Bayesian curve-fitting with free-knot splines. (English) Zbl 0986.62026

DiMatteo, Ilaria; Genovese, Christopher R.; Kass, Robert E.

Biometrika 88, No. 4, 1055-1071 (2001).

Summary: We describe a Bayesian method, for fitting curves to data drawn from an exponential family, that uses splines for which the number and locations of knots are free parameters. The method uses reversible-jump Markov chain Monte Carlo to change the knot configurations and a locality heuristic to speed up mixing. For nonnormal models, we approximate the integrated likelihood ratios needed to compute acceptance probabilities by using the Bayesian information criterion, BIC, under priors that make this approximation accurate.
Our technique is based on a marginalised chain on the knot number and locations, but we provide methods for inference about the regression coefficients, and functions of them, in both normal and nonnormal models. Simulation results suggest that the method performs well, and we illustrate the method in two neuroscience applications.

MSC:

62G08	Nonparametric regression and quantile regression
65C40	Numerical analysis or methods applied to Markov chains
62F15	Bayesian inference
62P10	Applications of statistics to biology and medical sciences; meta analysis

Keywords:

smoothing; unit-information prior; magnetic resonance imaging; neuron firing data; reversible-jump Markov chain Monte Carlo; BIC