Polynomial convergence rates of Markov chains.

By S. Jarner, Gareth O. Roberts. 2002

194 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8aedcf32f22237f605b9a57ea408fd4854726442

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Citations in the corpus

Practical drift conditions for subgeometric rates of convergence (2004, methodology): “In particular, by setting φ(v) := vα, α ∈ [0, 1), we retrieve the results in Jarner and Roberts (2002). Several applications are given in section 3.”
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.”
Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (2012, methodology): “Theorem 50 is a restatement of [17], Theorem 4.”
Fixed-Width Output Analysis for Markov Chain Monte Carlo (2006, background): “(2000, 2003), Geyer (1999), Jarner and Hansen (2000), Jarner and Roberts (2002) ,”
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(·).”
Convergence of Heavy‐tailed Monte Carlo Markov Chain Algorithms (2007, methodology): “We shall derive and apply a Foster–Lyapunov drift condition for the CLT to hold, improving the result of Chan (1993b), see also Jarner & Roberts (2002).”
Subgeometric rates of convergence of f-ergodic strong Markov processes (2006, background): “Following discrete-time usage [22, 31, 17], we call a measurable set C (f, r)-regular if sup x∈C GB(x, f, r; δ) <∞, for all δ > 0 and all accessible set B.”
Subgeometric rates of convergence of Markov processes in the Wasserstein metric (2012, unknown): “However, note that we cannot apply this proposition directly because in contrast to Fort and Roberts, we assumed neither that the set {V (x) ≤ R} is petite nor that the process X is Harris-recurrent with invariant measure.”
Exact and computationally efficient likelihood‐based estimation for discretely observed diffusion processes (with discussion) (2006, background): “→ [1, ∞/, bounded on C, such that E{V.Xn+1/|Xn =x} V.x/− c V α.x/+b 1[Xn∈C]: .34/ This drift condition implies that the chain is polynomially ergodic, as shown in Jarner and Roberts (2002).”
Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms (2007, unknown): “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.”
SUBGEOMETRIC ERGODICITY OF STRONG MARKOV PROCESSES (2005, methodology): “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]).”
Multivariate output analysis for Markov chain Monte Carlo (2015, background): “lt (see Jones (2004) for a review). Many Markov chains used in practice have been shown to be at least polynomially ergodic. See Acosta et al. (2015), Doss and Hobert (2010), Hobert and Geyer (1998), Jarner and Roberts (2002), Jarner and Hansen (2000), Jarner and Roberts (2002), Johnson et al. (2013”