Thursday September 6, 4pm, Building J12 room 538
Department of Mathematics, Imperial College London
Retail Planning in Future Cities: A stochastic formulation of a dynamical singly constrained spatial interaction model
One of the challenges of 21st-century science is to model the evolution of complex systems. One example of practical contemporary importance is urban structure, for which the dynamics may be described by a series of non-linear first-order ordinary differential equations. Whilst this approach provides a reasonable model of spatial interaction as are relevant in areas diverse as public health and urban retail structure, it is somewhat restrictive owing to uncertainties arising in the modelling process.
We seek to address these shortcomings by developing a dynamical singly constrained spatial interaction model, based on a system of nonlinear stochastic differential equations. The model is ergodic and the invariant distribution encodes our prior knowledge of spatio-temporal interactions. We proceed by performing inference and prediction in a Bayesian setting, and explore the resulting probability measures with a position-specific metropolis-adjusted Langevin algorithm. Insights from studies of interactions within the city of London from retail structure are used as illustration.
Joint work with Louis Ellam, Greg Pavliotis, and Sir Alan Wilson
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.