Spline smoothing in non- or semiparametric regression models is usually based on the roughness penalty approach. For regression with normal errors, the spline smoother also has a Bayesian justification: Placing a smoothness prior over the regression function, it is the mean of the posterior...

Elementary Bayesian Statistics is a thorough and easily accessible introduction to the theory and practical application of Bayesian statistics. It presents methods to assist in the collection, summary and presentation of numerical data. Bayesian statistics are becoming an increasingly important...

In applications, the linear multiple regression model is often modified to allow for nonlinearity in an independent variable. It is argued here that in practice it may often be desirable to specify a Bayesian prior that the unknown functional form is "simple" or "uncomplicated" rather than to...