Statistics Seminars at Imperial College
Friday 21 January, Room 642, Department of Mathematics, 6th floor Huxley
Building.
Program:
2:00 -- 3:00 Henry P Wynn, University of Warwick
Discrete Statistics using Grobner Basis Coding.
3:00 -- 3:30 Coffee Break (served in the same room - 642)
3:30 -- 4:30 Charles Taylor, University of Leeds
Analysis of Nearly Regular and Random Point Patterns
Abstracts of the talks:
Discrete Statistics using Grobner Basis Coding
by Henry P Wynn
University of Warwick
For discrete distributions with arbitrary support the Grobner basis
(G-basis) coding provides a unique way of representing distributions.
This uses the work of Pistone and Wynn (1986, Biometrika) in
experimental design by replacing the design by the support of the
distribution and interpolating the probability function or its
logarithm. The latter leads to representations of the exponential model
(family) and from there compact formulae for the standard quantities of
statistical inference: cumulants, score functions, information, saddle
points and so on. The methods also give formulations for Bayes networks
and associated issues such as hidden variables.
Analysis of Nearly Regular and Random Point Patterns
by Charles Taylor
University of Leeds
We consider a nearly regular point pattern in which a Delaunay
triangulation is comprised of nearly equilateral triangles of the same
size. We will motivate the problem with several examples taken from
biological and medical applications such patterns could arise from a
standard inhibition model. We propose to model this set of points with
Gaussian perturbations about a regular mean configuration. As will be
shown, this model allows us to evaluate the expected value, and variance
of the $K$-function which can then be used for inference without
recourse to simulation. In addition, instead of considering interpoint
distances, we investigate triangle subsets and obtain various
distributions of statistics based on size, or squared size of the
triangles which is closely related to the mean (squared) distance to
the six nearest neighbors.
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