Trans-dimensional Markov chain Monte Carlo

By Peter J. Green, Simon J. Godsill, Juha Heikkinen. 2000

364 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0e104b5192c0b1bb8a5bac21b72173f4fe053d62

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Citations in the corpus

Scalable Variational Inference for Bayesian Variable Selection in Regression, and Its Accuracy in Genetic Association Studies (2012, background): “Since the samples σ(2) β and σ̂ 2 β depend on each other, the extra term σ̂ 2 β/σ 2 β is needed so that the Metropolis-Hastings acceptance probability satisfies the detailed balance condition, as we need to account for the change of variables (Green 2003).”
Transdimensional inversion of receiver functions and surface wave dispersion (2012, background): “…with a generalization of the well known Metropolis-Hasting algorithm [Metropolis et al., 1953; Hastings, 1970] termed the reversible-jump Markov chain Monte Carlo (rj-McMC) sampler [Geyer and Møller, 1994; Green, 1995, 2003] which allows inference on both model parameters and model dimensionality.”
Frequentist Model Average Estimators (2003, methodology): “The tutorial by Hoeting, Madigan, Raftery and Volinsky (1999) discusses pertinent issues of interpretation and implementation via the machinery of Markov chain Monte Carlo, where the chains in question move between models of different dimensions; see also Green (2003) for a review of trans-dimension”
Model Averaging and Dimension Selection for the Singular Value Decomposition (2006, background): “Each of these approaches has its own notational and concep- tual hurdles, and which one to present is, to some extent, a matter of style (see Green 2003 for a discussion).”
Exact and efficient Bayesian inference for multiple changepoint problems (2006, methodology): “The reanalysis of the data in Green (2003), using a reversible jump MCMC algorithm run for 25 times as long, does fully explore the posterior distribution.”
Model choice using reversible jump Markov chain Monte Carlo (2012, methodology): “For a detailed consideration, the interested reader is referred to the original presentation in Green (1995) or the alternative, and we trust improved, discussion in Green (2003).”
Joint Bayesian model selection and parameter estimation of the generalized extreme value model with covariates using birth‐death Markov chain Monte Carlo (2009, methodology): “Parameter Estimation [24] In reality, for the GEV model with covariates, ‘‘the number of things you don’t know is one of the things you don’t know’’ [ Green, 2003 ].”
A UNIFIED FRAMEWORK FOR MODELLING WILDLIFE POPULATION DYNAMICS † (2005, methodology): “An algorithm for SIS in this circumstance remains to be developed (although algorithms for MCMC methods exist; see Green, 2003).”
Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling (2005, methodology): “Following Richardson and Green (1997) the standard way to simulate from a mixture with an unknown number of components is reversible jump MCMC (Green, 1995; for an up-to-date review, see Green, 2003).”
A Bayesian approach for detecting the impact of mass‐extinction events on molecular phylogenies when rates of lineage diversification may vary (2016, methodology): “…posterior distribution cannot be computed analytically; we therefore approximate the joint posterior distribution using reversible-jump Markov chain Monte Carlo (rjMCMC; Green 1995, 2003), which samples parameter values of the episodic birth-deathmodel in proportion to their posterior probability.”
Estimation of trace gas fluxes with objectively determined basis functions using reversible jump Markov Chain Monte Carlo (2016, background): “The reversible-jump algo-rithm (Green, 1995, 2003) expands on the ﬁxed dimension case, to provide a more general expression for the acceptance term, if we wish to consider changes in dimension.”
Sequential Monte Carlo samplers (2002, unknown): “The initial importance distribution was the prior.”
Marginal likelihood estimation via power posteriors (2008, methodology): “This data set appears in Han and Carlin (2001), and was also examined in Carlin and Chib (1995) and Bartolucci et al.”
Seismic tomography with the reversible jump algorithm (2009, methodology): “5 D I S C U S S I O N A N D C O N C LU S I O N S We have described a new algorithm for seismic imaging that uses the reversible jump technique (Green 1995, 2003) to adjust the underlying parametrization of the model while recovering a velocity field in 2-D.”
The BPP program for species tree estimation and species delimitation (2015, background): “The other three analyses (A01, A10, and A11) are transmodel inferences (in the terminology of Green, 2003), in which the Markov chain moves between different models.”
Bayesian forecasting in economics and finance: A modern review (2022, background): “See Green (2003), Marin et al. (2005), Chib (2011) and Fan and Sisson (2011) for reviews and more complete referencing. α(·|·), BPS is ultimately tied to a ‘likelihood-type’ framework, or at least a log-loss function, due to the presence of the latent variables x, which must be integrated out via…”
A tutorial on adaptive MCMC (2008, result): “Despite finding results similar to those of Green (2003) and Hastie (2005) we cannot in this approach as a reliable one.”