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 higherorder 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 higherorder 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 Singularvalue decomposition of the socalled 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 temporalspatial 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 ddimensional 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 nth 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 higherorder information (that is, information on the higherorder cumulant spectra). This theory allows analysis of nonlinear and nonGaussian models with both short and longrange 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 OrnsteinUhlenbeck 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 timespecific 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 nonparametric 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
Staff academaidd
All seminars will commence at 12:10 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 Bertrand Gauthier and Kirstin Strokorb for more details regarding Statistics lectures.
Seminars
Date  Speaker  Seminar 

9 March 2020 Room M/0.40  Almut Veraart (Imperial College London)  Volatility estimation in time and space The concept of (stochastic) volatility/intermittency is of central importance in many fields of science. In this talk I am going to discuss how stochastic volatility can be introduced in a stochastic model and which properties of the stochastic model have an influence on the methods available for volatility estimation. I will showcase some recent results on how stochastic volatility can be estimated in multivariate nonsemimartingale settings and show some first results in extending the classical stochastic volatility concept to spatial/spatiotemporal settings. The results presented in this talk are based on collaborations with Ole E. BarndorffNielsen, Fred Espen Benth, Andrea Granelli, Michele Nguyen, Riccardo Passaggeri. 
2 March 2020  Ioannis Kosmidis (Warwick University)  Improved estimation of models for ordinal responses For the estimation of cumulative link models and adjacent category models for ordinal data, we derive adjustments to the likelihood score functions, whose solution ensures an estimator with smaller asymptotic bias than the maximum likelihood estimator typically has. The form of the adjustments suggests a parameterdependent adjustment of the multinomial counts, which in turn suggests the solution of the adjusted score equations through iterated maximum likelihood fits on adjusted counts, greatly facilitating implementation. Like the maximum likelihood estimator, the reducedbias estimator is found to respect the key invariance properties that make cumulative link models a good choice for the analysis of categorical data. Its additional finiteness and optimal frequentist properties, along with the adequate behaviour of related asymptotic inferential procedures, make the reducedbias estimator attractive as a default choice for practical applications. We will also discuss the improved estimation of the adjacent category model, which is another popular model for ordinal data, and how this can be achieved using a modification of the socalled "Poisson trick". 
13 February 2020 Time:14:10 to 15:10 Room M/2.20  Tatiana Benaglia (University of Campinas)  Bayesian Mixture Models for longitudinal data on cognition loss in elderly people A regression mixture model to handle elderly’s cognitive ability up to their death is presented. Cognition is measured across time with standard questionnaires from geriatrics which involve, amongst others, memory, language and reasoning issues. The output of such questionnaires is recorded with a countable and finite score. Models for Binomial response variables are discussed here. The mixture specification rises to discriminate two prevalent behaviours in the data: one group of elderly people presents cognition decline at constant rate; whilst the other experiences a spontaneous accelerated decline at some time. The latter aspect is dealt with random change points nonlinear predictors. In addition, logit and complementary loglog link functions were used to model the mixture allocation with predictor variables. The study’s goal is to quantify associations amidst cognition loss and the diagnostics of dementias like Alzheimer’s disease, besides sociodemographic factors. The proposed model is evaluated in the database provided by the Rush University  Chicago, United States, through the Rush Memory and Aging Project from 1997 to 2016. The talk is based on joint work with Eric Krishna, Hildete P. Pinheiro (Campinas) and Graciela MunizTerrera (Edinburgh). 
10 February 2020  Xin Liu (University of Bath)  Diversification in LotteryLike Features and Portfolio Pricing Discounts I study the asset pricing implications of cumulative prospect theory on portfolio discounts. I extend Barberis and Huang (2008) and show that a portfolio consisting of lotterylike stocks should trade at a discount due to diversification. This discount can be partially mitigated if lotterylike stocks tend to produce extreme payoffs at the same time. I utilize three empirical settings to support this theoretical prediction: the closedend fund puzzle, the announcement returns of mergers and acquisitions, and conglomerate discounts. My findings support cumulative prospect theory from an alternative perspective and provide a novel and unifying explanation for three seemingly unrelated phenomena. 
