Bayesian Linear Regression with Conditional Heteroskedasticity

In this paper we consider adaptive Bayesian semiparametric analysis of the linear regression model in the presence of conditional heteroskedasticity. The distribution of the error term on predictors are modelled by a normal distribution with covariate-dependent variance. We show that a rate-adaptive procedure for all smoothness levels of this standard deviation function is performed if the prior is properly chosen. More specifically, we derive adaptive posterior distribution rate up to a logarithm factor for the conditional standard deviation based on a transformation of hierarchical Gaussian spline prior and log-spline prior respectively