Many multivariate statistics are expressed as functions of the hypergeometric function of a matrix argument, or more generally, as series of Jack functions. This work is a collection of formulas, identities, and algorithms useful for the computations of these statistics in practice. Numerical examples are presented. 1. Definitions 1.1. Partitions and hook lengths. For an integer k ≥ 0 we say th...

In this article, we discuss our attempt to teach applied statistics techniques typically taught in advanced courses, such as clustering and principal component analysis, a non-mathematical educated audience. Considering the negative attitude inclination toward mathematical disciplines of students introduce them topics using four different games. The games are all user-centric, score-based arcad...

Abstract As mentioned in the previous chapter, industrial data are usually divided into two categories, process and quality data, belonging to different measurement spaces. The vast majority of smart manufacturing problems, such as soft measurement, control, monitoring, optimization, etc., inevitably require modeling relationships between kinds variables. This chapter’s subject is discover corr...