Geometric ergodicity of Metropolis algorithms

By S. Jarner, Ernst Hansen. 2000

247 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8602089c74e14cdba77efdc4b051908ae1d65658

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

On the ergodicity of the adaptive Metropolis algorithm on unbounded domains (2008, methodology): “Our assumptions are very close to the well-known conditions proposed by Jarner and Hansen [10] to ensure the geometric convergence of a (nonadaptive) Metropolis process.”
Exponential ergodicity of the bouncy particle sampler (2017, unknown): “Random walk Metropolis No No Yes Yes [23] [23] [22, 39] [22, 39]”
Adaptive Gibbs samplers and related MCMC methods (2011, methodology): “· We shall work in the following setting, extensively studied for nonadaptive Metropolis within Gibbs algorithms in [17], see also [40] for related work and [23] for analysis of the random walk Metropolis algorithm.”
Multivariate output analysis for Markov chain Monte Carlo (2015, background): “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), Johnson and Jones (2015)”
Convergence of Heavy‐tailed Monte Carlo Markov Chain Algorithms (2007, methodology): “…to the onedimensional finite-variance case above and the multidimensional geometric and non-geometric cases considered in Roberts & Tweedie (1996b), Jarner & Hansen (2000), Fort & Moulines (2000) we will have to use the drift function V (x)= |x|s ∨ 1 instead of the ‘natural’ drift function V (x)=…”
On the Markov chain central limit theorem (2004, background): “(Jarner and Hansen,2000) Suppose is a positive density on Rk having continuous rstderivativessuch that lim jxj!”
On the stability of sequential Monte Carlo methods in high dimensions (2011, background): “nt notations. We will assume that for every s ∈ [φ0,1] one has • πs is bounded away from zero on compact sets and is upper-bounded. • πs is super-exponential with asymptotically regular contours; see [37] for details. We will add the condition C∗ := sup x∈R,s∈[φ0,1] ˆZ A(x)c G(x,z)qs(z)dz ˙ < +∞ ”
Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (2012, methodology): “We consider next conditions which allow us to establish a polynomial drift condition for the pseudo-marginal algorithm in the case where the marginal algorithm is a geometrically ergodic random-walk Metropolis (RWM) targeting a superexponentially decaying target with regular contours [16].”
Practical drift conditions for subgeometric rates of convergence (2004, background): “These results have later been extended to the multidimensional case by Roberts and Tweedie (1996) and Jarner and Hansen (2000) .”
Component-Wise Markov Chain Monte Carlo: Uniform and Geometric Ergodicity under Mixing and Composition (2009, background): “…and Tweedie (1996) and Tierney (1994) studied the MHIS while Johnson and Geyer (2012), Mengersen and Tweedie (1996), Roberts and Tweedie (1996), Jarner and Hansen (2000), Christensen, Møller and Waagepetersen (2001) have established conditions under which Metropolis yields a geometrically…”
On the geometric ergodicity of hybrid samplers (2003, methodology): “Consider the subexponential density p on R2 given by p(x) ∝ (1 + x2 1 + x2 2 + x8 1x(2) 2 ) exp(−(x2 1 + x2 2 )), x = (x1, x2), which was introduced in [9].”
On the ergodicity properties of some adaptive MCMC algorithms (2006, background): “s for any q∈ Qa,b and we can conclude that (48) is satisﬁed. Noting that the two sets A(x) and R(x) do not depend on the proposal distribution qand using the conclusion of the proof of Theorem 4.3 of [22], we have inf q∈Qa,b liminf |x|→+∞ Z A(x) q(z)λLeb(dz)>0, so that, from the conclusion of the”
Markov chain Monte Carlo: Can we trust the third significant figure? (2007, background): “…(1994) examined Gibbs samplers while Christensen, Moller and Waagepetersen (2001), Douc et al. (2004), Fort and Moulines (2000, 2003), Geyer (1999), Jarner and Hansen (2000), Jarner and Roberts (2002), Meyn and Tweedie (1994) and Mengersen and Tweedie (1996) considered Metropolis–Hastings…”
The Markov chain Monte Carlo revolution (2008, background): “For further discussion and references, see [23] and [50].”
Fixed-Width Output Analysis for Markov Chain Monte Carlo (2006, background): “(2000, 2003), Geyer (1999), Jarner and Hansen (2000) , Jarner and Roberts (2002),”