Below you can find details of the summer 2017 interns including a description of their research project.

## Edward Austin

### Lancaster University, BSc Mathematics

Supervisor: Chrissy Wright

Modelling Risk in Hazardous Material Transport

The risk of an accident is an important factor to consider when transporting hazardous materials.

Because accidents can be deadly the route with the least overall risk should be chosen.

This project looks at how best to model the risk to enable safer routes to be taken

## Callum Barltrop

### Lancaster University, BSc Mathematics

Supervisor: Anna Barlow

Investigating bias in return level estimates due to the use of a stopping rule

There are many situations in which rare and extremely large (or small) events are of interest. For example, the focus of my project is the statistical modelling of extreme flood events. Extreme Value Theory is concerned with the modelling of the tails of a distribution and provides a theoretically sound framework for the study of extreme values. In particular, the Generalised Extreme Value distribution is used to model the maxima of a process within blocks of time (often a year). Usually we are mostly interested in estimating the x-year return levels of a distribution, that is, the value we’d expect to be exceeded on average once every x years. However, the point at which we decide to stop sampling and analyse the data is not arbitrary and this choice of stopping point can result in biased return level estimates. After the December 2015 floods there was much interest in re-evaluating the return level estimates, as the inclusion of such a large event often led to significant changes in the value of these estimates. In this project we will consider possible ‘stopping criteria’ (i.e. rules that tell us when to stop sampling data and do our analysis) to approximate the procedures used in reality and investigate the bias in the standard estimates. We will implement a variety of new estimators developed with the intention to improve upon the existing standard methods.

## Jonathan Bevan

### Lancaster University, MSci Mathematics and Statistics

Supervisor: Harjit Hullait

Time series Classification

The internship project will be focused on Time series classification, an area that has applications in various fields. The idea is to build a classifier, which is able to label a time series from a defined list of possibilities.

For example if we have heart rate time series for people walking and people running, we have two label: runner or walker. There are two main challenges in classification, firstly a set of labels needs to be chosen and secondly a classifier needs to be built that can label the time series.

## Chloe Fearn

### Lancaster University, MSc Mathematics

Supervisor: Christian Rohrbeck

Analysis of Armed Conflict Data

The Armed Conflict Location & Event Data Project (ACLED) has aggregated the exact location, date, and other characteristics of several violent events in unstable and warring states. The analysis of this data is challenging due to the vast amount of factors influencing such events. Koren and Bagozzi (2017)( Journal of Peace Research, 54(3)) find, for instance, that, in times of war, violence against civilians occurs more frequently in areas with a high percentage of cropland. This result is derived based on a zero-inflated model which accounts for armed conflicts not being present in all areas at all times. The proposed project considers the publicly available data and aims to slightly extend the model by Koren and Bagozzi (2017), for instance, by accounting for the spatial aspect of the data. In particular, the project can be split over three steps: (i) Exploratory analysis of the Data, (ii) Estimation of a similar model which to the one by Koren and Bagozzi (2017) and (iii) Extending the model.

## Jake Grainger

### Lancaster University, MSc Mathematics

Supervisor: Rob Shooter

Assessing the Use of Spatial Models for Extremes

Being able to model spatial extremal behaviour (in particular spatial dependence) is an important area of Extreme Value Theory and this project will aim to give an introduction into the various methods of trying to capture this behaviour. The first part of this project will provide a short introduction to univariate extreme value theory and also will look at some methods of spatial statistics – in particular looking at Gaussian Processes, which will be simulated and have interpolation methods performed on them. The second part will introduce the Smith process (a particular type of max-stable process) and will compare this to using Gaussian Process techniques on data, with the aim of comparing how well the two types of spatial model are able to describe the nature of the data.

## Graham Laidler

### Durham University, MMath Mathematics

Supervisor: Sam Tickle

Sequential Changepoint Detection: Anticipating the next Financial Crash

Changepoint detection underpins virtually all questions of interest surrounding data analysis in a variety of contexts. Understanding the nature of a change, and when it occurred, is often of vital importance in preventing problems surfacing in the future. With the advent of Big Data, more sophisticated tools are increasingly required to search for changes on datasets of ever-growing size. Most existing methods for changepoint detection are offline, requiring the collection of an entire dataset prior to analysis, and interest in online techniques, where informed statements regarding changes of the recent past can be made in tandem with data collection, is growing.

