SAMBa Summer Conference

20-21 June 2017

Below is the finalised programme for the conference.

Abstracts

Invited Talks

Prof. Richie Gill (Department of Mechanical Engineering, University of Bath)
In Silico Clinical Trials for Musculo-skeletal Therapy Development

As the global population ages, musculoskeletal diseases are becoming a major healthcare burden. The most common and widespread musculoskeletal disease is osteoarthritis (OA). OA of the joints of the lower limb, in particular the hip and the knee, have significant negative burden on the overall health state of an individual. The importance of activity for overall health state has become apparent, thus joint disease not only carries a burden in terms of pain and disability of the affected joint but also carries a further burden by increasing the risk of systemic conditions such as diabetes and cardiac disease due to the imposed reduction in activity. OA of the knee is increasing in prevalence driven by the ageing of the global population and is associated with obesity. This increase in knee disease is driving demand for knee replacement; a demand that healthcare systems are already struggling to meet. This talk will describe the development of a subject specific treatment for early OA of the knee aimed at preserving the natural joint and delaying the need for joint replacement. Part of the methodology being employed in the development process is an in silico clinical trial; the opportunities of using such methods for reducing the development time of novel therapies will be discussed.​

Dr Colin Morice (Hadley Centre, Met Office)
Reconstruction of Daily Air Temperature Variations Globally Since the Mid 19th Century (PDF)

This talk will describe methods for merging historical observational data to reconstruct past air temperatures across the globe from the mid-19th century, based on satellite and terrestrial air temperature observations over land, ocean, lakes and ice. These methods are being developed as part of the EUSTACE project, which aims to produce daily estimates of near surface air temperatures over the whole Earth at high spatial resolution, with quantified uncertainties.

The talk will begin with a short overview of the EUSTACE project, describing the steps that it is taking to produce a climate dataset that is fit for a wide range of applications. The talk will then focus on the methods for merging observational data into the global analysis. A statistical model will be described that decomposes air temperature variability into variability at different spatial and temporal scales, permitting estimation of air temperature fields from sparse observational data. A model for observational biases and uncertainty is included to account for the heterogeneous observing network, which will also be described. Preliminary examples of application of the analysis system will be shown.

Prof. Anja Sturm (Institute for Mathematical Stochastics, Georg-August-University of Göttingen)
Long Time Behaviour of Cooperatively Branching and Coalescing Particle Systems (PDF)

Stochastic interacting particle systems describe the time evolution of particle systems that are distributed on a discrete space (such as the integer lattice). The random changes to these systems are local, and one of the main points of interest is to understand the global and long-time behaviour that arises from a particular set of local interaction rules.

In this talk, we will discuss properties such as long-time survival and the existence of (nontrivial) invariant laws for a particular model called the cooperative branching coalescent. Here, particles perform independent random walks, only pairs of particles occupying neighbouring sites can produce new particles (cooperative branching) and particles that land on an occupied site merge with the particle present on that site (coalescence). Depending on the underlying space this system undergoes a phase transition as the branching rate is increased: For small branching rates the so called upper invariant law is trivial and the process started with finitely many particles ends up with a single particle with probability 1. Both statements are not true for high branching rates.

The talk is based on joint work with Jan Swart (UTIA Prag) and work in progress with Tibor Mach (University of Göttingen).

Student Talks

Beth Boulton
Metapopulations and Macroparasites: An Introduction to the Icky and Random World of Parasite Epidemiology (PDF)

Macroparasites are complicated little blighters which cause infections which, due to the unconventional life cycles of parasites and the importance of variation in the severity of infection, can't be modeled like your standard bout of plague. This talk will explain why the classic SIS and SIR modelling falls apart when faced with macroparasitic infections and introduce an alternative method of modelling them, and why these models are important.

