Statistics Postgraduate Research Projects | School of Mathematics, Statistics and Physics

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 in 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.

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.

Supervisor: Dr Cristiano Villa