Lectures on Probability Theory and Statistics
Ecole d'Eté de Probabilités de Saint-Flour XXXI - 2001
This volume contains lectures given at the 31st Probability Summer School in Saint-Flour (July 8-25, 2001). Simon Tavaré’s lectures serve as an introduction to the coalescent, and to inference for ancestral processes in population genetics. The stochastic computation methods described include rejection methods, importance sampling, Markov chain Monte Carlo, and approximate Bayesian methods. Ofer Zeitouni’s course on "Random Walks in Random Environment" presents systematically the tools that have been introduced to study the model. A fairly complete description of available results in dimension 1 is given. For higher dimension, the basic techniques and a discussion of some of the available results are provided. The contribution also includes an updated annotated bibliography and suggestions for further reading. Olivier Catoni's course appears separately.
Simon Tavare holds the George and Louise Kawamoto Chair in Biological Sciences and is a Professor of Biological Sciences, Mathematics, and Preventive Medicine at the University of Southern California. Professor Tavare's research lies at the interface between statistics and biology, specifically focusing on problems arising in molecular biology, human genetics, population genetics, molecular evolution, and bioinformatics. His statistical interests focus on stochastic computation. Among the applications are linkage disequilibrium mapping, stem cell evolution, and inference in the fossil record. Dr. Tavare is also a professor in the Department of Oncology at the University of Cambridge, England, where his group concentrates on cancer genomics.