Sampling from Dirichlet process mixture models with unknown concentration parameter: mixing issues in large data implementations.

Statistics and Computing
David I HastieSylvia Richardson

Abstract

We consider the question of Markov chain Monte Carlo sampling from a general stick-breaking Dirichlet process mixture model, with concentration parameter [Formula: see text]. This paper introduces a Gibbs sampling algorithm that combines the slice sampling approach of Walker (Communications in Statistics - Simulation and Computation 36:45-54, 2007) and the retrospective sampling approach of Papaspiliopoulos and Roberts (Biometrika 95(1):169-186, 2008). Our general algorithm is implemented as efficient open source C++ software, available as an R package, and is based on a blocking strategy similar to that suggested by Papaspiliopoulos (A note on posterior sampling from Dirichlet mixture models, 2008) and implemented by Yau et al. (Journal of the Royal Statistical Society, Series B (Statistical Methodology) 73:37-57, 2011). We discuss the difficulties of achieving good mixing in MCMC samplers of this nature in large data sets and investigate sensitivity to initialisation. We additionally consider the challenges when an additional layer of hierarchy is added such that joint inference is to be made on [Formula: see text]. We introduce a new label-switching move and compute the marginal partition posterior to help to surmount these ...Continue Reading

References

Oct 6, 2010·Environmental Health Perspectives·Michail PapathomasPaolo Vineis
Jun 21, 2011·Journal of the Royal Statistical Society. Series B, Statistical Methodology·C YauC Holmes
Mar 20, 2015·Journal of Statistical Software·Silvia LiveraniSylvia Richardson
Jan 1, 2008·Journal of the American Statistical Association·David B DunsonAnna Maria Siega-Riz
Jan 1, 2009·Journal of the American Statistical Association·Jamie L Bigelow, David B Dunson

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Citations

Aug 9, 2016·Spatial and Spatio-temporal Epidemiology·Silvia LiveraniMarta Blangiardo
Dec 19, 2017·Statistics in Medicine·Chanmin KimLorenzo Cohen
Sep 18, 2018·Statistics and Computing·Riccardo Rastelli, Nial Friel

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PReMiuM R package

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