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

Abstract

Penalized B-splines are routinely used in additive models to describe smooth changes in a response with quantitative covariates. It is typically done through the conditional mean in the exponential family using generalized additive models with an indirect impact on other conditional moments. Another common strategy consists in focussing on several low-order conditional moments, leaving the complete conditional distribution unspecified. Alternatively, a multi-parameter distribution could be assumed for the response with several of its parameters jointly regressed on covariates using additive expressions. Our work can be connected to the latter proposal for a right- or interval-censored continuous response with a highly flexible and smooth nonparametric density. We focus on location-scale models with additive terms in the conditional mean and standard deviation. Starting from recent results in the Bayesian framework, we propose a quickly converging algorithm to select penalty parameters from their marginal posteriors. It relies on Laplace approximations to the conditional posterior of the spline parameters. Simulations suggest that the so-obtained estimators own excellent frequentist properties and increase efficiency as compared to approaches with a working Gaussian hypothesis. We illustrate the methodology with the analysis of imprecisely measured income data.