UNIVERSITY OF GLASGOW
STATISTICS SEMINAR PROGRAMME
Wednesday, 17th January, 3 pm
Statistical inference for continuous time
stochastic processes based on discrete data
Jordan STOYANOV (University of Newcastle)
Wednesday, 7th February, 3 pm
Bayesian variants of some classical semiparametric regression
techniques
Gary KOOP (University of Glasgow, Department of Economics)
Wednesday, 21st February, 3 pm
The simplex - its algebraic-geometric structure and application
in statistics
John AITCHISON (University of Glasgow)
Wednesday, 7th March, 3 pm
Sampling issues in forensic science
Colin AITKEN (University of Edinburgh)
Seminars take place in Room 1f(203), Mathematics Building,
University of Glasgow
For further information please contact the seminar organiser:
Ilya Molchanov
University of Glasgow : e-mail: [log in to unmask]
Department of Statistics : Ph.: + 44 141 330 5141
Glasgow G12 8QW : Fax: + 44 141 330 4814
Scotland, U.K. : http://www.stats.gla.ac.uk/~ilya/
ABSTRACTS
STATISTICAL INFERENCE FOR CONTINUOUS TIME STOCHASTIC PROCESSES BASED
ON DISCRETE DATA
The main discussion will be on models quite common in the real
practice when a complicated phenomenon is described by a continuous
time stochastic process and based on discrete observations we have to
make inference for unknown characteristics (parametric and/or
non-parametric). Specific models involving processes such as
Gaussian, stationary, diffusion, Markov, Poisson, etc. will be
analysed in details. Related topics, including possible applications,
will also be discussed.
BAYESIAN VARIANTS OF SOME CLASSICAL SEMIPARAMETRIC REGRESSION
TECHNIQUES
This lecture develops new Bayesian methods for semiparametric
inference in the partial linear Normal regression model: $y=z\beta
+f(x)+\varepsilon$ where $f(.)$ is an unknown function. These methods
draw solely on the Normal linear regression model with natural
conjugate prior. Hence, analytical finite sample results are available
which do not suffer from problems of theoretical and computational
complexity which plague the existing literature. Constrained and
unconstrained estimation are considered as is testing of parametric
regression models against semiparametric alternatives and
prediction. We discuss how these methods can, at some cost in terms of
computational complexity, be extended to other models
(e.g. qualitative choice models or those involving censoring or
truncation) and provide precise details for semiparametric probit and
tobit models. We show how the assumption of Normal errors can easily
be relaxed. Our methods are illustrated using artificial and real data
sets.
THE SIMPLEX - ITS ALGEBRAIC-GEOMETRIC STRUCTURE AND APPLICATION
IN STATISTICS
The unit simplex plays a central role in a number of situations in
statistical inference - as sample space in compositional and
probability statement analysis, as parameter space in Bayesian
analysis of multinomial and contingency tables, as design space in
some optimum experimental design. We motivate the construction of a
mathematical structure on the simplex through a sequence of logical
necessities of coherence and invariance in compositional data
analysis, resulting in a metric vector space. This mathematical
structure and its associated distributional and differential calculus
support all forms of compositional data analysis. We examine, with
applications, some of these, in particular inferences dependent on the
simplex singular value decomposition, compositional biplots,
differential perturbation processes, convex mixture or endmember
analysis, moment distribution profiles. Some conjectures are made
about the suitability of these simplicial ideas to the other forms of
involvement of the simplex in statistical work.
SAMPLING ISSUES IN FORENSIC SCIENCE
A review will be given of various approaches to statistical sampling
issues which have been taken in the forensic science community,
including the Bayesian method currently used by the Scottish forensic
science laboratories.
|