Professor of Statistics
Have you heard about the phenomenon that everyone is six handshakes away from the President? The six degrees of separation hypothesis relates to a model of social interactions that is phrased in terms of a network - individuals are nodes, and two individuals are linked if they know each other. Networks pop up in a variety of contexts, and recently much attention has been given to the randomness in such networks. My main research interest at the moment are network statistics to investigate such networks in a statistically rigorous fashion. Often this will require some approximation, and approximations in statistics are another of my research interests. It turns out that there is an excellent method to derive distances between the distributions of random quantities, namely Stein's method, a method I have required some expertise in over the years. The general area of my research falls under the category Applied Probability and many of the problems and examples I study are from the area of Computational Biology (or bioinformatics, if you prefer that name).
STATISTICAL NETWORKS IN MY RESEARCH:
A network is given by a set of vertices (also called nodes) and by a set of edges (also called links) between them. The set of vertices is usually finite, and so is the set of edges. Vertices and edges can stand for a number of different objects, such as: vertices represent proteins and edges represent protein-protein interactions, or: vertices represent residues in a protein and two vertices are connected if the residues are less than a given distance apart. Vertices could also stand for agents and edges could link agents which are connected by a common structure, for example geographical proximity, or membership of the same organisation. Vertices can have properties such as structure and function (of a protein), and edges can be weighted (such as by the strength of a protein-protein interaction). Edges can be directed or undirected, and we can think of multiple edges, possibly of different types, connecting vertices. That said, my research to date focuses on undirected networks without multiple edges and without weights. Current applications include not only protein-protein interaction networks but also the spread of epidemics and rumours on networks.