PhD Studentship in “Statistical inference for Ordinary Differential Equations using Automatic Differentiation.” (2024)

PhD studentship in the Groups “Numerical Analysis and Scientific Computing” and “Mathematics Applied to Biology” at the University of Sussex (UK).

PhD project

Statistical inference has proved to be an extremely important tool for mathematicians and statisticians. Whenever there is data to be analysed and a model to be calibrated, statistical inference techniques are employed. In this project, we will focus on the calibration of ordinary differential equations (ODEs) under an appropriate data generation process. The type of data we will consider can be interpreted either as a count of realisations of a random variable at a specific time, pointwise data, or over a specific length of time, integral data.

The novelty of this project is the application of automatic differentiation (AD) to statistical inference. AD allows for the automatic generation of higher derivatives and a method to improve techniques that numerically approximate the solution to ODEs. In this project, we will look to use AD on the variable being solved for and on the parameter that needs to be estimated. AD gives us access to entities in the Jacobian and Hessian of the likelihood without having to calculate them directly, allowing for better optimisation and root-finding algorithms. The parameter estimation techniques will be used to improve Maximum Likelihood Estimation and Bayesian inference approaches. We will also study the identifiability of parameters in specific ODE models, such as in the famous Susceptible-Infected-Removed models and the famous Lotka-Volterra model. Due to the use of ODE modelling, this work will have impact across many different mathematical fields, including, but not limited to, mathematical biology and ecology, healthcare statistics, and operational research.

We welcome students of all genders, ethnicities, races, sexual orientations, abilities, and socio-economic backgrounds. We believe diversity drives innovation in research.

Amount

• Fully-paid tuition fees for three and a half years at the home fee status.
• A tax-free bursary for living costs for three and a half years (£18,622 per annum in 2023/24).
• Additional financial support to cover short-term and long-term travel.
• If you are not a UK national, nor an EU national with UK settled/pre-settled status, you will need to apply for a student study visa before admission.

Eligibility

Applicants must hold, or expect to hold, at least a UK upper second class degree (or non-UK equivalent qualification) in Physics/Mathematics, or a closely-related area, or else a lower second class degree followed by a relevant Master's degree.

This award is open to UK and International students.

 Deadline

23:45, 28^th June 2024

How to apply

Apply through the University of Sussex on-line system, by clicking the 'Apply' button, above.

Select the PhD in Physics/Mathematics, with an entry date of September 2024.

In the Finance & Fees section, state that you wish to be considered for studentship MPS/2024/YPE

Contact us

If you have practical questions about the progress of your on-line application or your eligibility, contact mps-pgrsupport@sussex.ac.uk

For academic questions about the project, contact Dr James van Yperen at j.vanyperen@sussex.ac.uk.   

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