Generative Supervised Classification Using Dirichlet Process Priors.

Choosing the appropriate parameter prior distributions associated to a given Bayesian model is a challenging problem. Conjugate priors can be selected for simplicity motivations. However, conjugate priors can be too restrictive to accurately model the available prior information. This paper studies a new generative supervised classifier which assumes that the parameter prior distributions conditioned on each class are mixtures of Dirichlet processes. The motivations for using mixtures of Dirichlet processes is their known ability to model accurately a large class of probability distributions. A Monte Carlo method allowing one to sample according to the resulting class-conditional posterior distributions is then studied. The parameters appearing in the class-conditional densities can then be estimated using these generated samples (following Bayesian learning). The proposed supervised classifier is applied to the classification of altimetric waveforms backscattered from different surfaces (oceans, ices, forests, and deserts). This classification is a first step before developing tools allowing for the extraction of useful geophysical information from altimetric waveforms backscattered from nonoceanic surfaces

Using Dirichlet Process Priors For Bayesian Mixture Clustering

We describe a non-parametric Bayesian model using genotype data to classify individuals among populations where the total number of populations is unknown. The model assumes that a population is characterized by a set of allele frequencies that follow multinomial distributions. The Dirichlet Process is applied as the prior distribution. The method estimates the number of populations together with the allele frequencies and the ancestry coefficients of each individual. Distance matrices and bootstrap support numbers based on MCMC runs are generated to create a phylogeny of the ancestral populations

Spiked Dirichlet Process Priors for Gaussian Process Models

We expand a framework for Bayesian variable selection for Gaussian process (GP) models by employing spiked Dirichlet process (DP) prior constructions over set partitions containing covariates. Our approach results in a nonparametric treatment of the distribution of the covariance parameters of the GP covariance matrix that in turn induces a clustering of the covariates. We evaluate two prior constructions: the first one employs a mixture of a point-mass and a continuous distribution as the centering distribution for the DP prior, therefore, clustering all covariates. The second one employs a mixture of a spike and a DP prior with a continuous distribution as the centering distribution, which induces clustering of the selected covariates only. DP models borrow information across covariates through model-based clustering. Our simulation results, in particular, show a reduction in posterior sampling variability and, in turn, enhanced prediction performances. In our model formulations, we accomplish posterior inference by employing novel combinations and extensions of existing algorithms for inference with DP prior models and compare performances under the two prior constructions