Fast Bayesian inference using Laplace approximations in nonparametric double additive location-scale models with right- and interval-censored data

Penalized B-splines are commonly used in additive models to describe smooth changes in a response with quantitative covariates. This is usually done through the conditional mean in the exponential family using generalized additive models with an indirect impact on other conditional moments. Another common strategy is to focus on several low-order conditional moments, leaving the full 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. The latter proposal for a right- or interval-censored continuous response with a highly flexible and smooth nonparametric density is considered. The focus is on location-scale models with additive terms in the conditional mean and standard deviation. Starting from recent results in the Bayesian framework, a fast converging algorithm is proposed to select penalty parameters from their marginal posteriors. It is based on Laplace approximations of the conditional posterior of the spline parameters. Simulations suggest that the estimators obtained in this way have excellent frequentist properties and superior efficiencies compared to approaches with a working Gaussian assumption. The methodology is illustrated by the analysis of right- and interval-censored income data.