**********************************
UNIVERSITY OF CAMBRIDGE
**********************************
SEMINAR
Room 27, Statistical Laboratory,
University of Cambridge, 16 Mill Lane, Cambridge
*******************************
Friday 22 October 1999
*******************************
2.00 Navraj Pannu, Cambridge University
Improved Crystal Structure Refinement Through Maximum Likelihood
To elucidate the mechanism of a biological process, structural
information of the molecules involved is often necessary. X-ray
crystallography is an important method for the determination of a
molecule's three dimensional structure. In order to obtain the
most accurate atomic coordinates, structural refinement is an
essential part of a crystal structure determination. The
refinement of crystal structures is commonly based on least-squares
methods. However, these procedures are not optimal, since conditions
necessary for the application of a least-squares target are not
satisfied. Therefore, a more general maximum likelihood analysis is
considered and three maximum likelihood targets have been implemented
in commonly used crystallographic refinement packages. Preliminary
tests with protein structures give dramatic results. Compared to
least-squares refinement, maximum likelihood refinement can improve
a model two to four times and thus provide accurate atomic coordinates
faster.
SEMINAR
Room 27, Statistical Laboratory
University of Cambridge, 16 Mill Lane, Cambridge
*******************************
Friday 12 November 1999
*******************************
2.00 Andy Burbanks, Cambridge Univeristy
Some Natural Independence Phenomena
Part of Hilbert's famous Programme was the intention to
find a self-contained formal foundation for mathematics. However,
Godel's theorem demonstrates that sufficiently powerful formal systems
will always be incomplete. The undecidable statements constructed in
Godel's proof may seem rather artificial and contrived; does Godel's
theorem actually matter to ``everyday'' mathematics?
This talk will give some examples of ``natural
independence phenomena'' (more natural-looking undecidable
statements), showing along the way that Hercules can defeat the
many-headed Hydra. My interest in this area is mainly recreational; I
have always been fascinated by certain aspects of logic and would like
to help make these results accessible to a wider audience.
The talk does not assume any special previous knowledge.
SEMINAR
Room 27, Statistical Laboratory
University of Cambridge, 16 Mill Lane, Cambridge
*******************************
Friday 19 November 1999
*******************************
2.00 Professor Frank Ball,
Statistical inference for SIR epidemics among a population of
households.
This talk is concerned with a stochastic model for the spread of an
SIR (susceptible -> infected -> removed) epidemic among a population
consisting of a large number of small households, with different
rates for between-household and within-household infections. The
threshold behaviour of the model is briefly outlined. Methods for
making statistical inferences about the parameters governing such epidemics
from final outcome data are described and their asymptotic properties,
as the number of households becomes large, are determined. The theory is
illustrated by simulations and by an application to data on influenza
epidemics in Tecumseh, Michigan.
SEMINAR
Room 27, Statistical Laboratory
University of Cambridge, 16 Mill Lane, Cambridge
*******************************
Friday 26 November 1999
*******************************
2.00 Prof. J. Bertoin,
A system of sticky particles and the additive coalescent
We establish a connection between two different models of clustering: the
deterministic model of sticky particles which describes the evolution of a
system of infinitesimal particles governed by the dynamic of completely
inelastic shocks (i.e. clustering occurs upon collision with conservation
of masses and momenta), and the random model of the so-called additive
coalescent in which velocities and distances between clusters are not
taken into account. The connection is obtained when at the initial time,
the particles are uniformly distributed on a line and their velocities are
given by a Brownian motion.
e-mail: [log in to unmask]
SEMINAR
Room 27, Statistical Laboratory
University of Cambridge, 16 Mill Lane, Cambridge
*******************************
Friday 3 December 1999
*******************************
2.00 Dr Song Chen,
Confidence Intervals Based on a Local Linear Smoother
Point-wise confidence intervals for a nonparametric regression function
in conjunction with the popular
local linear smoother are considered. The confidence intervals are based
on the asymptotic normal
distribution of the local linear smoother. Their coverage accuracy is
evaluated by developing Edgeworth expansion for the coverage
probability.
We find two surprising results. One is that the coverage error near the
boundary of the support of the regression
function is of a larger order than that in the interior, which implies
that the local linear smoother is not adaptive to the boundary in term of
coverage. This is quite unexpected as the local linear smoother is
adaptive to the boundary in term of bias and variance.
The other is that confidence intervals based on the
Nadaraya-Watson estimator achieve
the same order of coverage error as that based on the local linear
smoother, but are shorter near the boundary.
The empirical likelihood provides a remedy to the boundary problem of the
asymptotic local linear confidence interval as it chooses its own variance
estimator "naturally", different from the standard asymptotic variance.
Seminar organizer, Susan Pitts
Please see also the /~grg/seminars/probsem.html - Informal Probability
Seminars.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
