Queen Mary and Westfield College
School of Mathematical Sciences
Spring 1999
STATISTICS SEMINAR: DESIGN OF EXPERIMENTS
All are welcome
The talks are held at 16.30,
with the exception of the last talk on 25 March, which will be held at 14.30,
all in the Mathematics Seminar Room (103) on Level 1,
Mathematics Building, Queen Mary and Westfield College.
Tea and coffee are available in the Mathematics Common Room (102) from 15.00.
The nearest underground station is Stepney Green.
Turn left at the exit and walk 400 yards.
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DATE SPEAKER TITLE
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28 Jan. 1999 G. J. S. Ross Some aspects of non-linear modelling.
Statistics Department,
IACR Rothamsted
11 Feb. 1999 R. A. Bailey Choosing designs for nested blocks.
School of Mathematical
Sciences, QMW
25 Feb. 1999 P. J. Laycock Linear modelling and optimal design
Mathematics Dept., UMIST for extreme values.
11 March 1999 A. A. Greenfield Experimental design:
Private Consultant Some challenges from industry.
25 March 1999 S. Gnot On maximum likelihood estimators in
(14.30) Mathematics Department, certain multivariate normal mixed
Pedagogical University of models with two variance components.
Zielona Gora, Poland
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For more information ask:
Barbara Bogacka
School of Mathematical Sciences
Queen Mary and Westfield College
Mile End Road
London E1 4NS
Tel: 0171 975 5497
e-mail: [log in to unmask]
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The seminar information is kept on:
http://www.maths.qmw.ac.uk/~rab/seminars.html
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A B S T R A C T S
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G. J. S. Ross
Some aspects of non-linear modelling.
Non-linear models such as exponential curves, ratios of polynomials
and solutions of differential equations are more suitable than linear
models in many situations. Difficulties in fitting such models can be
overcome by paying attention to parametrisation, and appropriate use
of optimization algorithms.
Three equivalent parameter systems can be defined for any given problem:
one set for easy algebraic description, one for optimal fitting and one
for making inference of quantities of interest to the user. This framework
makes it possible to compute reliable confidence regions for parameter
estimates, to understand why some models cannot be fitted, and to guide
the process of optimal design. Methods of comparing models for the same
data, and several data sets for the same model, will be discussed.
Graphical methods such as profile likelihood plots, parameter loci and
convergence plots will be described.
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R. A. Bailey
Choosing designs for nested blocks.
Consider a design for n treatments in N experimental units. Suppose that
the set of experimental units is partitioned into b blocks of
ck plots each, and that each block is partitioned into c subblocks
of k plots each. How should we allocate treatments to experimental
units?
If the effects of subblocks are fixed then blocks play no role in the
analysis and we may simply choose an optimal design for n treatments
in bc subblocks of size k. But frequently we assume that the
effects of subblocks are random, and we combine information from the
two lowest strata. In this situation, it may be a bad strategy to
choose a design that is optimal for subblocks (ignoring blocks) or for
blocks (ignoring subblocks).
Instead, I recommend choosing a design that it is near-optimal for all
plausible values of the ratio of the variances in the bottom two
strata. Strategies will be compared on various examples.
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P. J. Laycock
Linear modelling and optimal design for extreme values.
It is a commonplace situation in data collection for only the maxima
(or equivalently, minima) of appropriately grouped sets of values to
be observed, or recorded. In this talk the implications of such a
situation for the design of experiments will be considered. In
particular, additive models, an extension to the generalized linear
model form, Pareto regressions and a maximal regression format will
be considered.
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A. A. Greenfield
Experimental design: Some challenges from industry.
I shall briefly describe a few experimental problems that have come my
way in recent years. Then I shall present a theoretical approach to the
automatic design of fractional asymmetrical factorial experiments:
those in which there are several factors, each with any number of
categories.
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S. Gnot
On maximum likelihood estimators in certain
multivariate normal mixed models with two variance components.
We consider a problem of ML estimation of variances in certain mixed
linear models with two variance components. For these models
a procedure to obtain ML estimators is described. Solutions produced
by this procedure are given. It is shown that under some conditions the
solution of ML equation cannot give ML estimators, i.e. estimators which
maximize the loglikelihood function. Necessary and sufficiend conditions,
for which the solutions of ML equations lead to ML estimators, are given.
A two-way layout model and an equicorrelated model are considered in detail.
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