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Inference and optimal design for percolation and random graph models

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Many real-world phenomena can be modelled by random graphs, or more generally, by dynamically changing random graphs. Specifically, host-pathogen biological systems that may combine primary and nearest-neighbour or long-range secondary infection processes can be efficiently described by spatio-temporal models based on random graphs evolving in time. Although a continuous observation of an epidemic is not always possible, a spatial `snapshot’ may provide one with some, albeit highly incomplete, knowledge about the epidemic. In terms of the model this knowledge results in a random graph realised in some metric space. Moreover, under some circumstances it is not even possible to observe some or all of the edges of such a random graph – all one would know then are the vertices which correspond to the infected sites, i.e. to those sites which interacted as a result of the evolution of the process under consideration.

In this talk the problems of statistical inference and optimal design for percolation and random graph models posed within a Bayesian framework will be discussed. This is a joint work with Gavin Gibson and Stan Zachary, both at Heriot-Watt University, Edinburgh.


Andrei Bejan is a Research Associate at the Computer Laboratory, University of Cambridge. His principal research interests lie in the field of stochastic modelling and statistical inference. His PhD thesis dealt with optimal design problems for percolation and random graph models. His other research interests include the theory of priority queueing systems with switchover times, spectral theory of random matrices and development of advanced numerical methods in these areas. Andrei has recently joined the Computer Laboratory to take part in the project TIME , where he is working on statistical modelling and analysis of transport traffic data.

This talk is part of the Computer Laboratory Opera Group Seminars series.

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