On Bayesian Curve Fitting Via Auxiliary Variables

TL;DR

This paper enhances Bayesian spline regression by introducing a flexible auxiliary variable approach that allows random knot locations, extends to non-Gaussian errors, and connects to change-point detection, improving model adaptability.

Contribution

It develops a modified auxiliary variable method for Bayesian spline fitting with random knots and non-Gaussian errors, along with a new MCMC algorithm.

Findings

Improved performance over existing methods in simulated data.

Effective handling of non-Gaussian error models.

Connection established between change-point problems and variable selection.

Abstract

In this article we revisit the auxiliary variable method introduced in Smith and kohn (1996) for the fitting of P-th order spline regression models with an unknown number of knot points. We introduce modifications which allow the location of knot points to be random, and we further consider an extension of the method to handle models with non-Gaussian errors. We provide a new algorithm for the MCMC sampling of such models. Simulated data examples are used to compare the performance of our method with existing ones. Finally, we make a connection with some change-point problems, and show how they can be re-parameterised to the variable selection setting.