Computational and Inferential Difficulties with Mixture Posterior Distributions

By Gilles Celeux, Merrilee Hurn, Christian P. Robert. 2000

708 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0957ae54326e2332b31132a966d518fa7861fa29

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Citations in the corpus

A Split-Merge Markov chain Monte Carlo Procedure for the Dirichlet Process Mixture Model (2004, methodology): “Computational techniques for Dirichlet process mixture models were explored previously by Escobar (1994), Escobar and West (1995), MacEachem (1994), Bush and MacEachern (1996), Neal (1992, 2000), and Green and Richardson (2001).”
Wormhole Hamiltonian Monte Carlo (2013, background): “In Bayesian inference, it is well known that standard Markov Chain Monte Carlo (MCMC) methods tend to fail when the target distribution is multimodal (Neal 1993; 1996; Celeux, Hurn, and Robert 2000; Neal 2001; Rudoy and Wolfe 2006; Sminchisescu and Welling 2011; Craiu, R., and Y. 2009).”
Hierarchical Bayes versus Finite Mixture Conjoint Analysis Models: A Comparison of Fit, Prediction, and Partworth Recovery (2002, methodology): “…an HB model that incorporates mixtures of normal distributions because of the computational and inferential difficulties of dealing with the “label-switching” problem when the Gibbs sampler is used for inference (for an insightful discussion of this problem, see Celeux, Hurn, and Robert 2000).”
Model‐based clustering for social networks (2007, methodology): “Second, use the relabelling algorithm of Celeux et al. (2000) to solve the label switching problem.”
An exploration of aspects of Bayesian multiple testing (2006, methodology): “Inserting the first expression from (7) into (6), in place of the product, and performing an easy computation shows that the resulting integral is finite.”
JAGS Version 4.0.0 user manual (2015, methodology): “D <- dim(A) for (i in 1:D[1]) for (j in 1:D[2]) { B[i,j] <- A[i,j] + c } }”
Cluster Identification Using Projections (2001, background): “These procedures are very promising, but they are subject to the label switching problem (see Stephens 2000 and Celeux, Hurn, and Robert 2000 for recent analysis of this problem) and more research is needed to avoid the convergence problems owing to masking (see Justel and Peña 1996) and to develop…”
Model-Based Clustering of Non-Gaussian Panel Data Based on Skew-t Distributions (2010, methodology): “As pointed out by Celeux, Hurn, and Robert (2000), Stephens (2000b), and Casella, Robert, and Wells (2004), a number of difficulties may arise when constructing a sampler for a mixture model.”
Contemporary Bayesian Econometrics and Statistics (2005, background): “In applications in which the different states have a substantive interpretation, this creates serious conceptual complications (Celeux et al. 2000) and requires some explicit modifications of the posterior simulator like those suggested by FruhwirthSchnatter (2001).”
Bayesian Modelling and Inference on Mixtures of Distributions (2005, methodology): “Empirical approaches based on clustering algorithms for the parameter sample are proposed in Stephens (1997) and Celeux et al. (2000), and they achieve some measure of success on the examples for which they have been tested.”
Smoothly mixing regressions (2007, background): “If this were the case exchangeable priors would be inappropriate, and there are other problems of interpretation in that case as well (see Celeux et al. (2000)).”
Robust mixture regression modeling based on scale mixtures of skew-normal distributions (2015, methodology): “…an da rd er ro rs ba se d on th e pa ra m et ri c bo ot st ra p pr oc ed ur e are alternative methods to overcome the label switching problem, mainly from the Bayesian perspective, like the works of Stephens (2002), Celeux et al. (2000), Yao and Lindsay (2009), Sperrin et al. (2010) and Yao (2012).”