Introduction

In this Chapter, we provide all the necessary background to work with entropy measures for environmental data. Section 1.1 is devoted to the basic principles of entropy, initially introduced in Information Theory: we focus on the original entropy formula for categorical variables, and on its decomposition, that contains the potential for the extension to spatial entropy. The second Section focuses on environmental studies and provides some necessary background tools for spatial data analysis. Then, examples are given covering some environmental applications of entropy measures: a few datasets are introduced, ascribing to different fields of application, that will guide the reader to the case studies of the following Chapters. Afterwards, a brief introduction to Bayesian modelling and inference is given, together with a presentation of a recent approach to accurate and fast approximation for model fitting known as Integrated Nested Laplace Approximation; such Section, devoted to modelling, is more technical and needs solid statistical background; it can be skipped without affecting the rest of the Chapter, as it is specifically intended for a deep understanding of the contents of Chap. 4 only. The present Chapter concludes with a Section about the statistical software R, and one with the necessary preliminary information to get started with the practical and computational work.