Bayesian curve-fitting with free-knot splines

We describe a Bayesian method, for fitting curves to data drawn from an exp onential family, that uses splines for which the number and locations of kn ots 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 r atios needed to compute acceptance probabilities by using the Bayesian info rmation criterion, BIC, under priors that make this approximation accurate. Our technique is based on a marginalised chain on the knot number and loca tions, but we provide methods for inference about the regression coefficien ts, 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.