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Statistics Research Group

The group is active both in applications of statistical techniques and in theory.

The group is very active both in applications of statistical techniques and in theory.

The main areas of research within the current group are:

  • time series analysis
  • multivariate data analysis
  • applications to market research
  • search algorithms and stochastic global optimisation
  • probabilistic number theory
  • optimal experimental design
  • stochastic processes and random fields with weak and strong dependence
  • diffusion processes and PDE with random data
  • anomalous diffusion
  • Burgers and KPZ turbulence, fractional ordinary and PDE, and statistical inference with higher-order information
  • extreme value analysis.

Various topics in fisheries and medical statistics are also considered, such as errors in variables regression.

Collaborations

Statisticians within the School have been prominent in collaborating with researchers in other disciplines. There are strong links with:

  • the School of Medicine, working on applications of multivariate statistics and time series analysis in bioinformatics
  • the School of Engineering, in the areas of image processing and stochastic global optimisation of complex systems
  • the Business School, in the field of analysis of economics time series.

Ongoing international collaborations exist with many Universities including Columbia, Taiwan, Queensland, Aarhus, Roma, Cleveland, Pau, Hokkaido, Boston, Caen, Calambria, Maine, Trento, Nice, Bratislava, Linz, St.Petersburg, Troyes, Vilnius, Siegen, Mannheim, and Copenhagen.

Industrial sponsorship

Significant industrial sponsorship has been obtained from:

  • Procter and Gamble (USA) working on statistical modelling in market research
  • the Biometrics unit of SmithKline Beecham collaborating on different aspects of pharmaceutical statistics
  • ACNielsen/BASES (USA) on applications of mixed Poisson models in studying marketing consumer behaviour
  • General Electric HealthCare on environmental statistics.

Our main areas of research within the current group are:

  • time series analysis
  • multivariate data analysis
  • applications to market research
  • search algorithms and stochastic global optimisation
  • probabilistic number theory
  • optimal experimental design
  • stochastic processes and random fields with weak and strong dependence
  • diffusion processes and PDE with random data
  • anomalous diffusion
  • Burgers and KPZ turbulence
  • fractional ordinary and PDE, and statistical inference with higher-order information.

In focus

Time series analysis

In recent years a powerful technique of time series analysis has been developed and applied to many practical problems. This technique is based on the use of the Singular-value decomposition of the so-called trajectory matrix obtained from the initial time series by the method of delays. It is aimed at an expansion of the original time series into a sum of a small number of 'independent' and 'interpretable' components.

Also, the spatial analogies of the popular ARMA type stochastic time series have been developed based on the fractional generalizations of the Laplacian with two fractal indices. These models describe important features of processes of anomalous diffusions such as strong dependence and/or intermittency.

Multivariate statistics

The objective is development of a methodology of exploratory analysis of temporal-spatial data of complex structure with the final aim of construction of suitable parametric models.

The applications include various medical, biological, engineering and economical data. Several market research projects where the development of statistical models was a substantial part have taken place.

Stochastic global optimisation

Let ƒ be a function given on an d-dimensional compact set X and belonging to a suitable functional class F of multiextremal continuous functions.

We consider the problem of its minimization, that is approximation of a point x' such that ƒ(x')=min ƒ(x), using evaluations of ƒ at specially selected points.

Probabilistic methods in search and number theory

Several interesting features of the accuracy of diophantine approximations can be expressed in probabilistic terms.

Many diophantine approximation algorithms produce a sequence of sets F(n), indexed by n, of rational numbers p/q in [0,1]. Famous examples of F(n) are the Farey sequence, the collection of rationals p/q in [0,1] with q<=n, and the collection of all n-th continued fraction convergents.

Stochastic processes

New classes of stochastic processes with student distributions and various types of dependence structure have been introduced and studied. A particular motivation is the modelling of risk assets with strong dependence through fractal activity time.

The asymptotic theory of estimation of parameters of stochastic processes and random fields has been developed using higher-order information (that is, information on the higher-order cumulant spectra). This theory allows analysis of non-linear and non-Gaussian models with both short- and long-range dependence.

Burgers turbulence problem

Explicit analytical solutions of Burgers equation with quadratic potential has been derived and used to handle scaling laws results for the Burgers turbulence problem with quadratic potential and random initial conditions of Ornstein-Uhlenbeck type driven by Levy noise.

Results have considerable potential for stochastic modelling of observational series from a wide range of fields, such as turbulence or anomalous diffusion.

Topics in medical statistics

A number of topics that have been associated with medical statistics presently researched in Cardiff include time-specific reference ranges, and errors in variables regression. Current research focuses on the search for a unified methodology and approach to the errors in variables problem.

Extreme Value Analysis

Extreme value analysis is a branch of probability and statistics that provides non-parametric procedures for extrapolation beyond the range of data (as good as possible and depending on the quality of data, knowing the limits is also an important issue). Its methods are usually relevant for institutions that are exposed to high risks, for instance, financial services and insurance companies or environmental engineering institutions.

Group leader

Dr Jonathan Gillard

Dr Jonathan Gillard

Reader in Statistics
Director of Admissions

Email
gillardjw@cardiff.ac.uk
Telephone
+44 (0)29 2087 0619

Academic staff

Dr Andreas Artemiou

Dr Andreas Artemiou

Deputy Director, Data Science Academy
Senior Lecturer in Statistics

Email
artemioua@cardiff.ac.uk
Telephone
+44 (0)29 2087 0616
Dr Bertrand Gauthier

Dr Bertrand Gauthier

Lecturer

Email
gauthierb@cardiff.ac.uk
Telephone
+44(0)29 2087 5544
Professor Anatoly Zhigljavsky

Professor Anatoly Zhigljavsky

Chair in Statistics

Email
zhigljavskyaa@cardiff.ac.uk
Telephone
+44 (0)29 2087 5076
Professor Nikolai Leonenko

Professor Nikolai Leonenko

Professor

Email
leonenkon@cardiff.ac.uk
Telephone
+44 (0)29 2087 5521
Dr Andrey Pepelyshev

Dr Andrey Pepelyshev

Senior Lecturer

Email
pepelyshevan@cardiff.ac.uk
Telephone
+44 (0)29 2087 5530
Dr Kirstin Strokorb

Dr Kirstin Strokorb

Senior Lecturer

Email
strokorbk@cardiff.ac.uk
Telephone
+44 (0)29 2068 8833
Dr Robin Mitra

Dr Robin Mitra

Senior Lecturer

Email
mitrar5@cardiff.ac.uk
Telephone
+44 (0)29 2087 5052

Postgraduate students

No profile image

Matt Hoare

Research student

Email
hoarem3@cardiff.ac.uk
Telephone
07926467755

Seminars

All seminars will be held virtually via Zoom and commence at 14:10 on Thursdays (unless otherwise stated).

View the seminar calendar of the Statistics and OR group.

The calendar is maintained independently by members of the research groups.

Please contact Dr Mark Tuson for more details regarding Operational Research/WIMCS lectures and Bertrand Gauthier and Kirstin Strokorb for more details regarding Statistics lectures.

Past events

Past seminars 2019-20

Past seminars 2018-19

Past seminars 2017-18

Past seminars 2016-17

Past seminars 2015-16