Algebraic and Geometric Methods in Statistics

This up-to-date account of algebraic statistics and information geometry explores the emerging connections between the two disciplines, demonstrating how they can be used in design of experiments and how they benefit our understanding of statistical models, in particular, exponential models. This book presents a new way of approaching classical statistical problems and raises scientific questions that would never have been considered without the interaction of these two disciplines. Beginning with a brief introduction to each area, using simple illustrative examples, the book then proceeds with a collection of reviews and some new results written by leading researchers in their respective fields. Part III dwells in both classical and quantum information geometry, containing surveys of key results and new material. Finally, Part IV provides examples of the interplay between algebraic statistics and information geometry. Computer code and proofs are also available online, where key examples are developed in further detail.

Professor Paolo Gibilisco is a Researcher in Mathematical Analysis in the School of Economics at the University of Rome 'Tor Vergata'.

Eva Riccomagno is Associate Professor in the Department of Mathematics at the University of Genova.

Maria Piera Rogantin is Associate Professor in the Department of Mathematics at the University of Genova.

Henry P. Wynn is Professor of Statistics at the London School of Economics from 2003, where he leads the Decision Support and Risk Group. He holds the Guy Medal in Silver from the Royal Statistical Society, is an Honorary Fellow of the Institute of Actuaries, and a Fellow of the Institute of Mathematical Statistics.