3rd JOINT WARWICK-OXFORD STATISTICS SEMINAR

2:30 – 5:00 pm  at The Mary Ogilvie Lecture Theatre,

St. Anne’s College, University of Oxford

2:30 p.m.

Speaker 1:  Julian Besag (University of Bath, University of Washington, Seattle)

Title:  Continuum limits of Gaussian Markov random fields: resolving the conflict with geostatistics

Abstract:  For more than 30 years, Markov random fields (equivalently, graphical models with undirected edges) have been used with some success to account for spatial variation in data. Applications include agricultural crop trials, geographical epidemiology, medical imaging, remote sensing, astronomy, and microarrays. Almost all of the examples involve (hidden) Gaussian MRF formulations.

MRFs refer to fixed regular or irregular discrete lattices or arrays and questions arise regarding inconsistencies between MRFs specified at differing scales, especially for regional data. Ideally, one would often prefer an underlying continuum formulation, as in geostatistics, which can then be integrated to the regions of interest. However, limiting continuum versions of MRFs, as lattice spacing decreases, proved elusive until recently.

This talk briefly presents some motivating examples and shows that limiting processes indeed exist but are defined on arbitrary regions of the plane rather than pointwise. Especially common is the conformally invariant de Wijs process, which coincidentally was used originally by mining engineers but which became unfashionable as geostatistics developed. Convergence is generally very fast. The de Wijs process is also shown to be a natural extension of Brownian motion to the plane. Other processes, including the thin-plate spline, can be derived as limits of MRFs. The talk closes by briefly discussing data analysis.

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3:30 to 4.00 - Tea, Coffee and biscuits in foyer outside lecture theatre

4:00 p.m.

Speaker 2:   Susan Lewis (University of Southampton, UK)

Title:  Screening experiments

Abstract:  Discovery and development in science and industry often involves investigation of many features or factors that could potentially affect the performance of a product or process. In factor screening, designed experiments are used to identify efficiently the few features that influence key properties of the system under study. A brief overview of this broad area will be presented. This will be followed by discussion of a variety of methods with particular emphasis on industrial screening. Ideas will be motivated and illustrated through examples, including a case study from the automotive industry.