Bayesian estimation of number and position of knots in regression splines

Regression splines, based on piecewise polynomials, are useful tools to model departures from linearity in the regression context. The number and location of the knots can be of interest in many contexts since they can detect possible change points in the relationship between the variables. This work is focused on the estimate of both number and location of knots in the simple case where linear truncated splines are chosen to represent the relationship, in this case, the position of the knot detects a change in the slope. In a Bayesian context, we propose a two-step procedure, to first determine the true number of knots and then to fit the final model estimating simultaneously location of knots and regression and spline coefficients.