A tutorial on adaptive MCMC

By Christophe Andrieu, John A. Thoms. 2008

1,025 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Generalizing Hamiltonian Monte Carlo with Neural Networks (2017, background): “In addition, one could draw inspiration from the adaptive literature (Haario et al., 2001; Andrieu & Thoms, 2008) or component-wise strategies (Gilks & Wild, 1992).”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “2001, Andrieu and Thoms 2008). Sejdinovic et al. (2014) introduces a kernel adaptive Metropolis-Hasting (KAMH) algorithm for sampling from a target distribution with strongly non-linear support. The idea is similar to that proposed in Haario et al. (2001), but when the target distributions are stron”
Kernel Sequential Monte Carlo (2015, methodology): “We now review how these quantities were previously modelled using kernel methods in the context of MCMC. Note that any form of adaptation in MCMC requires care in order to preserve ergodicity of the resulting Markov chain, and some form of vanishing adaptation is needed [1, 18].”
Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families (2015, methodology): “For example, in Pseudo-Marginal MCMC (PM-MCMC) [2, 3], the posterior does not have an analytic expression, but can only be estimated at any given point, e.g. in Bayesian Gaussian Process classiﬁcation [4].”
Kernel Adaptive Metropolis-Hastings (2013, methodology): “By analogy with algorithms which use linear PCA directions to inform M-H proposals (Andrieu & Thoms, 2008, Algorithm 8), nonlinear PCA directions can be encoded in the proposal construction, as described in AppendixC.”
Handbook of Markov Chain Monte Carlo (2011, neutral): “Recent work on adaptive MCMC methods is reviewed by Andrieu and Thoms (2008).”
The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo (2011, methodology): “To set ǫ for both NUTS and HMC, we propose using stochastic optimization with vanishing adaptation (Andrieu and Thoms, 2008), specifically an adaptation of the primal-dual algorithm of Nesterov (2009).”
Bayesian Posterior Sampling via Stochastic Gradient Fisher Scoring (2012, positive): “Thus, this algorithm requires only O ( n ) computations to generate each sample, unlike traditional MCMC algorithms which require O ( N ) computations per sample.”
Riemannian Manifold Hamiltonian Monte Carlo (2009, methodology): “Whilst there have been a number of suggestions to overcome this inefficiency, guaranteeing detailed balance and ergodicity of the chain places constraints on what can beachieved in alleviating this problem (Andrieu and Thoms, 2008; Robert, 2004; Neal, 1993a).”
On the ergodicity of the adaptive Metropolis algorithm on unbounded domains (2008, background): “Recently, there has been a number of publications describing different adaptation techniques aiming to find a good proposal automatically [1, 3, 5, 9, 13] (see also the review article [4]).”
The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions (2019, methodology): “There are a number of efficient algorithms available to automate the selection of σq [54].”
Ensemble samplers with affine invariance (2010, background): “Markov chain Monte Carlo (MCMC) sampling methods typically have parameters that need to be adjusted for a specific problem of interest [9] [10] [1].”
A Semantic Approach for Estimating Consumer Content Preferences from Online Search Queries (2018, methodology): “Here, we apply an adaptive proposal distribution (with vanishing adaptation) for a random walk Metropolis–Hastings algorithm to sample each θq (Andrieu and Thoms 2008).”
Reinforcement learning with limited reinforcement: using Bayes risk for active learning in POMDPs (2008, positive): “First, using adaptive MCMC methods [52] could make the sampling more efficient.”
Particle Markov chain Monte Carlo methods (2010, methodology): “It is also possible to use an adaptive MCMC strategy to determine this covariance on the fly (Andrieu and Thoms (2008) , section 5.1).”
StarBEAST2 Brings Faster Species Tree Inference and Accurate Estimates of Substitution Rates (2016, methodology): “We have also developed a new adaptive MH (Andrieu and Thoms 2008) operator called “CoordinatedExponential” which changes the height of the species tree root node and the height of connected components by an amount g.”