TY - JOUR
T1 - Variance matrix priors for Dirichlet process mixture models with Gaussian kernels
AU - Jing, Wei
AU - Papathomas, Michail
AU - Liverani, Silvia
N1 - Funding: The first author would like to acknowledge the support of the School of Mathematics and Statistics, as well as CREEM, at the University of St Andrews, and the University of St Andrews St Leonard’s 7th Century Scholarship.
PY - 2024/9/15
Y1 - 2024/9/15
N2 - Bayesian mixture modelling is widely used for density estimation and clustering. The Dirichlet process mixture model (DPMM) is the most popular Bayesian non-parametric mixture modelling approach. In this manuscript, we study the choice of prior for the variance or precision matrix when Gaussian kernels are adopted. Typically, in the relevant literature, the assessment of mixture models is done by considering observations in a space of only a handful of dimensions. Instead, we are concerned with more realistic problems of higher dimensionality, in a space of up to 20 dimensions. We observe that the choice of prior is increasingly important as the dimensionality of the problem increases. After identifying certain undesirable properties of standard priors in problems of higher dimensionality, we review and implement possible alternative priors. The most promising priors are identified, as well as other factors that affect the convergence of MCMC samplers. Our results show that the choice of prior is critical for deriving reliable posterior inferences. This manuscript offers a thorough overview and comparative investigation into possible priors, with detailed guidelines for their implementation. Although our work focuses on the use of the DPMM in clustering, it is also applicable to density estimation.
AB - Bayesian mixture modelling is widely used for density estimation and clustering. The Dirichlet process mixture model (DPMM) is the most popular Bayesian non-parametric mixture modelling approach. In this manuscript, we study the choice of prior for the variance or precision matrix when Gaussian kernels are adopted. Typically, in the relevant literature, the assessment of mixture models is done by considering observations in a space of only a handful of dimensions. Instead, we are concerned with more realistic problems of higher dimensionality, in a space of up to 20 dimensions. We observe that the choice of prior is increasingly important as the dimensionality of the problem increases. After identifying certain undesirable properties of standard priors in problems of higher dimensionality, we review and implement possible alternative priors. The most promising priors are identified, as well as other factors that affect the convergence of MCMC samplers. Our results show that the choice of prior is critical for deriving reliable posterior inferences. This manuscript offers a thorough overview and comparative investigation into possible priors, with detailed guidelines for their implementation. Although our work focuses on the use of the DPMM in clustering, it is also applicable to density estimation.
KW - Bayesian non-parametrics
KW - Clustering
UR - http://arxiv.org/abs/2202.03946
U2 - 10.1111/insr.12595
DO - 10.1111/insr.12595
M3 - Article
VL - Early View
JO - International Statistical Review
JF - International Statistical Review
ER -