Data and Decisions
The theme of Data and Decisions covers the research areas of Optimisation, Operational Research, Statistics and Actuarial Mathematics
Members of the theme undertake research at the forefront of modern mathematical and computational problems related to optimisation, operational research, statistics and their application: core elements of Data Science.
Particular areas of interest include: Bayesian inference, computationally intensive inference techniques; extreme value theory; high-dimensional statistics; interior point methods; convex, proximal,nonlinear and global optimisation; nonparametric statistics; regression; stochastic optimization.
Application areas include: actuarial sciences; mathematical and computational imaging; ecology; energy; environment; finance; genomics; public health and medical statistics, with many members working closely with industrial partners and government bodies.
Several members of the theme are research fellows of the Alan Turing Institute. Members of the theme have recently established the Statistical and OR Consultancy Units, providing bespoke consultancy and data analysis services, and the Centre for Statistics that unites data-driven researchers across the University of Edinburgh, Heriot-Watt University and Associated Institutions, including Biomathematics and Statistics Scotland.
The Statistics seminars at the School of Mathematics is a part of Maxwell Institute seminar series. The seminars are organised jointly between the Statistics group in the School of Mathematics, University of Edinburgh and Biomathematics and Statistics Scotland. If you would like to give a talk at the Statistics seminar series, you can contact the Statistics seminar organisers. The seminar organisers of the Statistics seminar series are Tim Cannings and Serveh Sharifi Far.
Energy-Mathematics-Engineering (EME) seminars
Energy-Mathematics-Engineering is a discussion group between the Schools of Mathematics and Engineering in the University of Edinburgh. We run weekly seminars and we host external and internal speakers. Thanks to the EME group seminars, researchers from Academia and Industry collaborate and share their knowledge.
The fields of actuarial mathematics, financial mathematics and quantitative risk pose unique challenges ranging from the development of stochastic models for human life expectancy, the pricing of complex financial derivatives, the development of capital adequacy models and reserving models through to the design of pension products that are fit for an aging society. When this is coupled with the emergence of big data environments and machine learning entering into insurance, risk management and banking practice there is a unique confluence of multidisciplinary approaches being developed to bring solutions to tackle emerging financial modelling challenges. This often brings together experts in actuarial mathematics, statistics and data science, machine learning practitioners and quantitative risk management to bring their expertise for multidisciplinary solutions.
While some of our research focuses on developing the underlying mathematical and statistical methodology, we are also involved in many applied research projects. The interests of our group contain modelling stochastic volatility, quantitative risk management, genetics and insurance, stochastic models for mortality and morbidity, pension fund design and risk management, stochastic investment models, green finance, cyber risk and insurance, machine learning applications in risk and insurance, econometrics and time series modelling, mathematical finance and derivative pricing, numerical and computational finance, portfolio analysis, market dynamics and limit order book modelling, catastrophe modelling and insurance, time inconsistent control and applications in behavioural economics, credit risk, optimal control of power storage facilities, industrial applications of artificial intelligence, the ethical dimension of mathematics and ethics in quantitative finance, optimisation of investment strategies.
Computational Optimization and Software
Optimization is a key paradigm of numerous decision-making techniques. Models in most areas of a modern economy require minimizing the use of (limited) resources and/or maximizing output or other measures of efficiency. It is essential to have different optimization techniques implemented in robust software able to solve efficiently the large-scale models arising from applications in a diversity of areas. We possess world-leading expertise in the solution of very large scale linear and quadratic optimization problems. At the UK level, the group has unmatched competences in developing theory and software for solving huge scale problems.
Computationally Intensive Techniques
Modern frequentist and Bayesian analyses often require advanced statistical models, including, for example, generalised linear (mixed) models, generalised additive models (GAMs), non-parametric models and state-space models. Fitting such models to data often leads to computational challenges. Research interests focus on developing efficient computational model-fitting techniques such as integrated nested Laplace approximations (INLA), variational inference and Monte Carlo methods (including Markov chain Monte Carlo, sequential Monte Carlo and importance sampling); and associated software tools, such as the R packages mgcv and R-INLA.
