Bayesian Density Estimation and Inference Using Mixtures-英文文献.pdf

Bayesian Density Estimation and Inference Using Mixtures By Michael D Escobar Mike West Departmen t of Statistics Institute of Statistics University of Toronto Decision Sciences Toronto Ontario MS A Duke University CANADA Durham NC ABSTRA CT We describ e and illustrate Bayesian inference in mo dels for density estimation using mix tures of Dirichlet pro cesses These mo dels provide natural settings for density estimation and are exemplied by sp ecial cases where data are mo delled as a sample from mixtures of normal distributions Ecient simulation metho ds are used to approximate various prior p osterior and predictive distributions This allows for direct inference on a variety of prac tical issues including problems of lo cal versus global smo othing uncertainty ab out density estimates assessment of mo dality and the inference on the numb ers of comp onents Also convergence results are established for a general class of normal mixture mo dels Keywords Kernel estimation Mixtures of Dirichlet pro cesses Multimo dality Normal mixtures Posterior sampling Smo othing parameter estimation Michael D Escobar is Assistant Professor Department of Statistics and Department of Preven tive Medicine and Biostatistics University of Toronto MS A Canada Mike West is Professor and Director Institute of Statistics and Decision Sciences Duke University Durham NC Michael D Escobar was partially nanced by National Cancer Institute R OCA a National Research Service Award from NIMH Grant MH and by the National Science and Engineering Research Council