Dr Anastasia Papavasiliou (University of Warwick)

Statistical Inference for differential equations driven by rough paths

Differential equations driven by rough paths (RDEs for short) generalize SDEs by allowing the equation to be driven by any type of noise and not just Brownian motion. As such, they are a very flexible modelling tool for randomly evolving dynamical systems. So far, however, they have been ignored by the statistics community, in my opinion for the two followin reasons: (i) the abstract theory of rough paths is still very young and under development, which makes it very hard to penetrate; (ii) there are no statistical tools available. In this talk, I will give an introduction to the theory and I will also discuss how to approach the problem of statistical inference given a discretely observed solution to an RDE.

Evangelos Evangelou (University of Bath)

Spatial sampling design under cost constraints in the presence of sampling errors

A sampling design scheme for spatial models for the prediction of the underlying Gaussian random field will be presented. The optimality criterion is the maximisation of the information about the random field contained in the sample. The model discussed departs from the typical spatial model by assuming measurement error in the observations, varying from location to location, while interest lies in prediction without the error term. In this case multiple samples need to be taken from each sampling location in order to reduce the measurement error. To that end, a hybrid algorithm which combines simulated annealing nested within an exchange algorithm will be presented for obtaining the optimal sampling design. Consideration is made with regards to optimal sampling under budget constraints accounting for initialisation and sampling costs.

Joint work with Zhengyuan Zhu (Iowa State)

Catriona Queen (The Open University)

A graphical dynamic approach to forecasting flows in road traffic networks

Traffic flow data are routinely collected for many networks worldwide. These invariably large data sets can be used as part of a traffic management system, for which good traffic flow forecasting models are crucial. While statistical flow forecasting models usually base their forecasts on flow data alone, data for other traffic variables are also routinely collected. This talk considers how cubic splines can be used to incorporate information from these extra variables to enhance flow forecasts. The talk also introduces a new type of chain graph model for forecasting traffic flows. The models are applied to the problem of forecasting multivariate road traffic flows at the intersection of three busy motorways near Manchester, UK.