On adaptive Markov chain Monte Carlo algorithms

By Yves F. Atchadé, Jeffrey S. Rosenthal. 2005

401 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a732f05c75a8bee3132af3b4c16d9c77d33ff37d

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Citations in the corpus

On the ergodicity of the adaptive Metropolis algorithm on unbounded domains (2008, methodology): “Atchadé and Rosenthal [5] developed further the technique of [9].”
Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms (2007, methodology): “The results of Haario et al. were then generalised by Atchadé and Rosenthal (2005) and Andrieu and Moulines (2006), proving convergence of more general adaptive MCMC algorithms.”
Bayesian nonparametric vector autoregressive models (2018, neutral): “Atchadé and Rosenthal (2005) show that this algorithm is ergodic.”
On the ergodicity properties of some adaptive MCMC algorithms (2006, methodology): “ence result for the chain {Xk} under the probability Pρ x,θ, which is an important and direct byproduct of the property mentioned in the remark immediately above. This result improves on [19, 21] and [6]. Proposition 4. Assume (A1)–(A3), let ρ∈(0,1) be as in (16), let ¯ρ = {ρ¯k} be a positive and ﬁn”
General state space Markov chains and MCMC algorithms (2004, background): “(It may even be possible for the computer to adaptively modify σ(2) to achieve the appropriate acceptance rates; see [5] and references therein.”
Adaptively Scaling the Metropolis Algorithm Using Expected Squared Jumped Distance (2007, methodology): “A comparison of our method with the stochastic Robbins-Monro algorithm implemented by Atchadé and Rosenthal (2003, Graph 2), shows that our method converges faster and does not encounter the problems of the stochastic algorithm, which always goes in the first steps to a very low value and then conve”
A tutorial on adaptive MCMC (2008, background): “We however do not provide directly applicable technical conditions here that ensure the validity of such algorithms - more details can be found in Holden (1998), Atchadé and Rosenthal (2005), Andrieu and Moulines (2006), Roberts and Rosenthal (2006), Bai et al. (2008) and Atchadé and Fort (2008).”
An Adaptive Sequential Monte Carlo Sampler (2010, background): “One way of circumventing the need for analytical optimal scalings is to try to learn them online (Andrieu and Robert, 2001; Atchad´e and Rosenthal, 2005), this can include learning both a good scaling, h , and estimating the target covariance, ˆΣ π (Haario et al., 1998).”
Time-varying sparsity in dynamic regression models (2014, positive): “The variance τi,t is tuned adaptively using the method of Atchadé and Rosenthal (2005) which updates τi,t to τi,t + 1 γη (αγ − 0.3) where γ is the iteration number of the MCMC sampler, αγ is the acceptance probability of the Metropolis-Hastings step at the γ-th iteration and 0.5 η 1.”
Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models (2008, neutral): “Time-varying-parameter (TVP) models are written in the state-space form (1) and ( 2 ) with constant system matrices.”
Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo (AdPMCMC) (2010, methodology): “The first constructs a proposal kernel via an adaptive Metropolis scheme ([Roberts and Rosenthal, 2009], [Atchadé and Rosenthal, 2005]) that is used to sample the static parameters Θ. Introducing an adaptive MCMC proposal kernel into the Particle MCMC setting allows the Markov chain proposal…”
Optimal Proposal Distributions and Adaptive MCMC (2008, methodology): “For a simple counter-example (illustrated interactively by Rosenthal, 2004; see also Atchadé and Rosenthal, 2005, and Roberts and Rosenthal, 2005), let Y = {1, 2}, let X = {1, 2, 3, 4}, let π(1) = π(3) = π(4) = 0.333 and π(2) = 0.001.”
DRAM: Efficient adaptive MCMC (2006, background): “, 2001, Theorem 2) and consequently the proof of Theorem 3 above, to obtain a stronger result with less restrictive (but more implicit) assumptions, see (Atchade and Rosenthal, 2005).”
Model Averaging and Its Use in Economics (2017, methodology): “See Atchadé and Rosenthal (2005) for an introduction.”