Statistics Research Group

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; with the School of Engineering in the areas of image processing and stochastic global optimisation of complex systems; and with 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

Prof Anatoly Zhigljavsky photograpgh

Professor Anatoly Zhigljavsky

Chair in Statistics

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

Academic staff

Andreas Artemiou

Dr Andreas Artemiou

Lecturer

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

Dr Bertrand Gauthier

Lecturer

Email:
gauthierb@cardiff.ac.uk
Telephone:
+44(0)29 2087 5544
Photograph of Dr Jonathan Gillard

Dr Jonathan Gillard

Reader in Statistics
Director of Admissions

Email:
gillardjw@cardiff.ac.uk
Telephone:
+44 (0)29 2087 0619
Photograph of Professor Nikolai Leonenko

Professor Nikolai Leonenko

Professor

Email:
leonenkon@cardiff.ac.uk
Telephone:
+44 (0)29 2087 5521
Photograph of Dr Andre Pepelyshev

Dr Andrey Pepelyshev

Senior Lecturer

Email:
pepelyshevan@cardiff.ac.uk
Telephone:
+44 (0)29 2087 5530
Statistics illustration

Dr Kirstin Strokorb

Lecturer

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

All seminars will commence at 12:10pm in room M/0.34, The Mathematics Building, Cardiff University, Senghennydd Road (unless otherwise stated).

Please contact Dr Timm Oertel for more details regarding Operational Research/WIMCS lectures and Dr Andrey Pepelyshev for more details regarding Statistics lectures.

Seminars

DateSpeakerSeminar

15
March
2019

Prof Philip Broadbridge (La Trobe University)

Shannon entropy as a diagnostic tool for PDEs in conservation form

After normalization, an evolving real non-negative function may be viewed as a probability density. From this we may derive the corresponding evolution law for Shannon entropy. Parabolic equations, hyperbolic equations and fourth-order “diffusion” equations evolve information in quite different ways. Entropy and irreversibility can be introduced in a self-consistent manner and at an elementary level by reference to some simple evolution equations such as the linear heat equation. It is easily seen that the 2nd law of thermodynamics is equivalent to loss of Shannon information when temperature obeys a general nonlinear 2nd order diffusion equation. With the constraint of prescribed variance, this leads to the central limit theorem.

With fourth order diffusion terms, new problems arise. We know from applications such as thin film flow and surface diffusion, that fourth order diffusion terms may generate ripples and they do not satisfy the Second Law. Despite this, we can identify the class of fourth order quasilinear diffusion equations that increase the Shannon entropy.

25
February
2019

Oded Lachish (Birkbeck, University of London)

To be announced

18 February 2019 (Time 13:10 - 14:00)

Prof. Giles Stupfler (University of Nottingham)

Asymmetric least squares techniques for extreme risk estimation

Financial and actuarial risk assessment is typically based on the computation of a single quantile (or Value-at-Risk). One drawback of quantiles is that they only take into account the frequency of an extreme event, and in particular do not give an idea of what the typical magnitude of such an event would be. Another issue is that they do not induce a coherent risk measure, which is a serious concern in actuarial and financial applications. In this talk, I will explain how, starting from the formulation of a quantile as the solution of an optimisation problem, one may come up with two alternative families of risk measures, called expectiles and extremiles. I will give a broad overview of their properties, as well as of their estimation at extreme levels in heavy-tailed models, and explain why they constitute sensible alternatives for risk assessment using some real data applications. This is based on joint work with Abdelaati Daouia, Irène Gijbels and Stéphane Girard.

21 January 2019

Stefano Coniglio (University of Southampton)

To be announced

11 December 2018

Anatoly Zhigljavsky (University of Cardiff)

Multivariate dispersion

3 December 2018

Dr Ilaria Prosdocimi  (University of Bath)

Detecting coherent changes in flood risk in Great Britain

Flooding is a natural hazard which has affected the UK throughout history, with significant costs for both the development and maintenance of flood protection schemes and for the recovery of the areas affected by flooding. The recent large repeated floods in Northern England and other parts of the country raise the question of whether the risk of flooding is changing, possibly as a result of climate change, so that different strategies would be needed for the effective management of flood risk. To assess whether any change in flood risk can be identified, one would typically investigate the presence of some changing patterns in peak flow records for each station across the country. Nevertheless, the coherent detection of any clear pattern in the data is hindered by the limited sample size of the peak flow records, which typically cover about 45 years. We investigate the use of multi-level hierarchical models to better use the information available at all stations in a unique model which can detect the presence of any sizeable change in the peak flow behaviour at a larger scale. Further, we also investigate the possibility of attributing any detected change to naturally varying climatological variables.

26
November
2018

Prof Benjamin Gess (Max Planck Institute)

Random dynamical systems for stochastic PDE with nonlinear noise

In this talk we will revisit the problem of generation of random dynamical systems by solutions to stochastic PDE. Despite being at the heart of a dynamical system approach to stochastic dynamics in infinite dimensions, most known results are restricted to stochastic PDE driven by affine linear noise, which can be treated via transformation arguments. In contrast, in this talk we will address instances of stochastic PDE with nonlinear noise, with particular emphasis on porous media equations driven by conservative noise. This class of stochastic PDE arises in particular in the analysis of stochastic mean curvature motion, mean field games with common noise and is linked to fluctuations in non-equilibrium statistical mechanics.

Past events

Past Seminars 2017-18

Past Seminars 2016-17

Past Seminars 2015-16