Elchanan Mossel: Combinatorial Statistics and the Sciences

Explore a comprehensive lecture on combinatorial statistics and its applications in various scientific fields. Delve into the intricacies of broadcast on trees, probability and statistics of dependent variables, and their connections to phylogenetic inference in biology. Examine the block model conjecture and its implications, while gaining insights into linearization of belief propagation and non-backtracking random walks. Discover how these concepts relate to the cavity and replica method, and understand the fractal argument through visual representations. Reflect on the depth of data analysis and consider future directions in this fascinating field of study.

Intro
Combinatorial Statistics
Broadcast on Trees
Probability and Statistics of Dependent Variables
Connection 1: Phylogenetic Inference in Biology
Broadcasting on trees and Phylogenetics
The Phylogenetic Phase Transition for q-2
Connection 2: The Block Model Conjecture
The Block Model in pictures
Intuition: Coupling with the Tree Process
Linearization of BP and Non-Backtracking Random Walks
Breaking the kesten Stigum Barrier
Connection: The Cavity and Replica Method
A Fractal Argument in Pictures
A Reflection on Depth in Data
Future Directions