Bayesian adaptive penalized splines in nonparametric regression and in spectral time series analysis

A Bayesian approach to nonparametric regression using Penalized splines (P-splines) is presented. The approach uses the linear mixed model formulation of P-spines. The usual model assumes a single value for the smoothing parameter controlling the amount of smoothing of the fitted function. The main focus of the thesis is on spatially adaptive smoothing where the smoothing parameter is a function of the covariate so that different amounts of smoothing are applied in different regions of the covariate. An application to spectral time series analysis will be demonstrated. Markov chain Monte Carlo methods are used to make inference based on the posterior distribution.