From Statistical Physics to Data-Driven Modelling

Today’s science is characterised by an ever-increasing amount of data, due to instrumental and experimental progress in monitoring and manipulating complex systems made of many microscopic constituents. How can we make sense of such data, and use them to enhance our understanding of biological, physical, chemical, … systems? The primary objective of this textbook is to introduce the concepts and methods, at the crossroad between probability theory, statistics, optimisation, statistical physics, inference and machine learning, necessary to answer this question. The second objective of this book is to provide practical applications for these methods, which will allow students to really assimilate the underlying ideas and techniques. Most of the applications we propose here are related to biology, as they were part of a course to Master of Science students specialised in biophysics. The book's companion web site contains all the data sets necessary for the tutorials presented in the book, as well as other applications. The material presented here is accessible to MSc students in physics, in applied maths and computational biology. Readers will need basic knowledge in programming (Python or some equivalent language) for the applications. Emphasis is not put on mathematical rigour, but on the development of intuition and the deep connections with statistical physics. Our major goal is that students will be able to understand the mathematics behind the methods, and not act as mere consumers of statistical packages!