27 January 2020  Dino Sejdinovic (University of Oxford)  Noise Contrastive MetaLearning for Conditional Density Estimation using Kernel Mean Embeddings Current metalearning approaches focus on learning functional representations of relationships between variables, i.e. estimating conditional expectations in regression. In many applications, however, the conditional distributions cannot be meaningfully summarized solely by expectation (due to e.g. multimodality). We introduce a novel technique for metalearning conditional densities, which combines neural representation and noise contrastive estimation together with wellestablished literature in conditional mean embeddings into reproducing kernel Hilbert spaces. The method shows significant improvements over standard density estimation methods on synthetic and realworld data, by leveraging shared representations across multiple conditional density estimation tasks. 
17 December 2019  Eliana Christou (UNC Charlotte, North Carolina)  Central Quantile Subspace Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. There is a great amount of work about linear and nonlinear QR models. Specifically, nonparametric estimation of the conditional quantiles received particular attention, due to its model flexibility. However, nonparametric QR techniques are limited in the number of covariates. Dimension reduction offers a solution to this problem by considering lowdimensional smoothing without specifying any parametric or nonparametric regression relation. Existing dimension reduction techniques focus on the entire conditional distribution. We, on the other hand, turn our attention to dimension reduction techniques for conditional quantiles and introduce a new method for reducing the dimension of the predictor X. The novelty of this paper is threefold. We start by considering a single index quantile regression model, which assumes that the conditional quantile depends on X through a single linear combination of the predictors, then extend to a multi index quantile regression model, and finally, generalize the proposed methodology to any statistical functional of the conditional distribution. The performance of the methodology is demonstrated through simulation examples and real data applications. Our results suggest that this method has a good finite sample performance and often outperforms existing methods. Please note this talk takes place at 11:10 in room M/2.06. 
9 December 2019  Ruth Misener (Imperial College)  Scoring positive semidefinite cutting planes for quadratic optimization via trained neural networks Semidefinite programming relaxations complement polyhedral relaxations for quadratic optimization, but global optimization solvers built on polyhedral relaxations cannot fully exploit this advantage. We develop linear outerapproximations of semidefinite constraints that can be effectively integrated into global solvers for nonconvex quadratic optimization. The difference from previous work is that our proposed cuts are (i) sparser with respect to the number of nonzeros in the row and (ii) explicitly selected to improve the objective. A neural network estimator is key to our cut selection strategy: ranking each cut based on objective improvement involves solving a semidefinite optimization problem, but this is an expensive proposition at each Branch&Cut node. The neural network estimator, trained a priori of any instance to solve, takes the most time consuming computation offline by predicting the objective improvement for any cut. This is joint work with Radu BalteanLugojan, Pierre Bonami, and Andrea Tramontani. 
2 December 2019  Edilson Fernandes De Arruda (Rio de Janeiro / Cardiff)  Solving Markov Processes by Time Aggregation: Theory and Applications Markov decision processes are a natural way to model sequential decisions under uncertainty and find applications in many fields, such as healthcare, renewable energy and supply chains. Unfortunately, complex problems give rise to very large state spaces (curse of dimensionality), rendering classical algorithms intractable. In this talk, I will discuss some algorithms that make use of time aggregation (embedding) to tackle the curse of dimensionality and seek optimal or suboptimal solutions to complex systems in reasonable computational time. I will present some realworld applications to illustrate both the approach and the flexibility of Markov decision processes as a modelling tool. 
25 November 2019  Theo Economou (University of Exeter)  An Advanced Hidden Markov Model for Hourly Rainfall Time Series For hydrological applications, such as urban flood modelling, it is often important to be able to simulate subdaily rainfall time series from stochastic models. However, modelling rainfall at this resolution poses several challenges, including a complex temporal structure including long dry periods, seasonal variation in both the occurrence and intensity of rainfall, and extreme values. We illustrate how the hidden Markov framework can be adapted to construct a compelling model for subdaily rainfall, which is capable of capturing all of these important characteristics well. These adaptations include clone states and nonstationarity in both the transition matrix and conditional models. Set in the Bayesian framework, a rich quantification of both parametric and predictive uncertainty is available, and thorough model checking is made possible through posterior predictive analyses. Results from the model are interpretable, allowing for meaningful examination of seasonal variation and medium to long term trends in rainfall occurrence and intensity. To demonstrate the effectiveness of our approach, both in terms of model fit and interpretability, we apply the model to an 8year long time series of hourly observations. 
