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Nicole Augustin
Email: N.H.Augustin@bath.ac.uk
Alex Cox
Email: A.M.G.Cox@bath.ac.uk

Probability and
Statistics Seminars: Winter 2007
This page is now historical. Details of current seminars in Probability and Statistics.
Our seminars our usually held at 2.15 p.m. on Fridays
in room 3W
3.7 . If you wish to find out more, please
contact one of the organisers.
** LANDSCAPES ** 9/11/07: Wilfred Kendall
(Warwick)
Shortlength routes in lowcost networks
Note: Seminar in Landscapes Series: 4.15 in 3WN 2.1
16/11/07: Peter Jupp
(St Andrews)
Estimation of population size: conditioning has negligible effect
Many methods of estimating the size N of a homogeneous population are based on i.i.d. random variables x_1, ..., x_n (e.g. capture histories, distances from a transect), of which only a random number n are observed. Both the distribution of x_1, ..., x_n and the probability that x_i is observed depend on a (vector) parameter theta. Two appealing estimators of (N,theta) are
(a) the full m.l.e. ({\hat N},{\hat theta}),
(b) the conditional m.l.e. ({\hat N}_c,{\hat theta}_c), where {\hat theta}_c is the m.l.e. of theta obtained by conditioning on n, and {\hat N}_c is a Petersontype estimator.
In this talk I shall describe recent work with Rachel Fewster (Auckland) which has produced
(i) a formula showing that ({\hat N},{\hat theta}) and ({\hat N}_c,{\hat theta}_c) are remarkably close,
(ii) the asymptotic distribution of ({\hat N},{\hat theta}) and ({\hat N}_c,{\hat theta}_c).
An extension to nonhomogeneous populations will be indicated.
23/11/07: Klaus Ritter
(Darmstadt)
Quadrature of Lipschitz Functionals and Approximation of Distributions
We study randomized (i.e. Monte Carlo) algorithms to compute expectations of Lipschitz functionals w.r.t. measures on infinitedimensional spaces, e.g., Gaussian measures or distribution of diffusion processes. We determine the order of minimal errors and corresponding almost optimal algorithms for three different sampling regimes: fixedsubspacesampling, variablesubspacesampling, and fullspace sampling. It turns out that these minimal errors are closely related to quantization numbers and Kolmogorov widths for the underlying measure. For variablesubspacesampling suitable multilevel Monte Carlo methods, which have recently been introduced by Giles, turn out to be almost optimal.
Joint work with Jakob Creutzig (Darmstadt), Steffen Dereich (Bath), Thomas MüllerGronbach (Magdeburg).
30/11/07: Ayalvadi Ganesh
(Bristol)
Threshold phenomena for epidemics on graphs
We consider the contact process (SIS epidemic) on finite undirected
graphs and study the relationship between the expected epidemic
lifetime, the infection and cure rates, and properties of the graph.
In particular, we show the following: 1) if the ratio of cure rate to
infection rate exceeds the spectral radius of the graph, then the
epidemic dies our quickly. 2) If the ratio of cure rate to infection
rate is smaller than a generalisation of the isoperimetric constant,
then the epidemic is longlived. These results suffice to establish
thresholds on certain classes of graphs with homogeneous node degrees.
In addition, we obtain thresholds for epidemics on powerlaw graphs.
Finally, we use these techniques to study the efficacy of different
schemes for distributing curing resources among the nodes.
14/12/07: David Croydon
(Warwick)
The scaling limit of the random walks on a class of random graph trees

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