Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information
Rosa Bernardini Papalia · Journal of the Royal Statistical Society Series A (Statistics in Society) · 2019
This book presents tools and principles of information theory as a solution to analyse insufficient information for inference, model and theory building. Info-metrics is a term that was coined in 2009 by the author for an approach based on maximum entropy for constrained optimization. This book is a good mixture of theory and practical applications. It could be of interest for researchers, university professors and graduate students in the area of probability and statistics and their applications, such as neural networks, data mining and ‘big data’ analysis. The topics of the applications are well chosen; they represent contemporary tendencies in statistical science including a broad range of related subject material and interesting topics, from classical to modern. The tools and techniques that are presented here can be applied in various disciplines like finance, banking, economics, accounting, marketing, social and health sciences and even to areas like psychology, engineering, and medicine. The book covers many cross-disciplinary case-studies, as well as numerous applied empirical illustrations of the info-metrics methods. Inference from both quantitative and qualitative information, including experimental and non-experimental data, information embedded in theory and all types of mixed information stemming from varied sources or assumptions, represents a core issue in all the case-studies presented. The first chapter contains a chart illustrating the logical dependences among the remaining 13 chapters. An order in reading the chapters is provided for core chapters but also for readers who are interested in modelling and estimation topics or multidisciplinary examples and case-studies. Those relevant to the core framework are Chapters 3, 4, 8 and 9; Chapters 5, 6 and 14 are devoted solely to examples. Each chapter contains exercises and extended problems, and ends with a notes section summarizing the main references. Most of these exercises deal with real life applications and the book is complemented by a web site (http://infometrics.org) that provides useful code and data sets (or links to the data) for the main applications and examples that are presented in the book. The critical question of how to incorporate prior information in the info-metrics framework is emphasized by exploring different approaches and by encompassing specific problems in the social sciences. The book extends the info-metrics techniques to different settings, such as those with continuous and discrete dependent variables, flow data and panel data, by addressing the misspecification model issues that are very common in social and behavioural sciences where the researcher does not have sufficient information to determine the functional form of the structure to be inferred. The author develops a unified constrained optimization framework for modelling and making informed decisions when dealing with limited, complex or insufficient information. The book also connects the info-metrics framework with a wide range of alternative traditional statistical methods of inference, and applied modelling situations involving different circumstances. The book presents the development of simple common language and mathematical notation to promote the use of info-metrics methods across different disciplines and also to favour the exchange of ideas across many scientific fields. As such, there are more than good reasons why it should be strongly recommended to potential readers and users. The book has a clear structure and is understandable given undergraduate statistical prerequisites. It also represents a complete reference book for target audiences of graduate students, researchers and instructors.