# Interns 2014

Below you can find details of the summer 2014 interns including a description of their research project.

Anna Maria Barlow

University of Durham, MMath Mathematics

Supervisor: Christian Rohrbeck

*Spatio-temporal Modelling of Economic Data using Disease Mapping*

The field of statistics focusing on models incorporating spatial information is called Spatial Statistics. Spatial statistics generally distinguishes between three types of data: geostatistical data, lattice data and spatial point patterns. This project will focus on lattice data, where the number of sites at which observations are recorded is finite, for example the population in each county of the UK or the results of the last general election per district. Spatial statistical methods for lattice data are often applied in epidemiology to model the occurrence of a disease in a region depending on covariates. This is known as Disease Mapping, with models aiming to predict the occurrence rate or the number of cases of a particular disease. This project will investigate the basic methods used in Disease Mapping and apply them to economic data.

**View Anna's presentation and poster.**

**Dawid BernaciakUniversity of Glasgow, MSci MathematicsSupervisor: Burak Boyaci **

*Relocation Operations in One-Way Car-Sharing Problems*

Car-sharing is a new concept that enables the general public to access a fleet of vehicles for short rental periods. These systems have several benefits including environmental, energy and societal considerations. Car-sharing systems have two general types; the restrictive “two-way” system where users pick up and drop off the vehicle at the same location, and the more flexible “one-way” system enabling the users to choose a different drop-off location to the pick-up station. For the customer, the one-way system is generally preferred however one of the difficulties in implementing a one-way system is managing relocation of vehicles and personnel. This project will develop and implement models for improving relocation operations for the one-way car-sharing problem.

**View Dawid's presentation and poster.**

**Helen CouplandUniversity of Durham, MMath MathematicsSupervisor: Monika Kereszturi**

*Modelling ocean environments with extreme value theory*

Offshore structures such as oil platforms and vessels must be designed to have very low probabilities of failure due to extreme weather conditions. Inadequate design can lead to structural damage, lost revenue, danger to operating staff and environmental pollution. Design codes demand that all offshore structures exceed specific levels of reliability, most commonly expressed in terms of an annual probability of failure or return period. Hence, interest lies in environmental phenomena that occur extremely rarely, and we want to estimate the rate and size of future occurrences. The aim of this project is to gain a deep understanding of extreme value theory in the application of ocean environments.

**View Helen's presentation and poster.**

**Toby KingsmanUniversity of Birmingham, MSci Theoretical Physics and Applied MathematicsSupervisor: Trivikram Dokka**

*Analysis of Algorithms for yield optimization and batch scheduling problems*

A common scheduling problem in industrial settings is concerned with scheduling jobs on identical machines with the objective of minimizing the total active time. The problem finds important applications in the field of (energy-aware) scheduling especially in applications relating to optimal network design. The aim of this project is to investigate the performance of some natural heuristics proposed for finding near optimal solutions to these computationally hard problems. This will involve learning about the integer and linear programming formulation based methods and using computer programming to implement algorithms and solve linear programs.

**View Toby's's presentation and poster.**

**Aaron LowtherLancaster University, BSc MathematicsSupervisor: Rebecca Killick**

*Seasonally Adjusting Official Time Series*

The Office for National Statistics (ONS) publish thousands of seasonally-adjusted time series which are used to produce the official statistics that create the news headlines regarding, for example, increase/decrease in unemployment and double or triple dip recessions. Seasonal adjustment involves estimating and removing a seasonal component from a time series. This project aims to develop and test a method for the automatic detection of changes in the seasonal pattern of time series by comparing alternative methods and assessing the impact on the estimation of seasonal factors for series that do and do not present changes in the seasonal pattern.

**View Aaron's presentation.**

**Rachel NaylorUniversity of Bath, MMath MathematicsSupervisor: Lisa Turner**

*Fast inference for processing intelligence information*

Intelligence is information regarding threats to national security and potentially hostile forces. After raw intelligence data is collected it must be processed and screened, often in time-critical situations. Only relevant information is then passed on for further analysis. With huge amounts of intelligence data collected daily, potentially relevant information can be missed. Given a set of intercepted communications, how should we process the communications to maximise the amount of relevant information passed on for analysis? This project will develop a model for processing intercepted information and explore how to overcome problems associated with this type of model.

