Statistical Laboratory Seminars
Michaelmas Term 2002
Centre for Mathematical Sciences
Wilberforce Road, Cambridge, CB3 0WB
Tel: (01223) 337958
Fax: (01223) 337956
Email: [log in to unmask]

Seminars will be held in Meeting Room 12, CMS
All interested are welcome


Seminar Schedule:

This list is subject to revision

Abstracts and Further Details:

Friday 18 October
2.00pm D.Korshunov (Insitute of Mathematics, Novosibirsk and Heriot Watt
University)

Central Limit Theorem for Transient Markov Chains

Consider a Markov chain Xn with values in a d-dimensional Euclidean
space. First, assume that the mean drift of the chain is asymptotically
homogeneous in space and time. It means that the mean drift converges to
some limit a as x `goes to infinity in some direction' and n ? 8. We also
assume that the covariance matrix of the chain increment converges to some
limit matrix s2. We describe conditions under which (Xn-na)/ sqrt n
converges weakly to the d-dimensional normal law with covariance matrix
s2.
We also consider a Markov chain asymptotically homogeneous in space and
time. It means that the distribution of the chain increment converges
weakly to a limit as x "goes to infinity in some direction" and n? 8, and
the limiting distribution has a finite covariance matrix. Under certain
conditions we prove the local central limit theorem.


Friday 25 October

2.00pm Dr Anthony Ledford (Man Investment Products)

Statistics in finance -- development of a trading system
In this talk an overview is given of the main issues that must be
addressed for the development of a quantitative trading system. Our
treatment focuses on futures markets as these are particularly suited to
systematic trading, and deals with modelling temporal dependence in both
mean and variance (volatility), trading rule selection, the effect of
trading costs, risk assessment and the benefits of diversification through
trading more than one market. These concepts will be illustrated using
daily data on the FTSE Allshare and S&P 500 indices and for simplicity we
will restrict attention to relatively straightforward statistical models.

Man Investment Products is a FTSE 100 company specialising in alternative
investments. We manage funds based on systematic trading strategies
applied to a wide portfolio of international markets. A diverse range of
statistical modelling and analysis techniques is exploited in researching
and developing these trading strategies.


Friday 1 November

2.00pm Trevor Sweeting (University of Surrey/University College London)

Bayesian predictive performance via predictive entropy loss

We explore the performance of Bayesian prediction using a predictive
entropy loss criterion. In particular, we investigate asymptotically
constant risk minimax priors under a predictive relative entropy loss
function. Such priors arise as minimisers of a measure of prior predictive
information. An analysis of specific examples is illuminating; in standard
problems solutions often possess asymptotically negligible predictive
coverage probability bias. There are a number of appealing aspects of the
proposed approach. For example, there is no need to specify a set of
parameters deemed to be of interest and, importantly, the same asymptotic
risk criterion emerges regardless of whether one is interested in
predicting a single future observation or a large number of future
observations.

Friday 8 November

2.00pm David Spiegelhalter (MRC Biostatistics Unit, Cambrige)
Bayesian Model Criticism

Bayesian modelling is being increasingly used in complex applications, and
there is an accompanying need for diagnostics to check model fit. Standard
residual analyses can be adapted, but hierarchical modelling and prior
information introduces additional difficulties. A variety of
simulation-based techniques have been proposed for detection of divergent
behaviour at each level of a hierarchical model, and we investigate two
innovations. First, a diagnostic test based on contrasting two independent
sources of evidence regarding a parameter: that arising from its prior
given the remainder of the data, and that arising from its
likelihood. Good cross-validatory properties are shown for normal
hierarchical models and in an application featuring a spatial
model. Second, as an approximation to full cross-validation, we propose
replication of the parameter of interest based on the full data. Each of
these techniques leads to multiple Bayesian p-values and, somewhat
paradoxically for a Bayesian analysis, associated issues of multiple
testing. We conclude with a tentative overall strategy to detecting
divergent behaviour.

Friday 22 November

2.00pm Careers in the Pharmaceutical Industry
Speaker, title and abstract TBA

Tuesday 10 December

2.00pm Xiao-Li Meng

TBA

Thursday 12 December

2.00pm I.S. Borisov (Sobolev Institute of Mathematics of the Russian
Academy of Sciences, Novosibirsk)

Poisson approximation for expectations of functions of independent random
variables

We discuss some aspects of Poisson approximation for expectations of
unbounded functions of a finite family of independent random variables in
the Poissonian setting when the distributions of the random variables have
large atoms at zero. We study the random variables taking values in a
measurable Abelian group. In particular, under minimal moment conditions
complete asymptotic expansions for the expectations are obtained.


Seminar organizer, Susan Pitts, [log in to unmask]