Bayesian regression with B-splines under combinations of shape constraints and smoothness properties

In this paper, we approach the problem of shape constrained regression from a Bayesian perspective. A B-splines basis is used to model the regression function. The smoothness of the regression function is controlled by the order of the B-splines, and the shape is controlled by the shape of an associated control polygon. Controlling the shape of the control polygon reduces to some inequality constraints on the spline coefficients. Our approach enables us to take into account combinations of shape constraints and to localize each shape constraint on a given interval. The performance of our method is investigated through a simulation study. Applications to a real data sets in food industry and Global Warming are provided.