Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms

By Gareth O. Roberts, Richard L. Tweedie. 1996

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Citations in the corpus

Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families (2015, neutral): “Following [22, 30], it is sufficient to show”
On the convergence of Hamiltonian Monte Carlo (2017, unknown): “The classical approach to derive irreducibility of Hastings-Metropolis algorithms on Rd, outlined for example in [18] [24], is to use that the proposal distribution admits a (sufficiently regular) transition density with respect to the Lebesgue measure.”
Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (2012, background): “All uniformly (and geometrically) ergodic Markov chains satisfy this property [32], Proposition 5.”
Exponential ergodicity of the bouncy particle sampler (2017, unknown): “Random walk Metropolis No No Yes Yes [23] [23] [22, 39] [22, 39]”
Examples of Adaptive MCMC (2009, methodology): “…aperiodically geometrically ergodic , ie A natural approach to the establishment of simultaneously strongly aperiodically geometrically ergodicity is to use the drift function π − 1 / 2 as in Roberts and Tweedie (1996) for AM and Roberts and Rosenthal (1997) for Adaptive Metropolis-within-Gibbs.”
Variance bounding Markov chains. (2008, background): “By Gareth O. Roberts and Jeffrey S. Rosenthal1”
Log-concave sampling: Metropolis-Hastings algorithms are fast! (2018, methodology): “Roberts and Tweedie (1996b) established suﬃcient conditions on the proposal function p and the target distribution Π for the geometric convergence of several random walk Metropolis-Hastings algorithms.”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, methodology): “Whileintheprobability community Langevin diffusions and their equilibrium distributions had also been around for some time (Kent 1978), it was the Roberts and Tweedie (1996a) paper (motivated by Besag 1994 comment on Grenander and Miller 1994) that brought the approach to the centre of interest of…”
General state space Markov chains and MCMC algorithms (2004, methodology): “[34], [93], [15], [54], [76], [38], [6], [43]).”
BAYESIAN ESTIMATION IN SINGLE-INDEX MODELS (2004, background): “The random walk Metropolis Markov chain is therefore µ-irreducible, aperiodic and its state space is a small set, cf. Theorem 2.2 of Roberts and Tweedie (1996).”
On the ergodicity of the adaptive Metropolis algorithm on unbounded domains (2008, result): “The result in Proposition 15 is similar to the results obtained in [10, 15], with the exception that we have a common minorization set C for all proposal scalings.”
On the stability of sequential Monte Carlo methods in high dimensions (2011, unknown): “−y| < δq: qs(x,y) ≥ φ1/2 √0 2π exp ˆ − s 2 δ2 q ˙ ≥ φ1/2 √0 2π exp ˆ − 1 2 δ2 q ˙ . (56) This property will be used below. To establish the minorization, one can follow the proof of Theorem 2.2 of [50] to show that for any x, with y ∈ B(x,δq/2) (the open ball, centered x and of radius δq/2), A ∈ ”
Geometric ergodicity of Metropolis algorithms (2000, methodology): “(Roberts and Tweedie, 1996) showed geometric ergodicity of the random walk-based Metropolis algorithm with q satisfying (7) for a speci c class of sub-exponential target densities.”