'Stochastic Modelling of Urban Structure' and 'Diffusions and dynamics on statistical manifolds for statistical inference'

Date: 

Friday, 24 November 2017 - 4:00pm to Tuesday, 28 November 2017 - 11:00am

Venue: 

RC-4082, Red Centre building, UNSW Sydney

 

Professor Mark Girolami is visiting UNSW and presenting a seminar on “Stochastic Modelling of Urban Structure” and and three  discussions on  “Diffusions and dynamics on statistical manifolds for statistical inference”'.

These events are initiatives from the ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS). Everyone is welcome.

Seminar: Stochastic Modelling of Urban Structure,  24th November, 4pm, RC-4082.

Discussions/tutorials: Diffusions and dynamics on statistical manifolds for statistical inference, 27th November at  11:00am and  01:00pm; 28th November at 10:00am

Mark Girolami is an EPSRC Established Career Research Fellow (2012 - 2018) and previously an EPSRC Advanced Research Fellow (2007 - 2012). For  more information about  Mark Girolami:
https://warwick.ac.uk/fac/sci/statistics/staff/academic-research/girolami/

Seminar: Friday 24th November, 4pm, RC-4082.

Title: Stochastic Modelling of Urban Structure

Abstract: Urban systems are complex in nature and comprise of a large number of individuals that act according to utility, a measure of net benefit pertaining to preferences. The actions of individuals give rise to an emergent behaviour, creating the so-called urban structure that we observe. In this talk, I develop a stochastic model of urban structure to formally account for uncertainty arising from the complex behaviour. We further use this stochastic model to infer the components of a utility function from observed urban structure. This is a more powerful modelling framework in comparison to the ubiquitous discrete choice models that are of limited use for complex systems, in which the overall preferences of individuals are difficult to ascertain. We model urban structure as a realization of a Boltzmann distribution that is the invariant distribution of a related stochastic differential equation (SDE) that describes the dynamics of the urban system. Our specification of Boltzmann distribution assigns higher probability to stable configurations, in the sense that consumer surplus (demand) is balanced with running costs (supply), as characterized by a potential function. We specify a Bayesian hierarchical model to infer the components of a utility function from observed structure. Our model is doubly-intractable and poses significant computational challenges that we overcome using recent advances in Markov chain Monte Carlo (MCMC) methods. We demonstrate our methodology with case studies on the London retail system and airports in England.

Discussions/tutorials: 27th November at  11:00am and  01:00pm; 28th November at 10:00am in RC-4082.

 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.

 

There is no need to register for these events. For more information contact Boris Beranger b.beranger@unsw.edu.au