Modeling and Analysis of Compositional Data

Preface

This book is an illustration of the adage collected by Thomas Fuller in Gnomologia (1732, Adage 560): All things are difficult, before they are easy and cited by John Aitchison (1986, Chapter 3). It has been a long way to arrive at this point, and there is still a long and not always easy way to go in the light of the insights presented here. Therefore, we dedicate this work to all those researchers who are not mainstream and have to struggle swimming against the tide.

These pages are based on lecture notes originally prepared as support to a short course on compositional data analysis. The first version of the notes dates back to the year 2000. Their aim was to transmit the basic concepts and skills for simple applications, thus setting the premises for more advanced projects. The notes were updated over the years, reflecting the evolution of our knowledge about the geometry of the sample space of compositional data. The recognition of the role of the sample space and its algebraic-geometric structure has been essential in this process. This book reflects the state of the art at the beginning of the year 2014. Its aim is still to introduce the reader into the basic concepts underlying compositional data analysis, but it goes far beyond an introductory text, as it includes advanced geometrical and statistical modeling. One should also be aware that the theory presented here is a field of active research. Therefore, the learning process can just start with this book, and ...