Bayesian Inference of a Non normal Multivariate Partial Linear Regression Model

Bayesian Inference for the Multivariate Normal

Bayesian inference for the multivariate Normal is most simply instantiated using a Normal-Wishart prior over the mean and covariance. Predictive densities then correspond to multivariate T distributions, and the moments from the marginal densities are provided analytically or via Monte-Carlo sampling. We show how this textbook approach is applied to a simple two-dimensional example.

Bayesian regression with multivariate linear splines

A Bayesian Multivariate Functional Dynamic Linear Model

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data—functional, time dependent, and multivariate components—we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization fr...

Bayesian inference for the multivariate skew-normal model: A population Monte Carlo approach

Frequentist and likelihood based methods of inference encounter several difficulties with the multivariate skew-normal model. In spite of the popularity of this class of densities, there are no broadly satisfactory solutions for estimation and testing problems. In this paper we propose a general population Monte Carlo algorithm which exploits the stochastic representation of the skew-normal ran...

Bayesian multivariate logistic regression.

Bayesian analyses of multivariate binary or categorical outcomes typically rely on probit or mixed effects logistic regression models that do not have a marginal logistic structure for the individual outcomes. In addition, difficulties arise when simple noninformative priors are chosen for the covariance parameters. Motivated by these problems, we propose a new type of multivariate logistic dis...