Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference

By S. Ejaz Ahmed. Technometrics, 2008

1,532 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f6b28d9c2b4fc152546caa49ca4b9e99ff51f631

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Citations in the corpus

Model choice using reversible jump Markov chain Monte Carlo (2012, neutral): “For the remainder of this article some understanding of standard MCMC methods is assumed, and the unfamiliar reader is referred to Gamerman (1997) or Brooks (1998) for an introductory tutorial.”
Bayesian Changepoint Analysis for Extreme Events (Typhoons, Heavy Rainfall, and Heat Waves): An RJMCMC Approach (2010, methodology): “One efficient way to overcome such difficulty is through the use of the Markov chain Monte Carlo (MCMC) method (e.g., Gamerman and Lopes 2006; Gilks et al. 1996; Gelman et al. 2004).”
Quantifying intrinsic and extrinsic noise in gene transcription using the linear noise approximation: An application to single cell data (2013, methodology): “We use a standard Metropolis–Hastings algorithm [Chib and Greenberg (1995), Gamerman and Lopes (2006)] to generate a sample from the posterior distribution.”
Accelerated expansion from ghost-free bigravity: a statistical analysis with improved generality (2012, methodology): “An alternative approach that has become highly popular in cosmological data analysis is based on the Markov Chain Monte Carlo (MCMC) methods (for an introduction and overview of MCMC methods, see [81], and for their applications in cosmology, see e.”
Integrated Non-Factorized Variational Inference (2013, methodology): “Markov chain Monte Carlo (MCMC) methods [1] have been dominant tools for posterior analysis in Bayesian inference.”
Model Comparison and the Principle of Parsimony (2015, methodology): “…exact methods to facilitate the computation of the Bayes factor (e.g., Ardia, Baştürk, Hoogerheide, & van Dijk, 2012; Chen, Shao, & Ibrahim, 2002; Gamerman & Lopes, 2006); in this chapter we focus on BIC (a crude approximation), the Savage-Dickey density ratio (applies only to nested models) and…”
A Spatio-Temporal Model for Mean, Anomaly, and Trend Fields of North Atlantic Sea Surface Temperature (2009, methodology): “…define a suitable hierarchical model and begin exploring the posterior distribution of its processes (say, u and c) with Markov chain Monte Carlo methods (MCMC; see, e.g., Gamerman and Lopes 2006), summations are rapidly computed and we can make efficient use of a parallel computing architecture.”
Bayesian Model Uncertainty In Smooth Transition Autoregressions (2006, methodology): “For more details about Gibbs sampling and Metropolis–Hastings algorithms see Gilks et al. (1996) or the books by Gamerman (1997) and Robert and Casella (1999).”
Kronecker Graphs: An Approach to Modeling Networks (2008, methodology): “This immediately suggests the use of a Metropolis sampling algorithm (Gamerman, 1997) to simulate draws from the permutation distribution since Metropolis is solely based on such ratios”
Generalized Out-of-Distribution Detection: A Survey (2021, positive): “The most representative method is the Bayesian neural network [298], which draws samples from the posterior distribution of the model via MCMC [299], Laplace methods [300], [301] and variational inference [302], forming the epistemic uncertainty of the model prediction.”
Forecasting with Bayesian Vector Autoregression (2013, neutral): “Gelman (1996) suggested the rule of thumb to accept convergence if r < 1.”
An adaptive sparse‐grid high‐order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling (2013, methodology): “[13] Due to the nonlinearity of model f h ð Þ with respect to parameter h, it is often difficult to draw samples from the PPDF directly, so that the MCMC methods, such as Metropolis-Hastings (M-H) algorithm [Gamerman and Lopes, 2006] and its variants, are often used for sampling.”
Spatial dynamic factor analysis (2008, methodology): “In particular, Markov chain Monte Carlo (MCMC) simulation methods (Gamerman and Lopes, 2006, and Robert and Casella, 2004, for instance) have opened up access to fully Bayesian treatments of factor analytic and spatial models as described, for instance, in Lopes and West (2004) and Banerjee,…”
A NON‐GAUSSIAN FAMILY OF STATE‐SPACE MODELS WITH EXACT MARGINAL LIKELIHOOD (2013, methodology): “Bayesian inference for ' can be performed using MCMC algorithms ([2]), since the posterior distribution of the hyparameter is not analytically tractable.”
A New Robust Regression Model for Proportions (2012, methodology): “Additional studies including the use of new Bayesian algorithms (see for example Gamerman and Lopes 2006) are needed to study how to improve the performance of the MCMC procedure for the Beta Rectangular regression model when the number of observations is extremely large.”