Rate Distortion Theory for Descriptive Statistics

Abstract: Rate distortion theory was developed for optimizing lossy compression of data, but it also has a lot of applications in statistics. In this paper we will see how rate distortion theory can be used to analyze a complicated data set involving orientations of early Islamic mosques. The analysis involves testing, identification of outliers, choice of compression rate, calculation of optimal reconstruction points, and assigning "descriptive confidence regions" to the reconstruction points. In this paper the focus will be on the methods, so the integrity of the data set and the interpretation of the results will not be discussed.