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

We consider the question of Markov chain Monte Carlo sampling from a general stick-breaking Dirichlet process mixture model, with concentration parameter α . This paper introduces a Gibbs sampling algorithm that combines the slice sampling approach of Walker (Communications in Statistics - Simulatio...

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Vydáno v:Statistics and computing Ročník 25; číslo 5; s. 1023 - 1037
Hlavní autoři: Hastie, David I., Liverani, Silvia, Richardson, Sylvia
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.09.2015
Témata:
Algorithms
Artificial Intelligence
Computation
Computer simulation
Dirichlet problem
Mathematical models
Mathematics and Statistics
Probability and Statistics in Computer Science
Sampling
Source code
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Mixture model
Profile regression
Dirichlet process
Bayesian clustering
ISSN:0960-3174, 1573-1375
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Shrnutí:We consider the question of Markov chain Monte Carlo sampling from a general stick-breaking Dirichlet process mixture model, with concentration parameter α . 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 α . We introduce a new label-switching move and compute the marginal partition posterior to help to surmount these difficulties. Our work is illustrated using a profile regression (Molitor et al. Biostatistics 11(3):484–498, 2010 ) application, where we demonstrate good mixing behaviour for both synthetic and real examples.
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ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-014-9471-3