Locally Adaptive Nonparametric Binary Regression

TL;DR

This paper introduces a Bayesian nonparametric binary regression method that adaptively models data using mixtures of probit regressions with spline priors, offering enhanced flexibility over traditional methods.

Contribution

It presents a novel locally adaptive Bayesian estimator for binary regression that combines mixture models with spline priors, improving flexibility and adaptability.

Findings

Outperforms single spline estimators in simulations

Demonstrates effectiveness on real data examples

Provides a flexible, locally adaptive modeling framework

Abstract

A nonparametric and locally adaptive Bayesian estimator is proposed for estimating a binary regression. Flexibility is obtained by modeling the binary regression as a mixture of probit regressions with the argument of each probit regression having a thin plate spline prior with its own smoothing parameter and with the mixture weights depending on the covariates. The estimator is compared to a single spline estimator and to a recently proposed locally adaptive estimator. The methodology is illustrated by applying it to both simulated and real examples.