**View Rachel's**

**presentation and poster.**

**Emily OleskerUniversity of Cambridge, BA MathematicsSupervisor: Kaylea Haynes **

*Assessing Performance of Changepoint Detection Algorithms*

Changepoints are a widely studied area of statistics with applications including, but not restricted to, finance; detecting changes in volatility, computer science; detecting instant messaging worms and viruses and environmental such as oceanography and climatology. Changepoints are considered to be the points in a time-series where we experience a change in some statistical property, for example a change in mean or a change in variance. There are many different approaches to changepoint analysis however current methods have the trade-off of being fast but approximate or exact but slow. The aim of this project is to develop an understanding of changepoint detection methods and in particular explore ways in which we can assess the performance of different detection methods.

**View Emily's presentation and poster.**

**Luke Rhodes-LeaderLancaster University, MSci Physics with MathematicsSupervisor: Lawrence Bardwell**

*Explaining changes in aggregated time series*

In many applications there is some indicator that is constantly monitored as new data are collected, for example in an industrial setting, the number of faults recorded on a large network per week. Typically at a managerial level interest lies in the total number of faults over the entire network and patterns or changes that may occur. One important change in this indicator is a spike (outlier) where suddenly there is a large increase in the number of faults over the entire network. Understanding why these sudden increases occur is important so they can be prevented from happening again. This project will investigate methods for detecting outliers in large time series datasets.

**View Luke's presentation and poster.**

**Matthew RobinsonUniversity of Warwick, MMath MathematicsSupervisor: Wentao Li and Paul Fearnhead**

*Selection of Tolerance Level for Approximate Bayesian Computation|*

For many complex datasets, one feature is that the likelihood of the statistical model is intractable, in the sense that it is difficult to evaluate the likelihood values of the observations, and standard inference methods for unknown parameters, like Maximum Likelihood Estimation and Monte Carlo Markov Chain, do not work. For intractable problems of which sampling from the likelihood given parameter values is easy, Approximate Bayesian Computation (ABC) is a useful Bayesian inference method using Monte Carlo simulations. The project will investigate the impact of the tolerance level, a core parameter of ABC algorithm, in various situations and try to design an automatic algorithm to select the tolerance level.

**View Matthew's presentation and poster.**

**Emma Stubington**

**Sheffield University, BSc Mathematics**

**Supervisor: Ivar Struijker-Boudier**

*Travelling Salesman Problem*

Scheduling problems can be found in many industrial settings. The complexity of scheduling problems is often such that optimal solutions cannot be guaranteed to be found in short computational time. However, many companies need to produce schedules on a daily basis, so they need a computationally fast way of implementing this. A well-known example of a difficult to solve scheduling problem is the travelling salesman problem (TSP) which is concerned with finding the shortest route which visits each of a number of locations exactly once. If every location can be travelled to directly from every other location, then the number of possible solutions increases very quickly as more locations are added to the problem. Evaluating every possible solution then becomes impossible. This project will explore the travelling salesman problem and will assess and compare various solution methods for the TSP.

**View Emma's presentation and poster.**

**Luke WhincopUniversity of Bath, MMath MathematicsSupervisor: Nikos Kourentzes**

*Modelling solar irradiance for energy generation*

The increasing investment in renewable energy is essential to guarantee immediate answers both to the high and fluctuating prices of crude oil and to the diversification of energy supplies, thus reducing external dependence on oil, gas and coal. Therefore, solar power generation becomes an area of paramount research. Various time series methods have been implemented to forecast solar irradiance for power generation however a complication with solar irradiance data is that of multiple seasonalities- seasonality from the day-night cycle and the annual earth cycle. This project will attempt to tackle some of the questions related to modelling the seasonal element of solar irradiance using time series and forecasting models.

**View Luke's presentation and poster.**