Model selection: Bayes and Frequentist perspective

We discuss model selection, both from a Bayes and Classical point of view. Our presentation introduces a novel point of view about goals and methods of model selection. Our hope is that this will introduce a logical overview connecting all model selection rules. We start with old Bayes and Classical rules like AIC and BIC, then develop some new theory and a new novel Bayes strategy within this discussion. We introduce some new definitions of consistency and results and conjectures about consistency in high dimensional model selection problems. For model selection with Cross-validatory Bayes Factor, we show that when the number of parameters tends to infinity at a smaller rate than sample size, to achieve consistency it is best to use most of the data for inference and only a negligible proportion to result in a proper prior. In Chapter 2 we take up a major method of Bayes model selection, namely, Path Sampling (PS) for detailed study via new theorems and novel diagnostics, finally leading to a new method PS-SC. Most of this chapter contains new material. In the last two chapters we consider classical model selection. We first provide a new approach to selection for SNP\u27s of great interest in Bioinformatics as well as model selection methodology in high dimensional linear models. Our last chapter is a contribution to model selection in nonparametric regression. We take up model selection for variable selection in this context. We believe this has the potential to improve model selection in more traditional areas where LASSO and its modification are very popular. This will require much further work