18 November 2019  Jack Noonan (Cardiff University)  First passage time for Slepian process with linear barrier In 1971, L.A. Shepp found explicit formulas for the first passage probability Pr(S(t)<a for all t in [0,T]  S(0)=x), for all T>0, where S(t)is a Gaussian process with mean 0 and covariance E S(t)S(t')=max{0,1tt’}. In a recent paper, we extended Shepp’s results to the more general case of piecewiselinear barriers; previously, explicit formulas for even Pr(S(t)<a+bt for all t in [0,T]) were known only for the cases b=0 (constant barrier) or T <= 1 (short interval). In this talk, we outline applications to a change point detection problem; detecting temporary drift change of Brownian. After discussing Average Run Length (ARL) approximations, we formulatevery accurate approximations for the power of the test. We also investigate the performance of the test when the change in drift is permanent and compare performance to the known optimal CUSUM and ShiryaevRoberts procedures. 
11 November 2019  Enrica Pirozzi (University of Naples)  On a Fractional OrnsteinUhlenbeck Process and its applications The seminar is centred on a fractional OrnsteinUhlenbeck process that is solution of a linear stochastic differential equation, driven by a fractional Brownian motion; it is also characterised by a stochastic forcing term in the drift. For such a process, mean and covariance functions will be specified, concentrating on their asymptotic behaviour. A sort of short or longrange dependence, under specified hypotheses on the covariance of the forcing process, will be shown. Applications of this process in neuronal modelling are discussed, providing an example of a stochastic forcing term as a linear combination of Heaviside functions with random center. Simulation algorithms for the sample path of this process are also given. 
4 November 2019  Emma Aspland (Cardiff University)  Lung Cancer Clinical Pathway Modelling Clinical pathways are an effective and efficient approach in standardising the progression of treatment to support patient care and facilitate clinical decision making. Our review of the related literature highlighted a need to better integrate data engineering and OR techniques with expert/domain knowledge to assist with clinical pathway discovery and formation. Consequently, we have produced a decision support tool that facilitates expert interaction with data mining, through the application of clustering. This has involved the development of a new distance metric, modified from the NeedlemanWunsch algorithm, that considers weightings and groupings of activities as specified by an expert user. The resulting set of pathways are then automatically translated into the basis of a discrete event simulation to model patient flows through the captured clinical pathways. 
4 November 2019  Clement Twumasi (Cardiff University)  Comparative modelling of parasite population dynamics of two Gyrodactylus species Understanding fully hostparasite systems is challenging if employing just experimental approaches, whereas mathematical models can help uncover indepth knowledge of the infection dynamics. The current study compares the infection dynamics of two parasite species (Gyrodactylus turnbulli and Gyrodactylus bullatarudis) across three host populations (ornamental, Lower Aripo and Upper Aripo ﬁsh), by developing a Continuoustime Markov Chain (CTMC) model. The model simulates the movement of parasites for two age groups over the external surfaces (eight body regions) of a ﬁsh over a 17day infection period with population carrying capacity (dependant on host size and area of body regions). The model was parameterised by the birth, death and movement rates of young and older parasites, in the presence or absence of host’s immune response. Host death was assumed to occur at a rate proportional to the total number of parasites on the ﬁsh. The CTMC simulation model was ﬁtted using a novel Weightediterative Approximate Bayesian Computation (ABC). The ﬁndings from this study would help policy makers and biologists to better understand the Gyrodactylusﬁsh system using mathematical models and inform management decisions for the control of gyrodactylid infections. 
