Non-Stationary Gaussian Processes, Statistical Science - Mathematics- EPSRC DTP funded PhD Studentshi Ref: 2925

About the award

This project is one of a number funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership to commence in September 2018. This project is in direct competition with others for funding; the projects which receive the best applicants will be awarded the funding.

The studentships will provide funding for a stipend which is currently £14,553 per annum for 2017-2018. It will provide research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

Please note that of the total number of projects within the competition, up to 15 studentships will be filled.

Prof Peter Challenor

Dr Daniel Williamson

Streatham Campus, Exeter

Project Description
Gaussian processes are used extensively in statistics. In geostatistics they are used model spatial fields and in uncertainty quantification to model computer model output as emulators. They are also used as an alternative to neural networks in machine learning.  Almost all applications use stationary Gaussian processes where the statistical properties stay the same over the whole of space. However, in many applications we need non-stationary processes. Although a number of non-stationary models have been proposed, none have so far proved to be popular. In this project, we will look at a new model for non-stationarity. The stationary Gaussian process contains a parameter that is often described as the length scale. This sets the ‘wiggliness’ of the process, sometimes referred to as the ‘smoothness’ but different from the usual mathematical definition of smoothness involving derivatives. This parameter is usually taken as constant or varied in an ad hoc way. The proposed new class of non-stationary model would model this length scale as a second Gaussian process. Modelling it in this way allows us to include explanatory variables in the changing length scale. For example, in the geostatistical context we could easily vary the length scale with altitude, something very difficult to do with conventional methods, but which could be an important part of any modelling.

The proposed new methodology has some similarities to ‘deep Gaussian processes’ proposed in the machine learning literature. However, we will restrict ourselves to two layers of the Gaussian process. The one that models the process and one that models the length scale of that process. Deep Gaussian processes have many layers which makes inference very hard, with only two layers, inference, via standard Bayesian statistical techniques will be much easier.

The project will suit a student who is interested in uncertainty quantification, Gaussian processes, spatial statistics or computational statistics.


Entry Requirements

You should have or expect to achieve at least a 2:1 Honours degree, or equivalent, in mathematics (or equivalent) with a substantial statistical component. Experience in programming with R and with Gaussian processes is desirable.

If English is not your first language you will need to meet the English language requirements and provide proof of proficiency. Click here for more information and a list of acceptable alternative tests.

The majority of the studentships are available for applicants who are ordinarily resident in the UK and are classed as UK/EU for tuition fee purposes.  If you have not resided in the UK for at least 3 years prior to the start of the studentship, you are not eligible for a maintenance allowance so you would need an alternative source of funding for living costs. To be eligible for fees-only funding you must be ordinarily resident in a member state of the EU.  For information on EPSRC residency criteria click here.

Applicants who are classed as International for tuition fee purposes are NOT eligible for funding. International students interested in studying at the University of Exeter should search our funding database for alternative options.


Application deadline:10th January 2018
Value:3.5 year studentship: UK/EU tuition fees and an annual maintenance allowance at current Research Council rate. Current rate of £14,553 per year.
Duration of award:per year
Contact: Doctoral

How to apply

You will be required to upload the following documents:
•       CV
•       Letter of application outlining your academic interests, prior research experience and reasons for wishing to
        undertake the project.
•       Transcript(s) giving full details of subjects studied and grades/marks obtained.  This should be an interim
        transcript if you are still studying.
•       If you are not a national of a majority English-speaking country you will need to submit evidence of your current
        proficiency in English.  For further details of the University’s English language requirements please see

The closing date for applications is midnight (GMT) on Wednesday 10 January 2018.  Interviews will be held at the University of Exeter in late February 2018.

If you have any general enquiries about the application process please email:
Project-specific queries should be directed to the supervisor.

During the application process, the University may need to make certain disclosures of your personal data to third parties to be able to administer your application, carry out interviews and select candidates.  These are not limited to, but may include disclosures to:

• the selection panel and/or management board or equivalent of the relevant programme, which is likely to include staff from one or more other HEIs;
• administrative staff at one or more other HEIs participating in the relevant programme.

Such disclosures will always be kept to the minimum amount of personal data required for the specific purpose. Your sensitive personal data (relating to disability and race/ethnicity) will not be disclosed without your explicit consent.