Open Access
September 2019 Low Information Omnibus (LIO) Priors for Dirichlet Process Mixture Models
Yushu Shi, Michael Martens, Anjishnu Banerjee, Purushottam Laud
Bayesian Anal. 14(3): 677-702 (September 2019). DOI: 10.1214/18-BA1119


Dirichlet process mixture (DPM) models provide flexible modeling for distributions of data as an infinite mixture of distributions from a chosen collection. Specifying priors for these models in individual data contexts can be challenging. In this paper, we introduce a scheme which requires the investigator to specify only simple scaling information. This is used to transform the data to a fixed scale on which a low information prior is constructed. Samples from the posterior with the rescaled data are transformed back for inference on the original scale. The low information prior is selected to provide a wide variety of components for the DPM to generate flexible distributions for the data on the fixed scale. The method can be applied to all DPM models with kernel functions closed under a suitable scaling transformation. Construction of the low information prior, however, is kernel dependent. Using DPM-of-Gaussians and DPM-of-Weibulls models as examples, we show that the method provides accurate estimates of a diverse collection of distributions that includes skewed, multimodal, and highly dispersed members. With the recommended priors, repeated data simulations show performance comparable to that of standard empirical estimates. Finally, we show weak convergence of posteriors with the proposed priors for both kernels considered.


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Yushu Shi. Michael Martens. Anjishnu Banerjee. Purushottam Laud. "Low Information Omnibus (LIO) Priors for Dirichlet Process Mixture Models." Bayesian Anal. 14 (3) 677 - 702, September 2019.


Published: September 2019
First available in Project Euclid: 11 June 2019

zbMATH: 1421.62078
MathSciNet: MR3960766
Digital Object Identifier: 10.1214/18-BA1119

Keywords: Bayesian nonparametric methods , Density estimation , Dirichlet process mixture model , low-information prior , Survival analysis

Vol.14 • No. 3 • September 2019
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