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.

Group leader

Academic staff

All seminars will commence at 12:10pm in room M/2.06, The Mathematics Building, Cardiff University, Senghennydd Road (unless otherwise stated).

Please contact Dr Iskander Aliev for more details regarding Operational Research/WIMCS lectures and Dr Jonathan Gillard for more details regarding Statistics lectures.

Seminars

Date	Speaker	Seminar
1 June 2016	Chenlei Leng (University of Warwick)	TBC
27 May 2016	Rema Padman (CMU)	TBC
4 May 2016	Yuzhi Cai (Swansea)	TBC
13 April 2016	Matthias Ehrgott (Lancaster)	TBC
30 March 2016	Laszlo Vegh (LSE)	TBC
16 March 2016	Mathias Henze (FU Berlin)	TBC
2 March 2016	Paul Smith (Southampton)	Calibration estimators in official statistics Model-assisted estimation has been in use in surveys for a long time under different names. I will trace some examples showing its evolution, and give a summary of modern calibration estimation as used by National Statistical Institutes in the production of official statistics. I will consider the reasons for calibration and the properties of the resulting estimates from both theoretical and user points of view, and give a range of examples demonstrating particular challenges and issues, and some developments where calibration estimation may continue to improve official outputs.
24 February 2016	Professor Indrajit Ray (Cardiff Business School)	Information-Revelation and Coordination using Cheap Talk: Theory and Experiment
17 February 2016	Professor Theodore Turocy (East Anglia)	Two-bidder all-pay auctions with interdependent valuations: Equilibrium, complexity, competitiveness, and behaviour We present results from two related papers. In the first paper, we analyze symmetric, two-bidder all-pay auctions with interdependent valuations and discrete type spaces. Relaxing previous restrictions on the distribution of types and the valuation structure, we present a construction that characterizes all symmetric equilibria. We show how the search problem this construction faces can be complex. In equilibrium, randomization can take place over disjoint intervals of bids, equilibrium supports can have a rich structure, and non-monotonicity of the equilibrium may result in a positive probability of allocative inefficiency when the value of the prize is not common. Particular attention is paid to the case in which an increase in a bidder’s posterior expected value of winning the auction is likely to be accompanied by a corresponding increase for the other bidder. Such environments are "highly competitive" in the sense that the bidder’s higher valuation also signals that the other bidder has an incentive to bid aggressively. In the second paper, we focus on the relationship between monotonic equilibrium and those "highly competitive" cases. Having a high assessment of the value of the prize is good news, but only if the other participants in the contest are not too likely to believe the same. In a laboratory experiment, we study behavior in both private-values and common-values settings. We vary the degree of correlation between types. While bidding is consistently aggressive across treatments, we find general support of the comparative statics of Bayes-Nash equilibrium for private values. In constrast, behavior in common values settings in which bidders have very noisy information about the value of the prize differs greatly from the equilibrium predictions.
10 February 2016	Evangelos Evangelou (Bath)	The Value of Information for Correlated GLM In portfolio optimisation, one could potentially invest in several projects with an uncertain amount of revenue depending on the outcome of each project. Initially, the investor has a preliminary estimate about the outcome of each project and a prior value for the whole investment but is given the option to purchase some information (i.e. data) from some projects. When the projects are correlated, these data can be used to update the expected outcome of all projects and derive a posterior value for the investment. The information provided by the data has some value to the investor who must decide whether it is worth purchasing them. In this talk we will consider the case where the outcome of each project is modelled by an exponential family. When the distribution is non-Gaussian, the value of information does not have a closed form expression. Using Laplace's approximation for intergrals we will derive an approximation to the value of information and examine the sensitivity of the approximation under different parameter settings and distributions. The method will be illustrated using a spatial decision problem. Joint work with Jo Eidsvik (NTNU)
11 December 2015	Dr. Prabhani Kuruppumullage (Dana-Farber Cancer Institute/ Harvard School of Public Health)	TBC
25 November 2015	Dr Maggie Chen (Cardiff School of Mathematics)	TBC
11 November 2015	Professor Mark Tippett (Loughborough University & Sydney University)	TBC