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
This list is subject to revision
Select a date to view the relevant seminar abstracts:
Sampling (or probing) the status of communication systems by test traffic is a standard tool for performance evaluation. This is e.g. used in call center evaluations, where the distribution of the waiting time to service is estimated by the empirical distribution function of the call answer time for repeated phone calls. Another application is when a call admission controller in an ATM network decides, whether there are sufficient resources to allow a new connection to be established, based on information obtained by sampling the workload at neighbouring nodes. In the present talk we consider the inverse problem of inferring the status of the system by the fate of the test-traffic. In particular we focus on an /M/G/1/ queue with unknown service-time distribution and unknown traffic intensity. Given systematically sampled observations of the workload, we construct estimators of the traffic intensity, the service-time distribution function and study asymptotic properties of these estimators. Joint work with Susan M. Pitts, Cambridge University.
We propose a reformulation of the spectral analysis of {\it deterministic} families of ergodic random discrete Schrödinger operators, including almost-periodic operators. This allows us to apply to such families several methods that have been used so far only for {\it non-deterministic} random operators. The talk will focus on Schrödinger operators with non-ergodic, but stationary potentials; in particular, we will show that a direct analog of the well-known Wegner Lemma is valid for a class of such operator families.The method is based on a special type of expansions of the potential (which we call randelette expansions). These are close to wavelet expansions widely used in modern Analysis and its applications.
No preliminary knowledge of spectral theory of Schroedinger operators with random potential will be assumed.
This paper describes a Bayesian solution to the equity premium puzzle, that is, the inability of standard intertemporal economic models to account for the magnitude of the observed excess return earned by a risky security over the return on T-bills. We follow convention and assume a single representative agent, but the main difference is that we suppose that the agent is not certain about the parameters of the dividend process, modelling this uncertainty by a prior distribution, and making inferences in a Bayesian fashion. The price of the stock is still the NPV of future dividends, but the agent is now averaging not only over the possible future paths of the dividend process, but also over the parameters that govern its dynamics. We then use particle filtering to work out the posterior distribution of the parameters of the problem, and find a striking conclusion; coefficients of relative risk aversion lie in the interval (2,5) with high probability - in other words, there is no equity premium puzzle.
In this seminar, I will introduce the subject of claims reserving, explain why it is necessary for non-life insurance businesses and outline its relevance to solvency and capital modelling. I will cover some of the techniques which have been applied, in particular bootstrapping and Bayesian methods. In many cases, the aim is not to produce clever solutions to individual problems, but rather to formulate robust and simple approaches that can be applied to a wide variety of data sets.
The ideas of measurement are so ubiquitous that we often fail to notice them: they are simply parts of the conceptual universe in which we function. However, it has not always been thus and sometimes, even now, rips in this usually unnoticed background fabric appear, casting doubts on one's view of the way the world works. Occasionally these tears have serious, even fatal consequences. This talk looks at the conceptual infrastructure of quantification, showing how humans have constructed it, how it can be interpreted, and how it is manipulated to make valid inferences about the real world. The talk is illustrated with measurement tools from psychology, medicine, physics, economics and other areas.
Quantum Information Theory is the study of how the acquisition, storage, transmission and processing of information can be accomplished using quantum-mechanical systems. In this theory, quantum-mechanical properties of physical systems are exploited to perform important and otherwise intractable information processing tasks such as efficient factorization of large numbers, teleportation and the creation of fundamentally unbreakable cryptographic codes.I will give an elementary introduction to this fascinating field, highlighting some of its novel features and open questions. Prior knowledge of Information Theory or Quantum Mechanics will not be assumed.
We present a new class of estimators for the Shannon (Boltzmann-Gibbs) entropy of multi-dimensional probability density, based on the k-th nearest distances in a sample of i.i.d. vectors. This class of estimates is built of the bases of ideas of R.L. Dobrushin (A simple method of empirical estimation of the entropy of a stationary sequence, Theory Probab. Applic. (1958), Vol. 3, 462-464). This class of estimators is used to build both goodness-of-fit test and independence tests based on sample entropy (joint results with L.F. Kozachenko, M.N. Goria, V.V. Mergel and P.L.Novi Inverardi). A class of estimators of the Renyi and Tsallis (Havdra-Charvat) entropies of an unknown multidimensional distribution based on the k-th nearest distances in a sample of i.i.d. vectors is also presented. We show that entropies can be estimated consistently with minimal assumptions of the probability density (joint results with L. Pronzato and V. Savani). The method can be extended to the estimation of the statistical distance between two distributions using one i.i.d. sample from each. A connection of different entropies with nonlinear Fokker-Planck equations is discussed.
The lack of an agreed inferential basis for statistics makes life "interesting" for academic statisticians, but at the price of negative implications for the practice and status of statistics in industry, science and government. Our discipline will only mature when we come to a basic agreement about how to apply statistics to real problems. Some illustrations and implications of the existing Bayes/frequentist rift, specific and general, are offered in areas with which the speaker is familiar, including survey inference and missing data. Strengths and weaknesses of the frequentist and Bayes paradigms will be outlined. Can the rift be breached? In the talk a roadmap for a possible frequentist/Bayes compromise is provided based on the work of Box, Rubin and others. The compromise is sometimes called "calibrated Bayes", and asserts that inferences should be Bayesian and model-based, but model formation and assessment can and should involve frequentist ideas. Some implications of this proposed compromise for the future teaching and practice of statistics are offered.
Climate variability and species coexistence: Testing ecological theory with hierarchical BayesHow expected increases in climate variability will impact species diversity depends on the role of such variability in regulating the coexistence of competing species. Despite theory linking temporal environmental fluctuations to the maintenance of diversity, the importance of climate variability for coexistence remains unknown due to a lack of appropriate datasets and analyses. I used a hierarchical Bayesian model to link theoretical predictions with three decades of demographic data from a Kansas prairie. I found that interannual climate variability promotes diversity by stabilizing the coexistence of three common grass species. This result empasizes that forecasts of future species diversity need to consider changes in both climate means and variances.