Bayesian Conditional Transformation Models

12/20/2020
by   Manuel Carlan, et al.
0

Recent developments in statistical regression methodology establish flexible relationships between all parameters of the response distribution and the covariates. This shift away from pure mean regression is just one example and is further intensified by conditional transformation models (CTMs). They aim to infer the entire conditional distribution directly by applying a transformation function that transforms the response conditionally on a set of covariates towards a simple log-concave reference distribution. Thus, CTMs allow not only variance, kurtosis and skewness but the complete conditional distribution function to depend on the explanatory variables. In this article, we propose a Bayesian notion of conditional transformation models (BCTM) for discrete and continuous responses in the presence of random censoring. Rather than relying on simple polynomials, we implement a spline-based parametrization for monotonic effects that are supplemented with smoothness penalties. Furthermore, we are able to benefit from the Bayesian paradigm directly via easily obtainable credible intervals and other quantities without relying on large sample approximations. A simulation study demonstrates the competitiveness of our approach against its likelihood-based counterpart, most likely transformations (MLTs) and Bayesian additive models of location, scale and shape (BAMLSS). Three applications illustrate the versatility of the BCTMs in problems involving real world data.

READ FULL TEXT
research
05/11/2020

Fast Bayesian Inference in Nonparametric Double Additive Location-Scale Models With Right- and Interval-Censored Data

Penalized B-splines are routinely used in additive models to describe sm...
research
05/17/2022

Bayesian Discrete Conditional Transformation Models

We propose a novel Bayesian model framework for discrete ordinal and cou...
research
06/07/2019

Multivariate Conditional Transformation Models

Regression models describing the joint distribution of multivariate resp...
research
07/06/2019

XGBoostLSS -- An extension of XGBoost to probabilistic forecasting

We propose a new framework of XGBoost that predicts the entire condition...
research
01/04/2020

CatBoostLSS – An extension of CatBoost to probabilistic forecasting

We propose a new framework of CatBoost that predicts the entire conditio...
research
12/20/2017

Transformation Models in High-Dimensions

Transformation models are a very important tool for applied statistician...
research
05/09/2012

Improved Mean and Variance Approximations for Belief Net Responses via Network Doubling

A Bayesian belief network models a joint distribution with an directed a...

Please sign up or login with your details

Forgot password? Click here to reset