21 October 2019  TriDung Nguyen (University of Southampton)  Game of Banks – Keeping Free ATMs Alive? The LINK ATM network is a fundamental part of the UK's payments infrastructure  with nearly 62,000 ATMs  and cash machines are by far the most popular channel for cash withdrawal in the UK, used by millions of consumers every week. The record high daily withdrawal in 2019 was 10.7 million ATM transactions (29 March) and with over half a billion pounds paid out by ATMs (28 June). The UK's cash machine network is special in that most of them are currently free of charge. Underlying this key feature is the arrangement among the banks and cash machine operators to settle the fees among themselves instead of putting the burden on the consumers' shoulders. The ATM network in the UK has recently, however, been experiencing many issues as some members are not happy with the mechanism for interchange fee sharing. In this talk, we show how Game Theory, especially how to combine mathematical models developed by John Nash and Lloyd Shapley, two Nobel laureates in Economics, to resolve the current ATM crisis. We present a novel `coopetition' game theoretic model for banks to optimally invest in the ATM network and to share the cost. This coopetition game includes both a cooperative game theory framework as the mechanism for interchange fee sharing and a noncooperative counterpart to model the fact that banks also wish to maximise their utilities. We show that the current mechanism for sharing is unstable, which explains why some members are threatening to leave. We also show that, under some settings, the Shapley allocation belongs to the core and hence it is not only fair to all members but also leads to a stable ATM network. We prove the existence of a pure Nash equilibrium, which can be computed efficiently. In addition, we show that the Shapley value allocation dominates the current mechanism in terms of social welfare. Finally, we provide numerical analysis and managerial insights through a case study using real data on the complete UK ATM network. 
14 October 2019  Ruth King (University of Edinburgh)  Challenges of quantity versus complexity for ecological data Capturerecapture data are often collected on animal populations to obtain insight into the given species and/or ecosystem. Longterm datasets combined with new technology for observing individuals are producing larger capturerecapture datasets – for example, repeated observations on >10,000 individuals are becoming increasingly common. Simultaneously, increasingly complex models are being developed to more accurately represent the underlying biological processes which permit a more intricate understanding of the system. However, fitting these more complex models to large datasets can become computationally very expensive. We propose a two step Bayesian approach: (i) fit the given capturerecapture model to a smaller subsample of the data; and then (ii) “correct” the posterior obtained so that it is (approximately) from the posterior distribution of the complete sample. For a feasibility study we apply this twostep approach to data from a colony of guillemots where there are approximately 30,000 individuals observed within the capturerecapture study and investigate the performance of the algorithm. 
7 October 2019  George Loho (LSE)  To be confirmed 
30 September 2019  Rajen Shah (University of Cambridge)  RSVPgraphs: Fast Highdimensional Covariance Matrix Estimation Under Latent Confounding We consider the problem of estimating a highdimensional p × p covariance matrix S, given n observations of confounded data with covariance S + GG^T , where G is an unknown p × q matrix of latent factor loadings. We propose a simple and scalable estimator based on the projection on to the right singular vectors of the observed data matrix, which we call RSVP. Our theoretical analysis of this method reveals that in contrast to approaches based on removal of principal components, RSVP is able to cope well with settings where the smallest eigenvalue of G^T G is relatively close to the largest eigenvalue of S, as well as when eigenvalues of G^T G are diverging fast. RSVP does not require knowledge or estimation of the number of latent factors q, but only recovers S up to an unknown positive scale factor. We argue this suffices in many applications, for example if an estimate of the correlation matrix is desired. We also show that by using subsampling, we can further improve the performance of the method. We demonstrate the favourable performance of RSVP through simulation experiments and an analysis of gene expression datasets collated by the GTEX consortium. 
