Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms

By Gareth O. Roberts, Jeffrey S. Rosenthal. 2007

432 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

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Citations in the corpus

Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families (2015, background): “Intuitively, adaptation becomes less likely as the MCMC chain progresses, but never fully stops, while sharing asymptotic convergence with adaptation that stops at a ﬁxed point [23, Theorem 1].”
Kernel Adaptive Metropolis-Hastings (2013, background): “As adaptations occur with decreasing probability, Theorem 1 of Roberts & Rosenthal(2007) implies that the resulting algorithm is ergodic and converges to the correct target.”
Bayesian calibration of a large‐scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm (2011, methodology): “Adaptive MCMC sampling techniques [Haario et al., 2001; Atchade and Rosenthal, 2005; Andrieu and Moulines, 2006; Haario et al., 2006; Roberts and Rosenthal, 2007, 2009] offer great flexibility in the automatic tuning of these variables.”
Hierarchical Shrinkage Priors for Regression Models (2017, methodology): “Relatively simple conditions are given for the ergodicity of adaptive Metropolis-Hastings algorithms by Roberts and Rosenthal (2007).”
A tutorial on adaptive MCMC (2008, background): “…random e.g. such that it takes values in {δ,0} for some δ > 0 and such that P(γi = δ) = pi where {pi} ⊂ [0,1]N is a deterministic and non-increasing sequence (Roberts and Rosenthal 2007), although it is not always clear what the advantage of introducing such an additional level of randomness is.”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, background): “We present here the rather general but fairly simple coupling approach (Roberts and Rosenthal 2007) to establishing convergence.”
Bayesian inference of chemical kinetic models from proposed reactions (2015, background): “Roberts and Rosenthal (2007), in contrast, develop simpler conditions that ensure convergence of the adaptive MCMC scheme to the target distribution and provide a law of large numbers.”
Differential Evolution Markov Chain with snooker updater and fewer chains (2008, methodology): “Because of this diminishing adaptation (Roberts and Rosenthal 2007), we conjecture that DE-MC Z is ergodic and converges to a stationary distribution with pdf π(.)”
Adaptive Gibbs samplers and related MCMC methods (2011, methodology): “…of adaptive MCMC (see e.g. [18, 19, 5, 1, 20, 13, 44, 45, 25, 50, 51, 14, 8, 6, 7, 47, 49, 2, 3, 15]) which includes counterintuitive examples where X n fails to converge to the desired distribution π (c.f. [5, 44, 8, 25]), as well as many results guaranteeing ergodicity under various assumptions.”
Adaptive sequential Monte Carlo by means of mixture of experts (2011, background): “However, while lots of research has been devoted to adaptation of MCMC methods (see especially Haario et al., 2001; Roberts and Rosenthal, 2007; Andrieu and Moulines, 2006; Roberts and Rosenthal, 2009), adaptive methods for SMC is still in its infancy.”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, background): “We present here the rather general but fairly simple coupling approach (Roberts and Rosenthal (2007)) to establishing convergence.”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “This means that there are at least two ways to improve the eﬃciency of sampling with MCMC [54]: (1) Increase the eﬀective sample size for a given number of MCMC iterations with, e.g., adaptive MCMC [78, 79, 179, 90].”
Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation (2016, methodology): “The sampling from an external archive of past states violates the Markovian principles of the sampled chains, and turns the method into an adaptive Metropolis sampler (Roberts and Rosenthal, 2007; ter Braak and Vrugt, 2008).”
On the ergodicity of the adaptive Metropolis algorithm on unbounded domains (2008, background): “Atchadé and Rosenthal [5] developed further the technique of [9].”