Independence testing using bivariate splines in Bayes Space

Specialeforsvar: Emil Jakob Skindersø

Titel: Independence testing using bivariate splines in Bayes Space

Abstract: This project is about the statistical analysis of density functions. Based on Aitchison geometry, new metrics and inner products are defined specifically for densities. Density functions are considered as elements in a Bayes space of probability measures with associated densities, where the geometric properties of the space can be used to formulate independence through decomposition of bivariate densities into independence and interaction parts. The decomposition allows the definition of novel tests of independence, and two such tests are introduced, used, and discussed in this project. The first test is based on the relative norm of the interaction part, termed Relative Simplicial Deviance (RSD), and is compared with other independence tests (Spearman correlation, Hilbert-Schmidt Information Criterion, copulas and 2-test of independence) in a simulation study. The test is applied in a variety of settings, including simulations and an analysis of ice cores from Greenland. In the analysis, the RSD is used as a summary to examine the difference in distribution between cold and mild periods during the latest ice age. The second test is designed for a setting with several different observed densities and is applied to a financial data set of respondents’ expectation of inflation versus their expectation for changes in housing prices. Both tests show reasonable and expected behaviour in all applications.

Vejleder: Helle Sørensen
Censor:    Ege Rubak, Aalborg Universitet