This project will examine various existing methodologies which employ an online approach to changepoint detection, both Bayesian and frequentist, and attempt to apply these ideas to real-time datasets (for example, share price data for various FTSE100 companies) in order to find the best performing algorithms which can operate most efficiently in the greatest number of contexts. Depending on specific interests, this can involve exploring prior selection, investigating various 'control charts’ or using likelihood-based approaches among other options. There is also potential scope in helping to pioneer entirely new techniques which can then be tested against some of the existing methods.

## George Phillips

### University of York, MMath Mathematics

Supervisor: Emily Graham

Combination therapies: improving outcomes via the probability of success

Combination therapies are able to hit the many mechanisms of diseases/cancers simultaneously by combining existing drugs and new molecular entities. When developing a combination therapy, the aim is to produce a synergistic effect while reducing side effects. However, drug development is a long and expensive process which is subject to a considerable amount of uncertainty. Therefore it is important that the decisions made are well informed and are expected to be the most beneficial to both the pharmaceutical company and the patient population.

Methods for decision making often require several parameters relating to a drug. We are interested in the estimation of the probability of study success for combination therapies. Current methods do not allow information to be shared across similar combinations. We believe that incorporating this information in a Bayesian setting will improve the accuracy of our estimates. This will lead to better decision making and improve the outcomes of the development programmes.

## Harry Spearing

### Lancaster University, BSc Physics

Supervisor: Luke Rhodes-Leader

Simulation Optimisation Techniques for Time-Dependent Staffing Problems

In many real world problems, such as complex queueing problems, mathematical models of the system can be too complex to solve analytically. An alternative way to study stochastic systems is to use a simulation to produce realisations of the system. Simulation can be used to optimise a system by testing alternative settings. The choice of optimisation technique depends heavily on the properties of the problem, such as size of the solution space, how many objectives there are and whether the decision variables are discrete or continuous. Due to the stochastic nature of the problems, the optimisation is further complicated as the objective must be estimated, rather evaluated exactly. This project will focus on finding simulation optimisation techniques appropriate for the optimal staffing problem for a time dependent queueing system, such as that of an emergency call centre.

## Livia Stark

### Lancaster University, MPhys Physics

Supervisor: Toby Kingsman

Executing Offshore Maintenance Activities

At the start of the internship time will need to be spent learning about the general offshore maintenance problem and literature associated with it. This could be simpler sub-problems such as the travelling salesman problem, travelling repairman or scheduling of tasks. Depending on the student’s knowledge of linear programming and coding, time could be spent trying to implement one of these models on the computer.

The goal of the project is likely to be creating some simple construction heuristics to solve the offshore maintenance routing and scheduling problem. These could be extended to more general problems depending on the student’s interest, e.g. several vessels or tasks completed in stages. The performance and results of these heuristics could be compared across several instances.

## Jinran Zhan

### University of Southampton, BSc Mathematics and Statistics

Supervisor: David Torres Sanchez

Scheduling using Optimisation

The project will focus on one the main optimisation scheduling problems. Project planning, it refers to the programming of different activities that need completion for a given project. It is also heavily conditioned by the specifications on the resources and activities, making the problem really interesting for mathematicians. In this project we will be focussing on understanding the so-called resource-constrained project scheduling problems (RCPSP). The generality of the RCPSP allows it to have a wide range of applications where the aim is to schedule some activities or jobs over a period of time such that precedence and resource constraints are satisfied, and a certain objective function is optimised. Depending on the student’s knowledge of linear programming and optimisation we can study the varied formulations or if the student is familiar with it we can jump straight into the pre-emptive case for long term planning horizons. Either of these tie in with testing on Python using Gurobi which will be learnt if needed.

# Associated Interns 2017

## Waseem Aslam

### Management Science Intern

Waseem joins the STOR-i Internships from the Lancaster University Management Science department.