| The Bayesian meta-Gaussian model arises when the multivariate density functions input into Bayes theorem come from the meta-Gaussian family. Bayes theorem provides the optimal theoretic structure for obtaining the probability distribution of a predictand, conditional on the realization of a vector of predictors, while the meta Gaussian family of distribution functions allows the marginal distribution functions of the variates to take any form and the dependence structure between any two variates to be monotone nonlinear and heteroscedastic.; This work focuses on (1) developing practical procedures for estimating and validating the Bayesian meta-Gaussian model for a binary predictand and a continuous predictand, given a vector of continuous predictors, and (2) assessing, theoretically and empirically, the practical advantages that the model offers over some of the alternative models for data analysis and probabilistic forecasting. For the binary predictand, the alternative models are the Model Output Statistics and the logistic regression. For the continuous predictand, the alternative models are the multiple linear regression and the quantile regression. The theoretical and empirical assessments show that the Bayesian meta-Gaussian model offers significant advantages over the alternative models in terms of ease of development, superior calibration and informativeness, and meaningful interpretation of forecasts, especially when the variates are not Gaussian and the dependence structure among the variates is nonlinear and heteroscedastic. |
