Faculty/School

Faculty of Science

School of Mathematical Sciences

Topic status

We're looking for students to study this topic.

Research centre

Centre for Data Science

Primary Supervisor

Dr Leah South
Position
Senior Lecturer in Mathematical Sciences
Division / Faculty
Faculty of Science

Other QUT supervisors

Professor Chris Drovandi
Position
Professor
Division / Faculty
Faculty of Science
Dr Trung Tin Nguyen
Position
MACSYS Post-doctoral Research Fellow (Applied Statistics)
Division / Faculty
Faculty of Science

Overview

Monte Carlo integration is a cornerstone of modern Bayesian computation. However, standard estimators suffer from a slow root-N convergence rate, making variance reduction essential. Various so-called variance reduction methods have been proposed in the literature, notably Stein control variates, which leverage gradient information of the log target density function to construct variance-reduced estimators of integrands.

However, a common feature of many practical Monte Carlo problems (e.g., computing posterior means or specific marginal expectations) is that the integrand intrinsically lies in a lower-dimensional subspace. Current state-of-the-art Stein-based control variates utilise information across all dimensions indiscriminately, resulting in lower statistical and computational efficiencys. While recent developments like a priori ZVCV attempt to address this, they are strictly limited to scenarios where the low-rank structure of the integrand is known beforehand.

This project aims to validate a novel, data-driven methodology that aims to break this limitation. Specifically, the project will focus on learning the low-rank structure directly and obtaining a variance-reduced estimator.

This project is relevant to Dr Leah South's DECRA grant DE240101190.

Research activities

Research activities include:

  • Regular meetings to discuss the project with supervisors
  • Learning about variance reduction and control variates
  • Developing new methods with support from supervisors
  • Implementing and comparing methods in statistical software

Skills and experience

The following skills are required/beneficial:

  • Required: foundational skills in statistics, probability, and programming
  • Beneficial: proficiency in R
  • Beneficial: familiarity with Bayesian statistics
  • Beneficial: experience with Rcpp, autodiff and/or Torch

Start date

2 November, 2026

End date

19 February, 2027

Location

Gardens Point campus and/or Zoom

Keywords

Contact

Leah South

0731388469

l1.south@qut.edu.au