Examples of Adaptive MCMC

By Gareth O. Roberts, Jeffrey S. Rosenthal. 2009

1,135 citations recorded by the source corpus.

Subfields: Molecular Biology, Spectroscopy, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b377fa9c1a8455a1b5696b84b34f9d6bd220793a

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Citations in the corpus

Control variates for estimation based on reversible Markov chain Monte Carlo samplers (2012, methodology): “We consider an inference problem motivated by a simplified version of an example in Roberts and Rosenthal (2009).”
Electricity access and income inequality in South Africa: Evidence from Bayesian and NARDL analyses (2020, methodology): “The Bayesian linear regression is implemented in this study using the adaptive random-walk Metropolis-Hastings algorithm available in Giordani and Kohn [64]; Roberts and Rosenthal [65].”
Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo (AdPMCMC) (2010, methodology): “In this paper use a mixture proposal kernel known to satisfy these two ergodicity conditions when unbounded state spaces and general classes of target posterior distributions are utilised; see [Roberts and Rosenthal, 2009].”
On the ergodicity of the adaptive Metropolis algorithm on unbounded domains (2008, background): “For practical considerations of the AM algorithm, the reader may consult [8, 14].”
Conditional (2019, neutral): “To achieve a high degree of differentiation from the original identity while preserving the realistic essence of face appearance, we employ a Latent Diffusion-based ID Sampler, which is able to sample anonymized identities from the distribution of real human identities.”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, methodology): “Versions and refinements of the adaptiveMetropolis algorithm (Roberts and Rosenthal 2009; Andrieu and Thoms 2008) have served well in applications and motivated much of the theoretical development.”
Adaptive MCMC with Bayesian Optimization (2012, background): “…the strategy in the complex setting of sampling from constrained, discrete and densely connected probabilistic graphical models where, for each variation of the problem, one needs to adjust the parameters of the proposal mechanism automatically to ensure efficient mixing of the Markov chains.”
Boosting Variational Inference (2016, methodology): “We demonstrate this property on the “banana” distribution, which is widely-used for studying the performance of MCMC algorithms [Haario et al., 1999, 2001, Roberts and Rosenthal, 2009].”
Learning Stochastic Inverses (2013, methodology): “Adaptive MCMC techniques such as those presented in Roberts and Rosenthal (2009) and Haario et al. (2006) are used to tune parameters of MCMC algorithms, but do not allow arbitrarily close adaptation of the underlying model to the posterior, whereas our method is designed to allow such close…”
Exact Bayesian inference in spatiotemporal Cox processes driven by multivariate Gaussian processes (2015, methodology): “One attractive option is to use an adaptive Gaussian random-walk Metropolis–Hastings step where the covariance matrix of the proposal is based on the empirical covariance matrix of the previous steps, as proposed by Roberts and Rosenthal (2009).”
A Review of Extreme Value Threshold Estimation and Uncertainty Quantification (2012, positive): “Orthogonalisation of the GPD scale and shape parameters, or an adaptive posterior sampling scheme (Roberts & Rosenthal, 2009), may help with convergence.”
Optimal Proposal Distributions and Adaptive MCMC (2008, methodology): “Simulations on test problems involving hundreds of dimensions have been quite successful (Roberts and Rosenthal, 2006), and adaptive Metropolis-within-Gibbs has also been used on statistical genetics problems (Turro et al., 2007).”
Bayesian inference with optimal maps (2011, methodology): “A non-exhaustive list of recent methodological advances includes adaptivity based on past samples [11, 12], Langevin methods [13, 14], the use of Hessian information [15] and Hessians with low-rank structure [16], Hamiltonian dynamics [17], the exchange of information among multiple chains [18– 20],”
Robustifying Generalized Linear Mixed Models Using a New Class of Mixtures of Multivariate Polya Trees (2009, methodology): “Note that in the proposed adaptive schemes the corresponding parameters change at the lth scan of the Gibbs sampler by only O(1/l) and O(1/ √ l) for μ, and and c, respectively, thus satisfying necessary conditions for the ergodicity of the chain (see Roberts and Rosenthal 2006).”
Bayesian calibration of a large‐scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm (2011, methodology): “…of the Metropolis-Hastings algorithm (MH) [Metropolis et al., 1953; Hastings, 1970] by employing a reduced-order model and state-of-the-art techniques in adaptive MCMC sampling [Haario et al., 2001; Atchade and Rosenthal, 2005; Andrieu and Moulines, 2006; Roberts and Rosenthal, 2007, 2009].”