Predictive information criterion for nonlinear regression model based on basis expansion methods

MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」Nonlinear regression modeling based on basis expansions has been widely used to explore data with complex structure. A crucial issue in nonlinear regression model is the choice of adjusted parameters including hyper-parameters for prior distribution and the number of basis functions. The selection of these parameters can be viewed as a model selection and evaluation problem. We derive an information criterion for the Bayesian predictive distribution in the case of both of regression coefficient and variance are unknown. Our proposed method make a selection of the appropriate value of hyper-parameters and the number of basis functions. Real data and simulation data analysis show that our proposed modeling strategy performs well in various situations