Centre for Mathematical
Sciences
Wilberforce Road, Cambridge, CB3 0WB
Tel: (01223) 337958
Fax: (01223) 337956
Email: secretary@statslab.cam.ac.uk
All interested are welcome
Select a date to view the relevant seminar abstracts:
Since 1948, when Feynman introduced his famous path integral giving an explicit (but not rigorous) representation for the solutions of the Schroedinger equation, many mathematicians have contributed to the fascinating problem of how to give a rigorous meaning to this (infinite-dimensional) path integral. In the talk, firstly, several of the main approaches to this problem will be presented. Secondly, a new construction will be given which allows to define a rigorous Feynman integral for very general Schroedinger equations including the cases of singular potentials and magnetic fields.
The compound Poisson distribution associated with a distribution P on the real line and some λ >0 is defined to be the distribution of Y=X1 + .... + XN with N, X1, X2, .... independent, N Poisson-distributed with parameter λ > 0 and P the distribution of the X-variables. We consider the non-parametric estimation of P from a sample of Y.
A new approach for identification of the true author of anonymous text (among many other pretenders) is presented in this talk. To find the true author one should compute the relative entropy of anonymous text with respect to texts of each pretender and, in most cases, one obtains the minimal entropy on the true author. The relative entropy is calculated under the assumption that the sequence of letters in a text forms a Markov Chain of first order. Certainly, a natural language text is not a Markov chain, but, unexpectedly this method shows excellent results. Some results of cross-validation for the huge sample of texts of 82 Russian writers and for the sample of texts of 45 native English writers will be presented. Apparently, this technique does work for both languages and it is supposed to work for any non-pictographic language.
We shall also show that this method is useful for samples of small sizes, and, in particular, we shall consider the classification of The Federalist Papers. Finally, we come to the amazing conclusion that this method performs as well as any other quantitative method for identification of writers (and sometimes much better!), unless it is based on such a microscopic language unit as a pair of letters.
Richard Grove from PSI (Statisticians in the Pharmaceutical Industry) will be visiting the Laboratory on Friday 10 November 2000 to talk about the role of statistics within the drug development and to discuss careers opportunities for statisticians and SAS programmers within the pharmaceutical industry. The talk describes the pharmaceutical industry, gives an overview of the drug development process and allows students to find out about career opportunities and the working environments. Richard (a statistician working in the industry), will talk about his own experiences and will discuss his own career to date - giving you a personal insight into the industry. There will be plenty of opportunity to ask questions and find out anything and everything you want to know about statistics in the pharmaceutical industry. You will be able to pick up a copy of the PSI careers booklet (which has useful contacts and more detailed information to compliment the talk) and general information about PSI.
There is continued speculation about the likely future number of cases of variant Creutzfeldt-Jakob disease (vCJD) that may arise in Great Britain as a result of the BSE epidemic in cattle in the late 1980's and early 1990's. To date (September 2000), there have been 69 confirmed deaths from vCJD, with a further 5 awaiting confirmation and 8 patients diagnosed with probable vCJD. Predicting the size of the epidemic remains difficult because of the many gaps in our knowledge of key biological and epidemiological processes determining the typical course of infection and transmission. In this talk, I will describe the formulation of a time- and cohort-stratified model of the transmission dynamics of vCJD, which relates estimates of the numbers of BSE-infected cattle that entered the human food supply to the cases of vCJD which have arisen to date. Results from the model will demonstrate how the uncertainty in the future epidemic size depends on two key parameters - the average number of cases arising from the consumption of one late-stage animal and the incubation period distribution. The results will also be related to ongoing studies to estimate the number of asymptomatic infections through testing tonsil and appendix tissues.
I describe an approach to Bayesian analysis of discretely observed diffusion processes using MCMC methodology. The paths between any two data points are treated as missing data, utilizing the well known data augmentation algorithm. However, the rate of convergence of basic algorithms can be arbitrary slow if the proportion of imputed data points is large. I will describe a transformation of the diffusion which breaks down dependency between the transformed missing paths and the volatility of the diffusion. This leads to algorithms which are robust to the proportion of imputed data. Examples using interest rate data will be briefly described.