Marcus Kaiser
Why do Irreversible Processes Converge Faster to Equilibrium than Reversible Ones? (PDF)

In many applications one is interested in sampling from probability distributions known up to a multiplicative constant. A standard technique to estimate such distributions are Markov Chain Monte Carlo (MCMC) methods, like Metropolis Hastings, where one generates a large number of uncorrelated samples of the distribution.

An important question is the rate at which these samples convergence to the steady state. We can think of this as the efficiency of the sampling method, which has a direct influence on the computational cost. To improve this efficiency, it is important to gain a better understanding of the involved stochastic processes.

On that account, we investigate in this talk the question why irreversible processes tend to converge faster to equilibrium than reversible ones.

Sam Moore
Two Species Contact Processes (PDF)

Recent work in the physics literature has explored the two-species contact process as a model of staged infections. The work has a biological interpretation in terms of host-parasite invasions, for example, when a growing colony of bacteria is under threat from a developing bacteriophage infection. The problem has previously been explored from a deterministic angle, in the setting of the lattice.

In this talk we shall begin by introducing the two-species contact process in generality before moving on to suggest a novel stochastic approach to its analysis using a branching model. In particular we aim to show how a generalisation of the branching process, with a multi type offspring distribution, may be adopted to describe the evolution of the secondary wave of infection directly.

Robbie Peck
Bayesian Decision Theory with applications to Experimental Design (PDF)

"Should I take my umbrella with me today?"

Many problems one encounters in life involve making decisions, including ones about the evidence you might want to collect to help inform further decisions. Making optimal decisions may depend on unknown parameter values, about which one may hold particular degrees of belief. To make these optimal decisions, we need to be able to formulate the problem clearly, and then apply mathematical reasoning and optimisation​.

The Bayesian Decision Theory approach is based on quantifying the trade-offs between various decisions using current beliefs in probability and the costs that accompany such decisions. At the very least, the approach can be considered as making common sense deductions which are validated by rigorous mathematics by framing a problem in probabilistic terms.

After introducing the motivating examples and theory, the application to experimental design is briefly discussed, where Bayesian Decision Theory is used to help identify, and build sufficient evidence of the efficacy of, treatments that may be used to treat medical conditions.

Owen Pembery
Uncertainty Quantification for the Helmholtz Equation Using Preconditioning (PDF)

Uncertainty Quantification (UQ) for acoustics problems is valuable for improving safety in areas such as seismic imaging.

However, finding numerical solutions to the Helmholtz equation (the simplest model of acoustic wave propagation) is a very demanding computational task.

If we want to discover properties of sound waves moving in random media we may need to solve the Helmholtz equation thousands of times, which is computationally prohibitive, unless we can find methods which speed up our computations.

One approach to reducing the computational time needed to solve these equations is to use a preconditioner, which transforms our hard-to-solve problem into one that is easier to solve.

In this talk we will introduce current work on preconditioning for the Helmholtz equation in random media, motivated by the study of sound waves moving through random media.

In particular, we will show how, rather than needing to calculate thousands of preconditioners when we need to solve the Helmholtz equation thousands of times, in certain situations we can calculate one preconditioner, which we can then use every time we solve the Helmholtz equation, which leads to computational savings.

Kate Powers
Modelling Centrifugal Compressors (PDF)

Nearly all modern vehicle turbochargers are formed of a centrifugal compressor and turbine. Understanding how turbochargers act under various flow regimes is important for many reasons, including improving vehicle fuel efficiency. Current modelling of turbocharger performance is predominantly via CFD, which fails to capture system dynamics near unstable flow regimes.In this talk I will describe a more analytical method for modelling turbocharger compressors. I will formulate Euler equations in this setting and use averaging techniques to reduce the system to a 1-dimensional description of the flow. Finally, I will present results for the steady-state case.

