Bayesian analysis of mixture models with an unknown number of components- an alternative to reversible jump methods

By Matthew Stephens. 2000

648 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/92f9be0462a86b54d310130bb519fdb90c2e494b

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Citations in the corpus

Dealing with label switching in mixture models (2000, background): “when the number of clusters is allowed to vary (e.g. Richardson and Green, 1997; Stephens, 2000), although in this case problems with genuine multimodality are likely to arise.”
Improving the acceptance rate of reversible jump MCMC proposals (2004, background): “Stephens (2000) suggests an alternative to RJMCMC sampling of mixture distributions based on spatial birth and death processes.”
Reversible jump, birth‐and‐death and more general continuous time Markov chain Monte Carlo samplers (2003, methodology): “…5.3, is thus not to be sought in the continuous time nature of his algorithm, but rather in the different choices that are made in the sampler: Stephens (2000) used birth-and-death moves only for modifying the dimension of the model, and these moves did not involve the complete data, i.e.…”
Joint Bayesian model selection and parameter estimation of the generalized extreme value model with covariates using birth‐death Markov chain Monte Carlo (2009, methodology): “The BDMCMC approach was introduced by Stephens [2000] for normal mixtures and is based on a birth-death process where the mixture size changes.”
Visualizing spatial population structure with estimated effective migration surfaces (2014, background): “] In each step, we propose the birth (addition) or death (removal) of a cell, with equal probability (Stephens, 2000).”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, methodology): “For instance, the birth-and-death process developed by Stephens (2000) used a continuous time jump process to explore a set of models, only to be later shown (Cappé et al. 2002) to be equivalent to the (Metropolis–Hastings) reversible jump approach of Green (1995).”
Nonparametric Convergence Assessment for MCMC Model Selection (2003, methodology): “We have applied these methods to a range of model selection problems using both RJMCMC and the birth–death approach developed by Stephens (2000).”
Flexible modeling of conditional distributions using smooth mixtures of asymmetric student t densities (2010, methodology): “A Bayesian analysis via mixture models with an unknown number of components is possible using, e.g. Dirichlet process mixtures (Escobar and West, 1995), reversible jump MCMC (Richardson and Green, 1997) and birth-and-death MCMC (Stephens, 2000).”
Trans-dimensional Markov chain Monte Carlo (2000, background): “Stephens (2000) notes that various trans-dimensional statistical problems can be viewed as abstract marked point processes, and borrows the birth-and-death simulation idea to give a very promising methodology for finite mixture analysis.”
Marginal likelihood estimation via power posteriors (2008, background): “Other choices include (Stephens 2000), (Carlin and Chib 1995) and (Dellaportas, Forster and Ntzoufras 2001).”
Handbook of Markov Chain Monte Carlo: Hardcover: 619 pages Publisher: Chapman and Hall/CRC Press (first edition, May 2011) Language: English ISBN-10: 1420079417 (2012, methodology): “Stephens (2000b) gives an inferential method based on the relabeling of components with respect to the permutation which minimizes the posterior expected loss.”
Inference of population structure using multilocus genotype data. (2000, methodology): “Data were simu-methods [such as those described by Stephens (2000b)] may be required. lated under the following models.”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, methodology): “For instance, the birth-and-death process developed by Stephens (2000) used a continuous time jump process to explore a set of models, only to be later shown (Capp´e et al. 2002) to be equivalent to the (Metropolis–Hastings) reversible jump approach of Green (1995).”