensuring asymptotically valid Monte Carlo s”
Optimal Proposal Distributions and Adaptive MCMC (2011, methodology): “Many applications of MCMC make use of such Markov chain limit theorems as the Weak Law of Large Numbers (WLLN), Strong Law of Large Numbers (SLLN), and Central Limit Theorem (CLT), in order to guarantee good asymptotic estimates and estimate standard errors (see e.g. Tierney, 1994; Jones and Hobert,”
Multivariate output analysis for Markov chain Monte Carlo (2015, methodology): “by the univariate CLT p n( n;i i) !d N(0;˙2 i); (2) as n!1, where n;i and i are the ith components of n and , respectively and ˙2 i is the ith diagonal element of . Flegal and Jones (2010), Hobert et al. (2002) and Jones et al. (2006) propose strongly consistent estimators of ˙2 i using spectral”
Fixed-Width Output Analysis for Markov Chain Monte Carlo (2006, methodology): “Lemma A.1 (Hobert et al. 2002, lemma 1).”
The Markov chain Monte Carlo revolution (2008, background): “the variance of such averages can be usefully estimated [46].”
General state space Markov chains and MCMC algorithms (2004, background): “Now, the classical notion of “irreducibility” is that the chain has positive probability of eventually reaching any state from any other state, but if X is uncountable then that condition is impossible.”
Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression (2007, methodology): “We begin by deriving a minorization condition for the AC algorithm by using the ‘distinguished point’ technique that was introduced in Mykland et al. (1995).”
A Practical Sequential Stopping Rule for High-Dimensional Markov Chain Monte Carlo (2016, background): “2006; Flegal and Jones 2010), spectral variance estimation (Flegal and Jones 2010), and regenerative simulation (Mykland, Tierney, and Yu 1995; Hobert et al. 2002).”