22 August 2019 Time:11:10 to 12:00 Room M/2.06  Dr. Mofei Jia, Xi'an (JiaotongLiverpool University, China)  Curbing the Consumption of Positional Goods: Behavioural Interventions versus Taxation Little is known whether behavioural techniques, such as nudges, can serve as effective policy tools to reduce the consumption of positional goods. We study a game, in which individuals are embedded in a social network and compete for a positional advantage with their direct neighbours by purchasing a positional good. In a series of experiments, we test four policy interventions to curb the consumption of the positional good. We manipulate the type of the intervention (either a nudge or a tax) and the number of individuals exposed to the intervention (either the most central network node or the entire network). We illustrate that both the nudge and the tax can serve as effective policy instruments to combat positional consumption if the entire network is exposed to the intervention. Nevertheless, taxing or nudging the most central network node does not seem to be equally effective because of the absence of spillover effects from the center to the other nodes. As for the mechanism through which the nudge operates, our findings are consistent with an explanation where nudging increases the psychological cost of the positional consumption. 
18 July 2019 Time:11:10 to 12:00 Room M/2.06  Nina Golyandina (St. Petersburg State University)  Detecting signals by Monte Carlo singular spectrum analysis: the problem of multiple testing The statistical approach to detection of a signal in noisy series is considered in the framework of Monte Carlo singular spectrum analysis. This approach contains a technique to control both type I and type II errors and also compare criteria. For simultaneous testing of multiple frequencies, a multiple version of MCSSA is suggested to control the familywise error rate. 
1 July 2019 Room M/0.40  Dr. Joni Virta (University of Aalto)  Statistical properties of secondorder tensor decompositions Two classical tensor decompositions are considered from a statistical viewpoint: the Tucker decomposition and the higher order singular value decomposition (HOSVD). Both decompositions are shown to be consistent estimators of the parameters of a certain noisy latent variable model. The decompositions' asymptotic properties allow comparisons between them. Also inference for the true latent dimension is discussed. The theory is illustrated with examples. 
8 April 2019  Dr. Andreas Anastasiou (LSE)  Detecting multiple generalized changepoints by isolating single ones In this talk, we introduce a new approach, called IsolateDetect (ID), for the consistent estimation of the number and location of multiple generalized changepoints in noisy data sequences. Examples of signal changes that ID can deal with, are changes in the mean of a piecewiseconstant signal and changes in the trend, accompanied by discontinuities or not, in the piecewiselinear model. The method is based on an isolation technique, which prevents the consideration of intervals that contain more than one changepoint. This isolation enhances ID’s accuracy as it allows for detection in the presence of frequent changes of possibly small magnitudes. Thresholding and model selection through an information criterion are the two stopping rules described in the talk. A hybrid of both criteria leads to a general method with very good practical performance and minimal parameter choice. Applications of our method on simulated and reallife data sets show its very good performance in both accuracy and speed. The R package IDetect implementing the IsolateDetect method is available from CRAN. 
1 April 2019  Stephen Disney (Cardiff University)  When the Bullwhip Effect is an Increasing Function of the Lead Time We study the relationship between lead times and the bullwhip effect produced by the orderupto policy. The usual conclusion in the literature is that longer leadtime increase the bullwhip effect, we show that this is not always the case. Indeed, it seems to be rather rare. We achieve this by first showing that a positive demand impulse response leads to an always increasing in the lead time bullwhip effect when the orderupto policy is used to make supply chain inventory replenishment decisions. By using the zeros and poles of the ztransform of the demand process, we reveal when this demand impulse is positive. To make concrete our approach in a nontrivial example we study the ARMA(2,2) demand process. 
22 March 2019  Martina Testori (University of Southampton)  How group composition affects cooperation in fixed networks: can psychopathic traits influence group dynamics? Static networks have been shown to foster cooperation for specific costbenefit ratios and numbers of connections across a series of interactions. At the same time, psychopathic traits have been discovered to predict defective behaviours in game theory scenarios. This experiment combines these two aspects to investigate how group cooperation can emerge when changing group compositions based on psychopathic traits. We implemented a modified version of the Prisoner’s Dilemma game which has been demonstrated theoretically and empirically to sustain a constant level of cooperation over rounds. A sample of 190 undergraduate students played in small groups where the percentage of psychopathic traits in each group was manipulated. Groups entirely composed of low psychopathic individuals were compared to communities with 50% high and 50% low psychopathic players, to observe the behavioural differences at the group level. Results showed a significant divergence of the mean cooperation of the two conditions, regardless of the small range of participants’ psychopathy scores. Groups with a large density of high psychopathic subjects cooperated significantly less than groups entirely composed of low psychopathic players, confirming our hypothesis that psychopathic traits affect not only individuals’ decisions but also the group behaviour. This experiment highlights how differences in group composition with respect to psychopathic traits can have a significant impact on group dynamics, and it emphasizes the importance of individual characteristics when investigating group behaviours. 
