T\here is a very simple algorithm for the inference of posteriors for probability models on trees. This algorithm, known as “Belief Propagation” is widely used in coding theory, in machine learning, in evolutionary inference, among many other areas. The talk will be devoted to the analysis of Belief Propagation in some of the simplest probability models. We will highlight the interplay between Belief Propagation, linear estimators (statistics), the Kesten-Stigum bound (probability) and Replica Symmetry Breaking (statistical physics). We will show how the analysis of Belief Propagation allowed to proof phase transitions for phylogenetic reconstruction in evolutionary biology and develop optimal algorithms for inference of block models. Finally, we will discuss the computational complexity of this “simple” algorithm.

**Date**: 17 October 2019, 16:00 (Thursday, 1st week, Michaelmas 2019)**Venue**: 24-29 St Giles'

24-29 St Giles' OX1 3LBSee location on maps.ox**Details**: Large Lecture Theatre, Department of Statistics**Speaker**: Professor Elchanan Mossel (MIT Statistics + Data Center)**Organising department**: Department of Statistics**Organiser**: Professor Patrick Rebeschini (University of Oxford)**Organiser contact email address**: lane@stats.ox.ac.uk**Part of**: Annual Joint Maths/Stats Colloquium**Booking required?**: Not required**Audience**: Members of the University only- Editor: Beverley Lane