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Models for heteroskedastic data are relevant in a wide variety ofapplications ranging from financial time series to environmental statistics.However, the topic of modeling the variance function conditionally has not seennear as much attention as modeling the mean. Volatility models have been usedin specific applications, but these models can be difficult to fit in aBayesian setting due to posterior distributions that are challenging to samplefrom efficiently. In this work, we introduce a general model forheteroskedastic data. This approach models the conditional variance in a mixedmodel approach as a function of any desired covariates or random effects. Werely on new distribution theory in order to construct priors that yield fullyconjugate full conditional distributions. Thus, our approach can easily be fitvia Gibbs sampling. Furthermore, we extend the model to a deep learningapproach that can provide highly accurate estimates for time dependent data. Wealso provide an extension for heavy-tailed data. We illustrate our methodologyvia three applications. The first application utilizes a high dimensional soildataset with inherent spatial dependence. The second application involvesmodeling of asset volatility. The third application focuses on clinical trialdata for creatinine.

A General Bayesian Model for Heteroskedastic Data with Fully Conjugate Full-Conditional Distributions