18  Joe Paat (ETH Zurich)  The proximity function for IPs Proximity between an integer program (IP) and a linear program (LP) measures the distance between an optimal IP solution and the closest optimal LP solution. In this talk, we consider proximity as a function that depends on the right hand side vector of the IP and LP. We analyze how this proximity function is distributed and create a spectrum of probabilisticlike results regarding its value. This work uses ideas from group theory and Ehrhart theory, and it improves upon a recent result of Eisenbrand and Weismantel in the average case. This is joint work with Timm Oertel and Robert Weismantel. The proximity functions for IPs. 
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 nonnegative 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 fourthorder “diffusion” equations evolve information in quite different ways. Entropy and irreversibility can be introduced in a selfconsistent 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. 
4 March 2019  Dr. Emrah Demir (Cardiff Business School)  Creating Green Logistics Value through Operational Research Green logistics is related to producing and dispatching goods in a sustainable way, while playing attention to environmental factors. In a green context, the objectives are not only based on economic considerations, but also aim at minimising other detrimental effects on society and on the environment. A conventional focus on planning the associated activities, particularly for the freight transportation, is to reduce expenses and, consequently, increase profitability by considering internal transportation costs. With an evergrowing concern about the environment by governments, markets, and other private entities worldwide, organizations have started to realize the importance of the environmental and social impacts associated with transportation on other parties or the society. Efficient planning of freight transportation activities requires a comprehensive look at wide range of factors in the operation and management of transportation to achieve safe, fast, and environmentally suitable movement of goods. Over the years, the minimization of the total travelled distance has been accepted as the most important objective in the field of vehicle routing and intermodal transportation. However, the interaction of operational research with mechanical and traffic engineering shows that there exist factors which are critical to explain fuel consumption. This triggered the birth of the green vehicle routing and green intermodal studies in operational research. In recent years, the number, quality and the flexibility of the models have increased considerably. This talk will discuss green vehicle routing and green intermodal transportation problems along with models and algorithms which truly represent the characteristics of green logistics. 
25  Oded Lachish (Birkbeck, University of London)  Smart queries versus property independent queries In the area of property testing, a central goal is to design algorithms, called tests, that decide, with high probability, whether a word over a finite alphabet is in a given property or far from the property. A property is a subset of all the possible words over the alphabet. For instance, the word can be a book, and the property can be the set of all the books that are written in English  a book is 0.1 far from being written in English if at least 0.1 of its words are not in English. The 0.1 is called the distance parameter and it can be any value in [0,1]. The input of a test is the distance parameter, the length of the input word and access to an oracle that answers queries of the sort: please give me the i'th letter in the word. The quality of a test is measured by it query complexity, which is the maximum number of queries it uses as a function of the input word length and the distance parameter, ideally this number does not depend on the input length. Tests that achieve this ideal for specific properties have been discovered for numerous properties. In general, tests that achieve the ideal for different properties differ in the manner in which they select their queries. That is, the choice of queries depends on the property. In this talk, we will see that for the price of a significant increase in the number of queries it is possible to get rid of this dependency. We will also give scenarios in which this tradeoff is beneficial. 
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 ValueatRisk). 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 heavytailed 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)  Bilevel programming and the computation of pessimistic singleleadermultifollower equilibria in Stackelberg games We give a very broad overview of bilevel programming problems and their relationship with Stackelberg games, with focus on two classical limitations of this paradigm: the presence of a single follower and the assumption of optimism.

11 December 2018  Anatoly Zhigljavsky (Cardiff University  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 multilevel 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  Prof Benjamin Gess (Max Planck Institute Leipziz)  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 nonequilibrium statistical mechanics. 