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Fast Bayesian estimation using expectation propagation methods applied to inverse problems

PGR-P-245

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Country eligibility
International (open to all nationalities, including the UK)
Funding
Competition funded
Supervisors
Dr Robert Aykroyd
Schools
School of Mathematics
Research groups/institutes
Statistics
<h2 class="heading hide-accessible">Summary</h2>

The Bayesian modelling approach provides a natural framework within which many applied science problems can be considered. The resulting posterior distribution, derived from data likelihood and prior knowledge, is then the basis for inference. In many problems, however, it is not practical to work directly with the posterior distribution, as it is too complicated or complex, and hence it is popular to use Markov chain Monte Carlo (MCMC) methods. Such approaches are still computational expensive and so are impractical when rapid solution is needed. In contrast expectation propagation (EP) methods, based on suitable Gaussian approximations, are rapid with little reduction in accuracy. There has been little research examining the use of EP methods for inverse problem yet if successful they have the potential to have dramatic impact. For example, in PET/MR medical imaging or ECT for industrial monitoring, existing methods work well for static problems which can be analysed &ldquo;off-line&rdquo;, but are too slow for dynamic studies. This means that &ldquo;real-time&rdquo; applications are not practical hence dramatically limiting their use. This project will consider a range of Bayesian modelling situations involving linear and nonlinear inverse problems from geophysics, engineering and medicine. The project will begin by exploring the basic ideas of variational Bayesian methods and expectation propagation before moving on to propose methods for inverse problems working from simple linear problems through to the more computationally challenging nonlinear and big data problems. Where possible, the methods will be applied to real data examples. Through the project collaborators, the student will have access to real datasets covering a wide variety of applications and with significant practical experience.

<h2 class="heading hide-accessible">Full description</h2>

<p>The earliest date for this project is 1 October 2020.</p>

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/info/130206/applying/91/applying_for_research_degrees">University&#39;s website</a>. Please state clearly in the research information section&nbsp;that the research degree you wish to be considered for is &lsquo;Fast Bayesian estimation using expectation propagation methods applied to inverse problems&rsquo; as well as&nbsp;<a href="https://physicalsciences.leeds.ac.uk/staff/2/dr-robert-g-aykroyd">Dr Robert&nbsp;Aykroyd</a> as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>We welcome applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.</em></p>

<h2 class="heading heading--sm">Entry requirements</h2>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

<h2 class="heading heading--sm">English language requirements</h2>

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<h2 class="heading">Funding on offer</h2>

<p><strong>Self-Funding Students</strong></p> <p><strong>Funding Eligibility</strong></p> <p><strong>UK/EU</strong> &ndash;&nbsp;Leeds Doctoral Scholarship Award paying Academic Fees and Maintenance matching EPSRC rate of &pound;15,009 per year for 3 years, School of Mathematics Scholarship award paying Academic Fees and Maintenance matching EPSRC rate of &pound;15,009 per year for 3 years.&nbsp; Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p> <p><strong>International Students</strong> &ndash;&nbsp;China Scholarship Council-University of Leeds Scholarship Award paying Academic Fees for 3 years,&nbsp;School of Mathematics Scholarship award paying Academic Fees for 3 years, Commonwealth Scholarship and Commonwealth Split Site Scholarships.&nbsp; Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p>

<h2 class="heading">Contact details</h2>

<p>For further information regarding your application, please contact Doctoral College Admissions by&nbsp;email:&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a>, or by telephone: +44 (0)113 343 5057.</p> <p>For further information regarding the project, please contact Dr Robert Aykroyd by email:&nbsp;&nbsp;<a href="mailto:R.G.Aykroyd@leeds.ac.uk">R.G.Aykroyd@leeds.ac.uk</a></p>


<h3 class="heading heading--sm">Linked funding opportunities</h3>
<h3 class="heading heading--sm">Linked research areas</h3>