RA5a: Structure,environment and staffing policy
The statistics group contains five category A research-active statisticians. Four of the five, Professor B.G. Quinn, Professor T. Subba Rao, Dr J. Yuan and Dr G. Boshnakov, work mainly in time series analysis, carrying on the strong tradition established under the leadership of Professor M.B. Priestley. The main time series activities are non-linear, non-Gaussian time series; time series problems in signal processing; higher order spectral analysis of random fields; periodically correlated and continuous-parameter time series. The other member, Professor P.J. Laycock, works in experimental design, especially the use of extreme value theory in experimental design. The membership of the group has undergone considerable change since the last RAE. Professor Quinn joined the Department from Goldsmiths College in 1998, and Dr Boshnakov who was a senior scientist with the Bulgarian Academy of Sciences, arrived in 1999, to fill Professor Quinn’s dowry post.
Activities and achievements
The group is internationally renowned for its work in the theory of Time Series Analysis. Professor Priestley maintains a very active presence within the department and group, continues to edit the Journal of Time Series Analysis, of which he was the founding editor, and contributes much to the research environment. Professor Quinn has specialised for more than ten years on time series problems in signal processing, and published innovative work on the estimation of frequency in both statistical and engineering journals. Professor Subba Rao has continued his work in non-linear, non-stationary non-Gaussian time series and is considered by many to be the international leader in this field. Professor Laycock has continued diverse collaborations with Professor P. Rowley, a pure mathematician, Dr G. Levermore, a civil engineer, and Professor G. Gott, an electrical engineer, as well as his personal research in the use of extreme values in experimental design. In particular, his work with Professor Gott on the high frequency spectral occupancy problem has resulted in a number of research grants and publications, and the models produced are used to analyse and predict spectral occupancy data from experimental systems located in the UK, Germany and Sweden. Dr Boshnakov’s main current area of research is periodically correlated time series. Dr J. Yuan specialises in the application of higher order spectral techniques to random field problems and image processing.
Professor Quinn has concentrated his efforts on completing a research monograph on frequency estimation and related problems. The book was motivated by the interest shown in these problems by engineers, by the need for solutions to be used in Defence and because there was a proliferation of estimation techniques presented in the engineering literature, which had never been analysed adequately. The book uses extensively the asymptotic theory developed by Professor Quinn’s co-author, the late Professor E.J. Hannan. Both time-domain (autocovariance-based) and frequency-domain (Gaussian maximum likelihood or periodogram-based) techniques are presented, along with rigorous (asymptotic) statistical theory. A feature of the book is the use of a small number of Fourier coefficients (the Fourier transform at a small number of frequencies) of a time series to estimate a fixed frequency or track a time-varying frequency. Many of the results have not been published elsewhere. Unfortunately the book, which was expected to be published in early December, althoughed printed, bound and sent to book reviewers before Christmas, was not distributed until just after the New Year, for business reasons. Professor Quinn has also carried out new and original work on the estimation and tracking of frequency using Fourier coefficients in consecutive time-blocks, on estimating the number of sinusoids in a trigonometric regression and on correcting a Bayesian approach to frequency estimation developed by J. Andel, with his PhD student N. Daley from Goldsmiths College.
Professor Subba Rao has taken on four new PhD students during the period, and conducted joint research with them on the statistical analysis of non-stationary non-linear time series. He has developed non-stationary bilinear models for global temperatures, incorporating variables which are thought to be linked to the greenhouse effect. With L. Dugdale, a current Thomson-Marconi funded CASE EPSRC student, he has developed techniques for the estimation and detection of signals in the presence of non-stationary noise. With another EPSRC-funded PhD student, G. Hughes, he has been looking at the efficiency of regression techniques when the error process is non-stationary, and with A. Antunes, who is funded by a Science and Technology grant from the Portuguese government under the Praxis Scheme, he has formulated spatio-temporal models for environmental time series. He is also collaborating with Professor J. Franke, University of Kaiserslautern and Professor R. Dahlhaus, University of Heidelberg, on the development of estimation methods for nonstationary models suitable for describing variations in climate.
Professor Laycock has worked in the areas of design of experiments, extreme values, the statistical modelling of high frequency spectral occupancy data and the statistical modelling of medical databases. This has involved collaboration both with other statisticians (at the Universities of Salford, Salamanca, UCLA and the Warsaw Health Authority) and with academics in other disciplines, as noted above. The work on high frequency spectral occupancy is a major collaboration with the department of Electrical Engineering & Electronics at UMIST and will also feature in their Unit of Assessment. With Dr Levermore of the Department of Civil and Construction Engineering, he has collaborated on the joint occurrence of low wind speeds with high temperatures and the impact this has on the built environment. So far this has resulted in a paper at an international conference. With his current research student, I. McHale, funded under the Postgraduate Training Partnership (PTP) scheme, a joint inititiative of the DTI and EPSRC, he is investigating inference for regression models based on the four-parameter family of sum-stable distributions. An invited paper on this topic is to be presented at a conference in St Petersburg. Another invited paper on aspects of optimal choices for distance-sampling and capture-recapture designs is to be presented at the Spruce 2001 conference.
