Bayesian Conditional Transformation Models

Recent developments in statistical regression methodology shift away from pure mean toward distributional models. One important strand thereof is that of conditional transformation models (CTMs). CTMs infer the entire distribution directly by applying a function to response conditionally on set covariates simple log-concave reference distribution. Thereby, allow not only variance, kurtosis or skewness but complete depend explanatory variables. We propose Bayesian notion (BCTMs) focusing exactly observed continuous responses, also incorporating extensions randomly censored and discrete responses. Rather than relying Bernstein polynomials have been considered likelihood-based CTMs, we implement spline-based parameterization for monotonic effects are supplemented with smoothness priors. Furthermore, able benefit paradigm via easily obtainable credible intervals other quantities without large sample approximations. A simulation study demonstrates competitiveness our approach against its counterpart additive location, scale shape quantile regression. Two applications illustrate versatility BCTMs problems involving real world data, again including comparison various types competitors. Supplementary materials this article available online.