Continuous optimization focuses on unconstrained and constrained optimization problems with continuous decision variables that arise naturally in myriad applications. In addition, continuous optimization plays a central role in obtaining exact reformulations or tight approximations of various difficult discrete and combinatorial optimization problems. We have research expertise that encompasses several facets of continuous optimization, including linear, quadratic, nonlinear, convex, nonconvex, global, PDE-constrained, and stochastic optimization. We have strong industrial collaborations and extensive experience in the development and application of operational research methodology for solving problems arising from diverse applications such as truss topology design, finance, and wireless networks.
Decision-Making Under Uncertainty
Uncertainty is inherently present in almost all problems in life, and makes understanding, approaching and solving these problems significantly more complicated than for cases where everything is known with certainty. Decision-making under uncertainty deals with the question of how randomness should be properly incorporated in the modelling, analysis and optimization of real-world problems. We are one of the leading research groups in the world developing methods to solve the resulting huge scale stochastic optimization problems efficiently. The research interests of our members also include Gaussian process emulation and Bayesian decision analysis.
Future Energy Networks
The worldwide transition to renewable energy requires a major rethink of society’s energy networks. Both large-scale renewable projects like offshore wind-farms and decentralised solutions to power small communities are outside the realm of conventional electric grid planning approaches. Our research is concerned with both the modelling and optimization of energy networks, particularly electric and gas networks, as well as the methodological expertise to solve the resulting optimization models in practical applications. At the UK level we are part of the EPSRC-funded National Centre for Energy Systems Integration. Research interests include modelling different systems’ energy markets, and optimizing energy networks of different sizes from small-scale local smart grids to national and continental networks. There is also specialist expertise in calibration of large scale computer models, and in probabilistic security of supply risk modelling.
Integer and Combinatorial Optimization
Combinatorial optimization problems arise in situations where the set of possible solutions is finite. Such problems arise in a natural way in numerous areas of applications. When the number of solutions is very large, an integer programming model needs to be designed and solved. Our research activity encompasses cutting plane methods, convexification techniques, and the construction of efficient algorithms both to obtain exact and heuristic solutions. Applications of interest include energy, logistics (facility location, network design, supply chain, districting), and healthcare applications (junior doctor allocation, kidney exchange).
Statistical learning addresses fundamental questions in statistics, machine learning, computer science, finance, artificial intelligence and industry. Topics of interest include classification, clustering, data visualisation, deep learning, Gaussian processes, large scale regression, non-parametric methods, semi-supervised learning and transfer learning. The research members are particularly interested in contemporary challenges at the forefront of modern data science: for example, how to interpret the output of algorithms based on high-dimensional data; how to ensure that methods are robust to noisy and missing data; and developing data-driven approaches in diverse application areas such as precision medicine, genomics and neuroimaging.
Statistical models are used to mathematically represent a data generating process, with the aim of fitting the model to observed data to improve, for example, our understanding of the underlying system; predict future observations or answer specific hypothesis/questions. Areas of interest include regression models (generalised linear (mixed) models, general additive models, non-parametric models); spatio-temporal models; time series models; state-space/hidden (semi-)Markov models; emulators; Poisson point processes; Gaussian process models; capture-recapture models; and extreme value theory models. Associated challenges may include dealing with missing data; inference under model misspecification; model selection/averaging; smoothness selection; high-dimensional data and dimension reduction; integrated analyses; and efficient model-fitting techniques.
Mathematical underpinning of inference problems arising in modern statistics and data science is crucial to provide theoretical guarantees, particularly as more complex models are often required to analyse high dimensional data. Research areas of particular focus include understanding the behaviour of classification methods and Bayesian procedures, both asymptotically (for large sample size) and non-asymptotically, adaptation to unknown properties (e.g. smoothness or sparsity), and robustness to model misspecification. Examples of the types of problems studied relate to local approximations of the posterior distribution for finite dimensional models, including those with growing parameter dimension; rate of contraction of the posterior distribution for infinite dimensional models where the unknown parameter is a function, for instance in density estimation, nonparametric regression or inverse problems; and local nearest neighbour classification methods for data with imperfect labels or missing observations.
The mathematical tools developed are applied to a wide range of real-world problems and application areas including, but not limited to, precision medicine, energy, ecology, geosciences, public health, finance, medical imaging, forensics, retail, genomics, education and biostatistics. Members of the group collaborate and engage with a wide range of end-users including external research institutions, industry partners, government bodies, non-government organisations and charities.