Markov Transition Operators defined by Hamiltonian Symplectic Flows and Langevin Diffusions on the Riemannian Manifold Structure of Statistical Models

Friday September 7, 2pm, Carslaw 173

Mark Girolami
Department of Mathematics, Imperial College London

Markov Transition Operators defined by Hamiltonian Symplectic Flows and Langevin Diffusions on the Riemannian Manifold Structure of Statistical Models

The use of Differential Geometry in Statistical Science dates back to the early work of C.R. Rao in the 1940s when he sought to assess the natural distance between population distributions. The Fisher-Rao metric tensor defined the Riemannian manifold structure of probability measures and from this local manifold geodesic distances between probability measures could be properly defined. This early work was then taken up by many authors within the statistical sciences with an emphasis on the study of the efficiency of statistical estimators. The area of Information Geometry has developed substantially and has had major impact in areas of applied statistics such as Machine Learning and Statistical Signal Processing. A different perspective on the Riemannian structure of statistical manifolds can be taken to make breakthroughs in the contemporary statistical modelling problems. Langevin diffusions and Hamiltonian dynamics on the manifold of probability measures are defined to obtain Markov transition kernels for Monte Carlo based inference.

Mark Girolami holds the Chair of Statistics within the Department of Mathematics at Imperial College London where he is also Professor of Computing Science in the Department of Computing. He is an adjunct Professor of Statistics at the University of Warwick and is Director of the Lloyd’s Register Foundation Programme on Data Centric Engineering at the Alan Turing Institute where he served as one of the original founding Executive Directors. He is an elected member of the Royal Society of Edinburgh and previously was awarded a Royal Society - Wolfson Research Merit Award. Professor Girolami has been an EPSRC Research Fellow continuously since 2007 and in 2018 he was awarded the Royal Academy of Engineering Research Chair in Data Centric Engineering. His research focuses on applications of mathematical and computational statistics.