This book shows how to successfully adapt entropy measures to the complexity of environmental data. It also provides a unified framework that covers all main entropy and spatial entropy measures in the literature, with suggestions for their potential use in the analysis of environmental data such as biodiversity, land use and other phenomena occurring over space or time, or both.First, recent literature reviews about including spatial information in traditional entropy measures are presented, highlighting the advantages and disadvantages of past approaches and the difference in interpretation of their proposals. A consistent notation applicable to all approaches is introduced, and the authors' own proposal is presented. Second, the use of entropy in spatial sampling is focused on, and a method with an outstanding performance when data show a negative or complex spatial correlation is proposed. The last part of the book covers estimating entropy and proposes a model-based approachthat differs from all existing estimators, working with data presenting any departure from independence: presence of covariates, temporal or spatial correlation, or both. The theoretical parts are supported by environmental examples covering point data about biodiversity and lattice data about land use. Moreover, a practical section is provided for all parts of the book; in particular, the R package SpatEntropy covers not only the authors' novel proposals, but also all the main entropy and spatial entropy indices available in the literature. R codes are supplemented to reproduce all the examples. This book is a valuable resource for students and researchers in applied sciences where the use of entropy measures is of interest and where data present dependence on space, time or covariates, such as geography, ecology, biology and landscape analysis.

Autorentext

Dr.Linda Altieri is a senior assistant professor in the Department of Statistical Sciences of the University of Bologna, after having served as a research fellow there. She has a bachelor's degree in political science, a master's and a Ph.D. in statistics. She completed her M.D. thesis and part of her Ph.D. project in the University of Glasgow, with short-term visits at the University of St. Andrews, and she has taken part in many national and international statistical conferences. In 2021, she obtained the National Scientific Qualification, an official Italian recognition for university professor position recruiting, based on scientific qualification criteria. Her research interests include Bayesian spatial modelling applied to environmental data, especially point process data, and diversity and entropy measures with a focus on urban data. She also works on temporal point processes for capture-recapture data with behavioural responses. She teaches statistics in diplomatic and international science and economics courses as well as environmental statistics in statistics and math courses. She has authored many papers and has been a reviewer in reputed journals of statistics.Professor Daniela Cocchi has been a full professor in the Department of Statistical Sciences of the University of Bologna since 1994. She has a Ph.D. in statistics from the Université Catholique de Louvain (Belgium). She has been a member of several scientific committees and councils of national and international statistical associations, an editor of statistical journals and principal investigator of a number of projects. From 2014 to 2016, she was a member of the Committee for Research Evaluation for the University of Bologna. From 2015 to 2022, she covered a number of positions within the Italian National Institute of Statistics (ISTAT), the most recent being as a coordinator of the ISTAT Methodology Advisory Committee. From 2017 to 2020, she was the principal investigator of an interdisciplinary project for statistical applications to environmental data (EPHASTAT), funded by the Italian Ministry of Education, Universities and Research. Since 2021, she has been a member of the European Statistical Governance Advisory Board (ESGAB). Her scientific research includes methods for finite population sampling and Bayesian spatial modelling, diversity measures and applications to environmental and epidemiological data. She has authored many papers in reputed journals of statistics and is active in promoting contacts with institutions interested in statistical analysis. Her teaching activities at the University of Bologna include Bayesian statistics, survey sampling and record linkage in undergraduate, master's and Ph.D. courses.