ABSTRACT
This chapter introduces the principles of confidence interval estimation. We essentially focus on the Bayesian approach for confidence interval estimation because of its efficiency and natural interpretation that provides its wide applicability in statistical practice. However, the comments shown in this chapter can be easily adapted to the frequentist framework of confidence interval (or region) estimation. The following approaches are considered: (1) the equal-tailed confidence interval estimation; and (2) the highest posterior density confidence interval estimation. An optimal property of Method (2) is derived.
Chapter 9 provides novel concepts regarding p-values-based considerations in statistical practice. We introduce the expected p-value (EPV) approach. This approach is extended in order to compare different test procedures, e.g. a Wilcoxon rank-sum test versus Student's t-test. We prove that there is a strong association between the EPV concept and the well-known receiver operating characteristic (ROC) curve methodology (Chapter 7). In parallel with the ROC curve methodology, we develop a partial expected p-value and a novel method for visualizing the properties of statistical tests in an ROC curve framework. We prove that the conventional power characterization of tests is a partial aspect of the presented EPV/ROC technique. Corresponding R codes are provided.
