Number of awards
1
Start date and duration
42 months from September 2021.
Overview
At the core of the Bayesian framework there is the determination of suitable prior distributions for any unknown. Whether this is a parameter of a model, a model itself or some sort of structure, experimenters and decision makers are faced with the task of translating any available prior information into a suitable probability distribution. However, there are many circumstances where this is not achievable, for example, because the number of parameters is a model is too large, or simply because there is no sufficient prior information to be exploited. In these cases, the option is to revert to methods that allow to build prior distribution in absence of information, and these methods go under the name of Objective Bayes.
There are two possible directions of research.
1. Objective prior distributions from scoring rules: Regular objective methods to derive prior distributions have reached their natural ceiling, making them unsuitable for the fast growing complexity of Bayesian models. The project aims to develop on a recent novel methodology based on scoring rules to explore mathematical aspects and applications of objective prior distributions.
2. Loss based Bayesian Additive Regression Trees: We live in a world that is, by nature, non-linear. Although linearity is often assumed, this is in general a convenient, yet forced, simplification. Overall, the project looks into improving the implementation of a statistical tool suitable to represent non-linear phenomenon: the Bayesian Additive Regression Tree (BART) model. In detail, the aim is to enhance the applicability of BART models through the delivery of two key outputs. First, we will develop a novel prior distribution for the structure of the trees in the BART. Second, we will develop a prior distribution to estimate the number of trees in the BART. This project aims to propose a novel loss-based approach to solve the above problems.
Sponsor
EPSRC / School of Mathematics, Statistics and Physics
Name of supervisor(s)
Dr Cristiano Villa ([Email Address Removed])
Eligibility Criteria
This studentship is available to all candidates who have/expect a 2:1 honours degree in computing science, mathematics, physics, statistics or another strongly quantitative discipline, or an international equivalent.
If English is not your first language, you must have IELTS 6.5 overall (with a minimum of 5.5 in all sub-skills).
The award is available to home and international applicants.
How to apply
You must apply through the University’s online postgraduate application system.
- Insert the programme code 8080F in the programme of study section, select ‘PhD Mathematics - Statistics as the programme of study, insert the studentship code MSP035 in the studentship/partnership reference field.
- Attach a cover letter and CV. The covering letter must state the title of the studentship, quote reference code MSP035 and state how your interests and experience relate to the project. CV should list details of two references.
- Attach degree transcripts and certificates and, if English is not your first language, a copy of your English language qualifications.
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