Bayesian semiparametric analysis of multivariate continuous responses, with variable selection
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We develop models for multivariate Gaussian responses with nonparametric models for the means, the variances and the correlation matrix, with automatic variable selection based on spike-slab priors. We use the separation strategy to factorize the covariance matrix of the multivariate responses into a product of matrices involving the variances and the correlation matrix. We model the means and the logarithm of the variances nonparametrically, utilizing radial basis function expansion. We describe parametric and nonparametric models for the correlation matrix. The parametric model assumes a normal prior for the elements of the correlation matrix, constrained to lie in the space of correlation matrices while the nonparametric model is utilizes Dirichlet process mixtures of normal distributions. We discuss methods for posterior sampling and inference and present results from a simulation study and two applications. The software we implemented can handle response vectors of arbitrary dimension and it is freely available via R package BNSP.
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