[Statistics & Probability Seminar]
2nd year PhD student talks: Rowland Seymour, Simon Maurer, Tom Lowbridge, Emily Mitchell.
Rowland Seymour
Bayesian Non-Parametric Inference for Stochastic Epidemic Models
Simulating from and making inference for epidemic models are key strategies for controlling the spead of diseases such as Avian Flu. In this talk we are concerned with inference for models, where the infection rate between two farms may depend on their characteristics, for example location and size. Current methods for these models are almost exclusively parametric, where one needs to make assumptions about the functional form of the infection rate. In this talk we will present a non-parametric method for inferring this rate, removing the need to make such assumptions, and allow us to be more flexible. We adopt a Bayesian approach to inference and develop efficient Markov Chain Monte Carlo methodology to estimate infection rates and unobserved infection times. We illustrate our methods using a simulation study.
Simon Maurer
Simplest random walks for solving the Dirichlet problem for integro-partial differential equations
We propose new numerical methods for the Dirichlet problem for integro-partial differential equations (IPDE) based on the method of characteristics. Using the Feynman-Kac formula, the solution of the IPDE can be represented as an expectation with respect to solutions of ordinary stochastic differential equations (SDEs), which play the role of characteristics. These SDEs are driven by Levy processes, possibly with infinite activity. To approximate solutions of the SDEs in the weak-sense, we construct random walk-type algorithms suitable for bounded domains. These algorithms together with the Monte Carlo technique give an approximation of the IPDE solution. We aim at proving convergence theorems for the algorithms and to illustrate the proposed numerical methods via numerical experiments, in particular on pricing fixed-income barrier options.
Tom Lowbridge
Patrolling games on graphs
Patrolling an area to find an intruder is a scenario used widely in security applications, with the aim to catch the intruder before he is able to do something nefarious. For example a guard patrolling a museum and a thief stealing from an exhibit. In this talk we shall introduce one game theoretic description of such a scenario and highlight known optimal solutions to some types of graphs, such as the Hamiltonian and line graphs. We will present a problem with the proposed line graph solution and correct the optimal strategy accordingly, seeking to expand on the idea to generate more general strategies for a variety of different graphs.
Emily Mitchell
An extreme value analysis of top performing UK winter wheat producers
Using the responses to a UK-based survey, we present the first application of extreme value theory in an agricultural setting to complement the previous studies conducted from a classical central perspective in this field. The Farm Business Survey collects a substantial amount of information annually from farms across England and Wales with the purpose of providing farmers with an overview of farming performances. Winter wheat is the most popular crop grown in the UK due to its optimal growing conditions; therefore, we focus on winter wheat production from 2006 to 2015 and extract a subset of variables from this data set, among which the obtained yield and net margin, and apply a number of established extreme value analysis methods. We conclude by discussing the implications of our results regarding top UK winter wheat producers, and especially how their financial results compare to these of top earners in the UK.