The use of spline, Bayesian spline and penalized Bayesian spline regression for modeling

The nonparametric regression methods which are called spline, penalized spline and Bayesian spline bring great advantages such as not depending on the fixed model and flexibility in modeling. In particular, penalized spline regression uses the idea of nonparametric spline smoothing and it is in fact just a generalization of smoothing splines that should allow more flexibility in a choice of the spline model, the basis functions, and the penalty. In this study, distribution graph of ratios of export to import in Turkey is modeled using the nonparametric regression methods that are spline and Bayesian spline regression. For both methods, the knot sequence coincides with the end points of the interval. The results of these regression models are compared and interpreted. Then, we focus on a penalized spline regression with Bayesian perspective on the same data set and the smoothing for a variety of lambda values is performed. In addition, the contribution of a prior distribution is explained to determine the smoothing parameter. Then, we propose a new smoothing parameter by using the amount of information contained in the normal distribution. It has been observed that this parameter is very sensitive against small changes. This result denotes that the proposed smoothing parameter we obtained is appropriate for using in the penalized Bayesian spline regression applications. Keywords: Spline function, bayesian spline regression, penalized bayesian spline regression, mcmc, smoothing parameter.