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Bayesian tree based models and applications


Key facts

Type of research degree
Application deadline
Ongoing deadline
Project start date
Tuesday 1 October 2024
Country eligibility
International (open to all nationalities, including the UK)
Competition funded
Source of funding
University of Leeds
Dr Georgios Aivaliotis and Dr Lanpeng Ji
Additional supervisors
Prof Charles Taylor
Research groups/institutes
Probability and Financial Mathematics, Statistics
<h2 class="heading hide-accessible">Summary</h2>

We are looking for strong candidates to work on this exciting project described below!<br /> <br /> Bayesian classification and regression tree (BCART) and its ensemble version &ndash; Bayesian additive regression tree (BART) models &ndash; are powerful semiparametric learning techniques for modelling nonlinear regression functions that outperform many other machine learning methods. Classical BCART and BART models were proposed for continuous (Gaussian) and binary response variables (see, [1-3]), and over the years these have been extended to analyse a large class of response variables, including count data (see, [4]). Their excellent empirical performance has also motivated works on their theoretical foundations (see, [5]). <br /> <br /> One direction of research on this project is to try to understand the mechanism of the BCART and BART methods from a theoretical point of view. Another direction of research is to explore extended BCART and BART models with applications to areas such as insurance pricing (see [6]) or/and spatial-temporal data analysis (e.g., environmental or climate data modelling). Some key questions to be explored in these applications include feature selection, choice of loss functions, class-imbalance problem with zeros, model stability, and interpretability.<br /> <br /> References:<br /> <br /> [1] H. A. Chipman, E. I. George, and R. E. McCulloch, &ldquo;Bayesian CART model search,&rdquo; Journal of the American Statistical Association, vol. 93, no. 443, pp. 935&ndash;948, 1998.<br /> [2] D. G. Denison, B. K. Mallick, and A. F. Smith, &ldquo;A Bayesian CART algorithm,&rdquo; Biometrika, vol. 85, no. 2, pp. 363&ndash;377, 1998.<br /> [3] H. A. Chipman, E. I. George, R. E. McCulloch, et al., &ldquo;BART: Bayesian additive regression trees,&rdquo; The Annals of Applied Statistics, vol. 4, no. 1, pp. 266&ndash;298, 2010.<br /> [4] J. S. Murray, &ldquo;Log-linear Bayesian additive regression trees for multinomial logistic and count regression models,&rdquo; Journal of the American Statistical Association, vol. 116, no. 534, pp. 756&ndash;769, 2021.<br /> [5] V. Rockova, S. Van der Pas, et al., &ldquo;Posterior concentration for Bayesian regression trees and forests,&rdquo; Annals of Statistics, vol. 48, no. 4, pp. 2108&ndash;2131, 2020.<br /> [6] Y. Zhang, L. Ji, Aivaliotis, and C.C. Taylor, &lsquo;&rsquo;Bayesian CART models for insurance claims frequency&rdquo;. 2023. Available at<br />

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

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="">University&#39;s website</a>. Please state clearly in the Planned Course of Study Section that you are applying for <em><strong>PHD Statistics FT,</strong></em>&nbsp;in the research information section&nbsp;that the research degree you wish to be considered for is&nbsp;<em><strong>Bayesian tree based models and applications</strong></em><span style="font-size:11pt"><span style="line-height:107%"><span style="font-family:Calibri,sans-serif"><span style="font-family:&quot;Arial&quot;,sans-serif">&nbsp;</span></span></span></span>as well as <a href="">Dr Lanpeng Ji</a>&nbsp;as your proposed supervisor&nbsp;and in the finance section, please state clearly&nbsp;<em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</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>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p class="MsoNoSpacing">Applications will be considered after the closing date. &nbsp;Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. &nbsp;We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p>Please note that you must provide the following documents in support of your application by the closing date of 3 April 2024 for&nbsp;Leeds Opportunity Research Scholarship and 8 April 2024 for Leeds Doctoral Scholarship:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

<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-Funded or externally sponsored students are welcome to apply.</strong></p> <p>UK&nbsp;&ndash;&nbsp;The&nbsp;<a href="">Leeds Doctoral Scholarships</a>,&nbsp;<a href="">Leeds Opportunity Research Scholarship</a>&nbsp;and&nbsp;<a href="">School of Mathematics Scholarships</a> are available to UK applicants. <a href="">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p>Non-UK &ndash;&nbsp;The&nbsp;<a href="">China Scholarship Council - University of Leeds Scholarship</a>&nbsp;is available to nationals of China (now closed for 2024/25 entry). The&nbsp;<a href="">Leeds Marshall Scholarship</a>&nbsp;is available to support US citizens. <a href="">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Important:</strong>&nbsp; Any costs associated with your arrival at the University of Leeds to start your PhD including flights, immigration health surcharge/medical insurance and Visa costs are <strong><em>not </em></strong>covered under this studentship.</p> <p>Please refer to the <a href="">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

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

<p>For general enquiries about applications, contact our admissions team by email to&nbsp;<a href=""></a>.&nbsp;</p> <p>For questions about the research project, contact Dr Lanpeng Ji by email to&nbsp;<a href=""></a></p>

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