Anna Senkevich
Condensation in Reinforced Branching Processes with Fitness (PDF)

This talk will describe the asymptotic behaviour of the reinforced branching processes with fitness on the example of the preferential attachment tree of Bianconi and Barabasi. In this random graph model a popularity of a node is determined by its degree and a so-called fitness value, drawn from a specified distribution. The dynamics of these networks depend on the properties of the distribution, leading to three distinct behaviours, namely non-condensation phase, and extensive and non-extensive condensation phases. Such model provides a useful tool for understanding the growth characteristics of complex networks such as the Internet, social networks and online communities.

Matt Thomas
Global Estimation of Air Quality (PDF)

Calculating the burden of disease attributed to air pollution requires accurate estimation of population level exposures to pollutants. Although coverage of ground monitoring networks is increasing, these data are insufficient to independently estimate exposures globally. Information from other sources, such as satellite retrievals, chemical transport models and land use covariates must therefore be used in combination with ground monitoring data. Each of these data sources will have their own biases and uncertainties that may vary over space. Set within a Bayesian hierarchical modelling framework, the recently developed Data Integration Model for Air Quality (DIMAQ) integrates data from multiple sources and allows spatially-varying relationships between ground measurements and other factors that estimate fine particulate matter (PM2.5) concentrations. The outputs of the model are estimated exposures that can be combined with population estimates to produce population-level distributions of exposures for each country. DIMAQ was used to estimate exposures of PM2.5, together with associated measures of uncertainty, on a high-resolution grid (~11 km × 11 km) covering the entire globe for use in the 2016 WHO report ‘Ambient air pollution: A global assessment of exposure and burden of disease’, and in the 2015 and 2016 updates of the Global Burden of Disease.

For 2015, 92% of the world’s population lived in areas that exceeded the WHO 10 µg/m3 guideline. Fifty percent of the global population resided in areas with PM2.5 concentrations above the WHO Interim Target 1 (IT-1 of 35 µg/m3 ); 64% lived in areas exceeding IT-2 (25 µg/m3 ); and 81% lived in areas exceeding IT-3 (15 µg/m3 ). Nearly all (86%) of the most extreme concentrations (above 75 µg/m3 ) were experienced by populations in China, India, Pakistan, and Bangladesh.

Posters

• Jack Betteridge

  Higher Order Discontinuous Galerkin Methods for Numerical Weather Prediction (e-Poster)

• Emiko Dupont

  Statistical Modelling of Time Dependence in Peak River Flows

• Matt Durey

  Droplets Walking on a Vibrating Fluid Bath

• Dorottya (Dorka) Fekete

  Connection of Skeletal and Spine Decompositions for Subcritical Continuous-State Branching Processes

• Emma Horton

  Stochastic Analysis of the Neutron Transport Equation

• Kgomotso Susan Morupisi

  Ice Age Model of Climate Change: PP04 Model

• Robert Peck

  Phase II/III Programs: Optimal Setup and Decision Making

• Adwaye Rambojun

  Segmentation of Psoriatic Arthritis X-rays

• Benjamin Robinson

  Stochastic Optimal Control Problems Related to Martingale Optimal Transport

• Shaerdan Shataer

  Imaging the Electric Activity of the Brain

• Cameron Smith

  The Auxiliary Region Method for Reaction-Diffusion Systems

• Sebastian Stolze

  Using Bayesian Networks for Quantitative Risk Analysis

• Hayley Wragg

  The Method of Geometric Optics and the Application to High-Frequency Wave Propagation

Short Student Talks

• Aoibheann Brady

  Attribution of Large Scale Drivers for Environmental Change

• Elizabeth Gray

  Spatial Statistics and Preferential Sampling

• Matthew Griffith

  An Increased Model Height in the Met Office's Unified Model

• Nadeen Khaleel

  Log-Gaussian Cox Processes

• Daniel Ng

  Understanding Measure-valued Martingales

• Tom Pennington

  Large Scale Differential Geometric MCMC

• Lizzi Pitt

  First in Human Trials

• Tsogzolmaa (Tsogii) Saizmaa

  Spatial Branching Processes

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