Reversible jump Markov chain Monte Carlo computation and Bayesian model determination

By Peter J. Green. 1995

Subfields: Probabilistic & Bayesian Methods

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Probabilistic & Bayesian Methods

Citations in the corpus

A-NICE-MC: Adversarial Training for MCMC (2017, background): “This form is very common in Bayesian statistics [22], computational physics [23] and graphics [24].”
A Bayesian model for repeated measures zero-inflated count data with application to outpatient psychiatric service use (2010, methodology): “For clarity of presentation, we have graphed only two of the three MCMC chains.”
Bayesian Online Changepoint Detection (2007, background): “Most Bayesian approaches to changepoint detection, in contrast, have been oﬄine and retrospective [24, 4, 26, 13, 8].”
Exploiting compositionality to explore a large space of model structures (2012, methodology): “While PMF assumes a ﬁxed latent dimension, we choose the dimension automatically by placing a Poisson prior on the dimension and moving between states of differing dimension using reversible jump MCMC (Green, 1995).”
A tale of worldwide success: Behind the scenes of Carex (Cyperaceae) biogeography and diversification (2019, methodology): “The method models transitions in net diversi ﬁ cation rates by allowing changes in the numbers and locations of nodes at which speciation and extinction rates shift, averaging over models and parameters using reversible ‐ jump Markov chain Monte Carlo (rjMCMC; Green, 1995).”
‘All models are wrong...’: an introduction to model uncertainty (2012, background): “Green (1995) has shown that this is possible in a fundamental way even for model probabilities by ingeniously constructing a transdimensional Markov Chain.”
Improving the acceptance rate of reversible jump MCMC proposals (2004, methodology): “Green (1995) gives the formula mn(x;x 0) = min 1; n(x 0)qnm(x 0;x) m(x)qmn(x;x0) ; (1) for the acceptance probability needed to maintain detailed balance with respect to .”
The Controlled Thermodynamic Integral for Bayesian Model Comparison (2014, background): “In many cases it is possible to choose h(θ) such that Vπ[g̃(θ)] Vπ[g(θ)], leading to a reduction in Monte Carlo variance.”
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach (2011, methodology): “, 2009) would not work; as the dimension of θ may even be varying, a reversible jump MCMC method (Green, 1995) may be needed when updating θ from its full conditional.”
Sharing Features among Dynamical Systems with Beta Processes (2009, unknown): “We instead develop a “birth and death” reversible jump MCMC (RJMCMC) sampler [8], which proposes t o either add a single new feature, 4”
Bayesian selection of continuous-time Markov chain evolutionary models. (2001, methodology): “We use the following update cycle: t, T z a, g, p, m m z t, T, a, g, p T z t, a, g, p, m, and a, g, p z t, T, m. (4) Previous MCMC approaches have updated t and T simultaneously (Larget and Simon 1999; Mau, Newton, and Larget 1999); however, these approaches consider, at most, proportional rates of ”
Model selection in historical biogeography reveals that founder-event speciation is a crucial process in Island Clades. (2014, methodology): “Second, reversible-jump MCMC (Green 1995) was used to sample both DEC and DEC+J according to their posterior probabilities.”