The Role of the Statistician in Numerical Analysis

This talk is about an exciting new area of research called Probabilistic Numerics. I will argue that statisticians have a central role to play in contemporary numerical analysis and provide an overview of recent results in this direction, from optimisation through to the solution of partial differential equations. Then, focussing on integration due to the local interest in Quasi Monte Carlo, I will present probabilistic versions of Monte Carlo and Quasi Monte Carlo integrators. Finally, if time permits, I will describe recent work that attempts to establish probabilistic versions of Markov chain Monte Carlo integrators.