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Cambridge seminars-updated

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Fri, 22 Jan 1999 11:57:14 +0000

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 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 -------------------- 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. ---------------------------------------------------------------------- Friday, 29th January -------------------- 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. ---------------------------------------------------------------------- Friday, 5th February -------------------- 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. ------------------------------------------------------------------------ Friday, 12th February --------------------- 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. ------------------------------------------------------------------------ Friday, 26th February --------------------- 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. ------------------------------------------------------------------------ Friday, 12th March ------------------ 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. ------------------------------------------------------------------------                    ******************************                      ALL INTERESTED ARE WELCOME                    ****************************** 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] %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%