SEMINARS in the Easter Term 1998
Room S27, Statistical Laboratory
University of Cambridge
16 Mill Lane, CAMBRIDGE, CB2 1SB
Tel: (01223) 337958 Fax: (01223) 337956
Email:
secretary@statslab.cam.ac.uk or
g.o.roberts@statslab.cam.ac.uk
All interested are welcome
Wednesday, 22 April
4.00pm Francois Baccelli (INRIA)
WINDOW FLOW CONTROL IN FIFO NETWORKS WITH CROSS TRAFFIC
We focus on window flow control as used in packet-switched communication networks. In the simplest model, the route followed by the data packets and the acknowledgements of the controlled connection is modeled by a series of infinite capacity FIFO queues, each of which receives in addition some cross traffic represented by an exogenous flow.
We investigate the stability region of the system under general stochastic assumptions, that is stationary and jointly ergodic input processes. In particular, we show the existence of a minimal stationary regime and establish tight bounds on the maximal throughput allowed by the flow control. Such systems are intrinsically non-monotonous w.r.t. each cross traffic. A few surprising consequences of this are stressed at the end of the paper, including cases of networks with a stability region admitting a fractal boundary.
Keywords: Window flow control, TCP, stability, multiclass network, stationary ergodic point process, (max,+)-linear system.
Tuesday, 28 April
2.00pm Gareth Roberts (Cambridge) and Jeff Rosenthal (Toronto)
SLICE SAMPLER MARKOV CHAINS
A recently popular Markov chain Monte Carlo technique is the so-called slice sampler. This talk will present the algorithm and examine some of its theoretical properties.
Friday, 1 May [TWO seminars]
2.00pm A.C. Yusuf Brooms (Bristol)
STOCHASTIC GAME ANALYSIS OF VARIOUS QUEUEING SYSTEMS
Customers arrive sequentially to a queueing system which offers a choice between using either a private server or a shared server. The service rate at the shared server is faster than that of the private server. Each customer chooses one of the two service options, basing its decision on the length of the queue at the shared server, with the aim of minimising its own expected service time. The best action for an individual customer depends on the actions taken by subsequent customers arriving at the system, so we consider equilibrium rather than optimal policies. We estabish the existence of a unique symmetric Nash equilibrium point for a variety of queueing systems and show that its structure is characterised by a threshold strategy. A procedure for the computation of this symmetric equilibrium is presented and we discuss its descriptive value within the context of dynamic learning.
3.30pm Dorje Brody (Cambridge)
STOCHASTIC APPROACH TO THERMALISATION
The notion of stochastic process on manifold is applied to various physically appealing circumstances, in order to study the approach to thermal equilibrium for a given initial quantum state. In particular, the geometry of the quantum state manifold is briefly reviewed. The cases concerning canonical and microcanonical ensembles are then considered.
Friday, 15 May
2.00pm Marina Kleptsyna (Russian Academy of Sciences, Moscow)
HOMOGENIZATION OF RANDOM PARABOLIC OPERATOR WITH LARGE POTENTIAL
We study the averaging problem for a divergence-form random parabolic operator with a large potential and with coefficients rapidly oscillating both in space and time variables. It is shown that the asymptotic behaviour of the solution to the Cauchy problem crucially depends on the relationship between the oscillations of coefficients in the space and the time variables.
Tuesday, 19 May
2.00pm Peter Hall (Australian National University)
INTENTIONALLY BIASED BOOTSTRAP METHODS
A class of weighted bootstrap techniques, called biased bootstrap or b-bootstrap methods, is proposed. It is motivated by the need to adjust more conventional empirical methods, such as the `uniform' bootstrap, in a surgical way so as to alter some of their features while leaving others unchanged. Depending on the nature of the adjustment, the b-bootstrap can be used to reduce bias, or reduce variance, or render some characteristic equal to a predetermined quantity. Examples of the latter application include a b-bootstrap approach to hypothesis testing in nonparametric contexts, where the b-bootstrap enables simulation `under the null hypothesis', even when the latter is false; and a b-bootstrap competitor to Tibshirani's variance stabilisation method. An example of the bias-reduction application is adjustment of Nadaraya-Watson estimators of a regression mean, to make them competitive with local linear smoothing. Other applications include density estimation under constraints, outlier trimming, sensitivity analysis, skewness or kurtosis reduction and shrinkage.
Wednesday, 20 May
4.00pm Ros Walley
MY LIFE AS A STATISTICIAN IN NEPAL
Ros Walley graduated from Cambridge in mathematics in 1987, and gained the Cambridge Diploma in Mathematical Statistics in 1988. After several years working as a statistician for the pharmaceutical company Pfizers in Kent, she left the UK to work for the International Nepal Fellowship. Her work in Nepal has included work for the World Health Organisation on a database and analysis program for Nepal tuberculosis data, and work on the Tuberculosis Leprosy Project.
Ros is back in England for a brief visit before returning to her work in Surkhet, Nepal.
Friday, 22 May
2.00pm Wendelin Werner (Paris-Sud, Orsay)
SELF-REPELLING MOTION
We construct and study a continuous real-valued random process, which is of a new type. It is self-interacting (self-repelling) but only in a local sense: it only feels the self-repellance due to its occupation-time measure density at `immediate neighbourhood' of the point it is just visiting. We focus on the most natural process $X$ with these properties that we call `true self-repelling motion'. This is the continuous counterpart to the interger-valued so-called `true' self-avoiding walk. We describe various properties of $X$ (existence and properties of the occupation time densities $L_t(x)$, local variation etc.) and an identity that shows that the dynamics of $X$ can, very loosely speaking, be described as follows: $-dX_t$ is equal to the gradient (in space) of $L_t(x)$, in a generalized sense, even if $x\mapsto L_t(x)$ is not differentiable. (This is joint work with Balint Toth.)
Wednesday, 27 May
THREE SEMINARS ON MCMC THEORY AND APPLICATION
2.00pm Simon Godsill (Dept of Engineering, Cambridge)
Bayesian methods in Signal and Image Processing
2.40pm Laird Breyer (Statistical Laboratory, Cambridge)
Calibration issues in MCMC
3.20pm TEA
3.50pm Randall Douc (Ecole Polytechnique, Paris)
Harris recurrence for MCMC algorithms with no dominating
measure
Friday, 3 July
2.00pm Ioannis Kontoyiannis (Stanford)
WAITING TIMES, STRING MATCHING AND DATA COMPRESSION
We discuss the asymptotic behavior of waiting times between stationary processes: given two independent realizations produced by two processes X={X_n} and Y={Y_n}, we are interested in the waiting time W_n(D) until a D-close version of the initial pattern (X_1,X_2,...,X_n) first appears in (Y_1,Y_2,...), where closeness is measured by some L^p `distortion' criterion (e.g., the average number of mismatches or mean-squared-error). This problem is motivated primarily by its important applications in data compression, and in the analysis of string matching algorithms for DNA and protein sequences.
We identify an associated random walk on the same probability space as the waiting times W_n(D) and we prove a strong-approximation theorem between that random walk and [log W_n(D)]. From this, we can determine the first- and second-order asymptotics of W_n(D) as n increases, in particular identifying its limiting mean and variance. We show that, with probability one, W_n(D) increases exponentially with a rate given by the solution to an explicit variational problem in terms of relative entropy. Moreover, the asymptotic deviations from that limiting rate are Gaussian, and precise results on the rates of convergence of these limit theorems are given.
Time permitting, we will discuss how the intuition provided by these results allowed us to solve a long-standing open problem in data compression: that of finding a practical extension of the celebrated Lempel-Ziv coding algorithm to the case of _lossy_ compression.