Department of Mathematical Sciences

Dini's helix - a pseudospherical surface Brownian motion Willmore cylinder with umbilic lines (Babich-Bobenko) Triadic Von Koch Snowflake - Fleckinger, Levitin and Vassiliev Darboux transform of a Clifford torus (Holly Bernstein) Mandelbrot fractal geometry

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Nicole Augustin

Alex Cox

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)

Short-length routes in low-cost 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 Peterson-type 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 non-homogeneous 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 infinite-dimensional 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: fixed-subspace-sampling, variable-subspace-sampling, and full-space sampling. It turns out that these minimal errors are closely related to quantization numbers and Kolmogorov widths for the underlying measure. For variable-subspace-sampling suitable multi-level 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 Müller-Gronbach (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 long-lived. These results suffice to establish thresholds on certain classes of graphs with homogeneous node degrees. In addition, we obtain thresholds for epidemics on power-law 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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