Polynomial ergodicity of Markov transition kernels

By Gersende Fort, Eric Moulines. 2003

72 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/95778aacb5cc76386f4ead8ea697f7f2cba6889f

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Convergence of Heavy‐tailed Monte Carlo Markov Chain Algorithms (2007, result): “In the case where Q has bounded support this result is proved in Fort & Moulines (2003) under slightly different conditions on .”
SUBGEOMETRIC ERGODICITY OF STRONG MARKOV PROCESSES (2005, background): “This compromise between the rate function and the norm of convergence is well known for the discrete parameter Markov chain ([35]; see also [4, 8, 14]).”
Markov chain Monte Carlo: Can we trust the third significant figure? (2007, background): “A rule of thumb suggested by Gelman et al. (2004) is to set δ = 1.”
Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms (2007, background): “While some results about polynomial ergodicity (e.g. Jarner and Roberts (2002) and Fort and Moulines (2003)) do not provide explicit quantitative convergence bounds, Theorems 3 and 4 of Fort and Moulines (2000) do.”
Fixed-Width Output Analysis for Markov Chain Monte Carlo (2006, methodology): “Consider the method of Geweke (1992), which is a diagnostic that seems close in spirit to the current work.”
On the Markov chain central limit theorem (2004, background): “Several m otivating exam ples are given which range from toy one-dim ensionalsettings to com plicated settingsencountered in M arkov chain M onte Carlo.”
General state space Markov chains and MCMC algorithms (2004, background): “We conclude that, for such “typical” target distributions π(·), both the Gibbs sampler and appropriate Metropolis-Hastings algorithms perform well in practice, and allow us to sample from π(·).”
Practical drift conditions for subgeometric rates of convergence (2004, methodology): “Polynomial rates of convergence have been widely studied recently under various conditions [see Veretennikov (1997, 2000), Tanikawa (2001), Jarner and Roberts (2002) and Fort and Moulines (2003)].”