UNIVERSITY OF CAMBRIDGE
DEPARTMENT OF PURE MATHEMATICS AND MATHEMATICAL STATISTICS
STATISTICAL LABORATORY
16 MILL LANE, CAMBRIDGE CB2 1SB
Tel: (01223) 337958
Fax: (01223) 337956
Room S27, Statistical Laboratory
SEMINARS
(updated)
Friday, 22nd January
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2.05pm David Siegmund (Stanford)
TAIL PROBABILITIES VIA A CHANGE OF MEASURE
Starting from Cramer's large deviation estimates and Wald's analysis
of the sequential probability ratio test, many authors have used a
change of measure to derive approximations in statistics and applied
probability. Important examples involve first passage distributions
and maxima of random fields. I will review some of these problems,
present a method motivated by change-point analysis, and discuss
applications to ARCH (1) processes (Goldie's (1991) approximation) and
to p-values for sequence alignments.
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Friday, 29th January
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2.05pm Peter Whittle (Cambridge)
NEURAL NETS, FADING DATA AND THE OLFACTORY SYSTEM
An *associative memory* has the task of determining which of $p$
known characters (`traces') a given image (`data array') might
represent, and so essentially decides between $p$ hypotheses on the
basis of the data. It is also *autoassociative* if it outputs the
actual character inferred rather than just identifies it.
However, many of the standard associative memories of neural net
theory seem to operate rather differently, and it is argued that the
task they implicitly attempt is that of coping with *fading data*,
i.e. of forming an inference from the data even as its memory of that
data degrades. Rather simple statistical considerations lead to a net
with optimality properties and a simple interpretation. In the
particular case when composite traces can be formed by linear
superposition, this net exhibits a structure which shows striking
parallels with some of the anatomy of the olfactory system.
This seminar is complete in itself, but the ideas will be developed in
a different direction in the seminar on 12th February.
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Friday, 5th February
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2.05 Andrew Dales (Barclays Global Investors)
USING STATISTICS IN GLOBAL PORTFOLIO CONSTRUCTION
This seminar will discuss ways that quantitative investment models can
be used to construct international portfolios. In particular I shall
look at the role of mean variance optimisation and the impact of
currency on international investment decisions.
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Friday, 12th February
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2.05 Peter Whittle (Cambridge)
NEURAL NETS, OSCILLATORY OPERATION AND CHAOTIC CARRIERS
Biological neural nets show an irregularly oscillatory behaviour which
is certainly `chaotic' in a naive sense and possibly also in a
technical one. The occurrence of oscillation is not surprising.
Absolute signal levels are almost meaningless in biological contexts,
and information must be conveyed by variation in a signal rather than
by the level of a static signal. W.J. Freeman has proposed models of
the biological neuron and oscillating systems of such neurons which
seem to show a particular insight. These ideas are grafted on to the
associative memory proposed in the seminar of 29th January; the
combination produces some remarkable effects.
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Friday, 26th February
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2.05 Richard Dybowski (King's College London)
SCORING SYSTEMS FOR INTENSIVE-CARE PATIENTS:
PAST, PRESENT AND FUTURE
There is strong interest within the intensive-care community for
models that indicate the severity of a patient's state. The standard
modelling technique for this is logistic regression. In this seminar,
I will examine alternative approaches in the context of model accuracy
and model interpretability, including Bayesian belief nets.
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Friday, 12th March
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2.05 Peter McCullagh (University of Chicago)
LINEAR MODELS AND CATEGORY REPRESENTATIONS
The topic of this talk is the connection between statistical models as
vector subspaces and vector subspaces as representations of some
category in the algebraic sense of LacLane. Group representations, in
general, lack the logical properties required by statistical models.
It will be shown that the standard factorial models (also called
hierarchical interaction models) are intimately connected with the
category of all morphisms between finite sets, and also with the
injective and surjective sub-categories. The factorial models are
precisely the representations of the product category in the tensor
product space. The marginality principle whereby no interaction is
included without the associated main effects, is thus given the purely
algebraic interpretation of category representation. Certain
statistical designs such as citation studies and genetic experiments
have the property that two or more factors have the same set of levels
(homologous factors). The natural extension of factorial models
obeying the marginality principle to this context turns out to be the
representations of the category of finite sets or the injective
sub-category. These representations constitute a distributive lattice
of subspaces, whose relevance will be illustrated by an example.
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ALL INTERESTED ARE WELCOME
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For the full list of Statistical Laboratory seminars being given in the
Michaelmas Term, please see our web page
http://www.statslab.cam.ac.uk/Dept/Seminars
Enquiries to: [log in to unmask]
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