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

• DOI: 10.1007/s11222-014-9471-3
• Publication Date: 2014-05-02T07:32:36Z
• Authors: David I. Hastie; Silvia Liverani; Sylvia Richardson
• Keywords: Dirichlet Process; Implementation

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 Gibbs algorithm that combines slice approach Walker (Communications in Statistics - Simulation and Computation 36:45-54, 2007) retrospective Papaspiliopoulos Roberts (Biometrika 95(1):169-186, 2008). Our is implemented as efficient open source C++ software, available an R package, based on blocking strategy similar to suggested by (A note posterior models, 2008) Yau et al. (Journal Royal Statistical Society, Series B (Statistical Methodology) 73:37-57, 2011). discuss difficulties achieving good mixing MCMC samplers this nature large data sets investigate sensitivity initialisation. additionally challenges when additional layer hierarchy added such joint inference be made introduce new label-switching move compute marginal partition help surmount these difficulties. work illustrated using profile regression (Molitor Biostatistics 11(3):484-498, 2010) application, where we demonstrate behaviour for both synthetic real examples.