Dr Boshnakov’s main area of work during this RAE period has been periodically correlated time series. He has established recursive techniques for parameter estimation parameters in periodic ARMA models and derived necessary and sufficient conditions on the parameters for the existence of weakly stationary solutions to the defining equations. General results on multi-companion matrices have been obtained and applied in the area of periodically correlated autoregressive processes. He has investigated the existence and use of sufficient statistics in Gaussian ARMA models with some parameters fixed, and has recently begun working on the estimation and representation of continuous parameter processes using discrete-time observations.
Dr Yuan has developed his earlier work on spectral estimation for random fields and its applications. He has considered the problem of testing for Gaussianity and linearity in time series and random fields. In particular, he has gained insight in, and improved on, a test due to Hinich, and derived likelihood ratio-tests for the Gaussianity and linearity of random fields. The linearity test is almost as simple as the Gaussianity test, and the asymptotic power is available as a function of the deviation from the null hypothesis. He has also been involved in innovative collaborative work on combustion noise and flame pattern recognition with Dr Y. Zhang, of UMIST’s Dept of Mechanical Engineering, which has so far produced a JRSS publication, output 4.
The Department actively encourages the taking of sabbatical leave at the rate of one semester per six, and attendance at conferences and symposia and provides funds for travel and conference attendance. The Group organises regular seminars, in conjunction with the statistics group at the University of Manchester. The Department has also been able to keep the number of teaching courses down to three (semester-long) per annum per academic member of staff, in order to provide the time to do quality research. With recent appointments, the Group has been able to adopt a more flexible approach to the granting of leave to do research. Thus, for example, one member, Dr Yuan, was relieved of his lecturing duties for one semester in order to complete work on a particularly time-consuming research task, which resulted in his output number 3, while the newest member of staff, Dr Boshnakov, has had a reduced lecturing load, so that his research might be uninterrupted while he settled in. Each new member of staff in the department has both a personal supervisor and a mentor, who has the prime role in guiding the research programme. This policy has been extended to the two long-standing members who have not been research-active for much of the RAE period.
The Department has a Research Committee which has responsibility for all aspects of research carried out within the department. The committee formulates research policy, approves applications for small travel grants, especially for newer members of staff and postgraduate students, and assists members of the Department in their applications for research grants. The staff development and promotions committee is responsible for all aspects of the development of academic staff, including promotion.
Besides the contacts with other departments at UMIST mentioned above, the Group has links with industry, mainly through collaborative research and consulting, but also via the MSc programme. Several of our PhD students have substantial external contacts. L. Dugdale is partially funded by Thomson Marconi Systems (TMS), and spends several weeks per year at TMS in Manchester, discussing his work and researching signal processing problems and applications of interest to TMS. Professors Subba Rao and Quinn have also spent several days there exploring problems of mutual interest. Two of Professor Laycock’s students, A. Lane, who graduated in 1998, and I. McHale, have undertaken their PhDs under the DTI-EPSRC PTP scheme. The industrial link in these two cases was EATL, the energy research company. Professor Laycock also has substantial research links through his extensive statistical consulting with several major international oil companies and many of the UK’s utilities. He has been sought as an expert advisor on many occasions, and recently gave expert advice in what is believed to be the world’s largest law suit, over responsibility for the failure of water wells in Libya. His collaborative research work on high frequency spectral occupancy began as consulting work. His long-term theoretical interest in extreme values was stimulated by questions asked by the UMIST Corrosion and protection Centre on the Gumbull distribution.
The statistics Group has formal links with the Mathematics Department of the University of Manchester. As the Manchester Centre for Statistical Science, the two statistics groups operate regular statistics seminars which are advertised by mail, email and on ‘allstat’. The Centre organises between six and ten seminars per semester, held at either of the two sites. The speakers are selected from across the UK, and from international visitors to the UK. The two departments have planned to establish a Research Institute for Mathematical Science in a refurbished building on the UMIST site near our current building. One of the main objectives of the Institute is to foster inter-disciplinary research between the mathematical sciences and the users of mathematics in Science and Engineering at the Manchester Universities.
Copyright 2002 - HEFCE, SHEFC, ELWa, DEL
Last updated 17 October 2003