STOCHASTIC MODELLING AND ESTIMATION OF RENEWABLE ENERGY PRODUCTION DATA WITH APPLICATIONS IN OPERATIONAL DECISION MAKING
Project supervised by Dr Almut Veraart from Imperial College and dr Oliver Feron from EDF.Climate change threatens the economic prosperity of future generations, which makes it urgent to strive for sustainable economic growth. This is in fact one of the key priorities within the UK Sustainable Development Strategy, which has been drawn up as a response to Agenda 21 of the United Nations. Mathematics and statistics play a key role in tackling this challenge and can deliver the reliable, urgently needed tools for risk assessment. The ultimate objective of my PhD is to develop new methods of stochastic modelling and statistical inference to reliably quantify risk and uncertainty related to renewable sources of energy production, such as wind or solar. While there is a plethora of weather modelling and forecasting methodologies around, such models are typically not tailored to applications in operational decision making, which limits their practical appeal in this context. My project aims to tackle this challenge through a collaborative effort with EDF, who provide expert advice from the perspective of the worldleading power company. I develop statistical models for renewable sources of energy with a particular focus on wind energy production data. Renewables are often regarded as unreliable due to their highly random and unpredictable behaviour. However, in order to achieve sustainable economic growth, investments in renewable sources of energy are needed. The question big energy suppliers are facing is which investment decision will result in a reliable energy supply for the population while minimising risk at the same time. Given the current situation in Europe, it is particular interesting to find the ideal mix between wind and solar energy production. In order to help with such investment decision, energy providers need to know the corresponding forward prices of electricity and how they depend on the supply and the variations of renewable sources of energy. My focus is on deriving suitable stochastic models for wind energy prices characterised by two criteria. First, while they need to be flexible enough to accurately describe the random evolution of renewables over time, they also have to allow for efficient calibration. Second, they have to be analytically tractable, so that forward prices of electricity generated from renewable sources of energy can be computed in explicit form, which allows operational decision making based on such models. I am developing suitable continuoustime stochastic process models which can account for nonstationarities in terms of strong seasonal behaviour and trend, stochastic volatility and the existence of jumps. A starting point is the class of socalled multivariate volatility modulated Volterra processes. The particular modelling challenge is to allow for dependencies on wind and also to find a suitable mechanism, which is likely to be via a regimeswitching approach, which can model the impact of renewables on the corresponding electricity price.

BAYESIAN INFERENCE FOR EXPENSIVE SIMULATORS
Project supervised by Richard Everitt and Richard Sibly from University of Reading.
This project concerns Bayesian inference of parameters of models, and of Bayesian model comparison, cases where a model takes the form of a computationally expensive computer simulator. This general problem is encountered in many different areas of science. This project is motivated by partial differential equation simulators as used in weather and climate models, and also the use of Agent Based Models (ABMs) and differential equation models in Ecology. There is a strong link between some of the statistical methods applied to these two situations: the use of emulators being commonplace in weather and climate, and in ABMs approximate Bayesian computation (ABC) has been applied. Both of these methodologies are based on the estimation of a model from points simulated from that model and indeed this link has been explored a little in the recent literature.
The particular interest of this project is in the use of ABClike methodologies that make use of a very computationally expensive simulator. In this situation the number of model simulations that can be run limits the exploration of the parameter space. Recent work has explored the parameter space by brute force, running rejection sampling using a large number of parallel simulations, however the curse of dimensionality limits the use of this approach to low dimensional parameter spaces. The use of more sophisticated Monte Carlo methods is limited by their being more difficult to parallelise.
This project proposes to explore the use of a new Bayesian optimisation method, which has a strong link to emulators, in this setting. This work on an existing ABM (modelling earthworms) will be conducted with a view to using a similar approach in weather and climate models (building on current work at the University of Reading on using ABC for inference in paleoclimate models). In parallel, an investigation into making use of a rarely exploited structure will be conducted, using a decomposition of the model as a deterministic transformation of a realisation of a random variable.