Project Overview
Bayesian inference allows us to turn observations into insights by updating a prior distribution to a posterior distribution. If we have a choice in how we collect data (“when/how/where do we measure?”), we can use Optimal Experimental Design (OED) to maximize the information gained.
In this position, you will work on deriving mathematical models and computational methods for solving Bayesian OED on temporal and spatial inverse problems, with a focus on ideas from optimal control and stochastic filtering. This project builds on recent work on Bayesian OED for temporal inverse problems, see Pathiraja, Schillings, Wacker, 2025 for reference.
Additional Details
There is no formal teaching requirement attached to the funding, though optional tutoring or teaching opportunities may be available.
International applicants are welcome. Applicants will need to arrange the appropriate visa.
The successful applicant will be enrolled as a PhD student in Mathematics or Statistics at the University of Canterbury.
Research Environment
The PhD student will be part of a supportive and collaborative research environment within the School of Mathematics and Statistics at the University of Canterbury. Supervision will emphasise regular discussion, intellectual independence, and a positive and inclusive working environment in which students can develop their own research direction with confidence.
The position will be embedded in a collaborative project between researchers in New Zealand, Australia, and Germany. There will be opportunities for wider scientific collaboration and conference travel subject to funding availability.
Diversity & Inclusion
The School of Mathematics and Statistics is to fostering an inclusive and supportive research environment. We particularly encourage applications from women and others who are underrepresented in mathematics and statistics.
Job posting also available here: https://www.math.canterbury.ac.nz/~p.wacker/position
Supervisors
Primary Supervisor: Philipp Wacker
Key qualifications and skills
Successful applicants are expected to have completed a Master’s degree in Mathematics or Statistics (with a strong emphasis on analysis and probability) and should be familiar with at least a few of the following topics, and be willing to learn about the rest:
- Bayesian inference
- Differential Equations (Ordinary, Stochastic, Partial), Numerics and computational mathematics
- MCMC sampling, Sequential Monte Carlo, the Kalman filter, and the Bootstrap Particle Filter
- Numerical Optimisation methods
- Basic information theory (entropy, KL-divergence)
- Stochastic filtering (Kushner-Stratonovich equation etc.)
- Optimal Transport, (Wasserstein) Gradient flows
- Experience in coding with Python
- Applicants are not expected to know all listed topics. The most important criteria are motivation, independence, and the ability to learn new material.
Does the project come with funding
This is a 3-year fully funded PhD position supported by the Royal Society of New Zealand’s Marsden Fund. It covers the PhD student fees and levy, and includes a stipend of NZD 35,000 per year (in line with standard PhD funding in New Zealand).
Final date for receiving applications
31 January 2026
How to apply
Apply by sending your documents (Cover Letter responding to the specific points in this ad, CV, transcript of your degrees) to philipp.wacker@canterbury.ac.nz by 31 January 2026. Reference letters will not be required initially but may be requested later for shortlisted candidates. Applicants are encouraged to apply even if they do not meet all listed criteria; informal enquiries are welcome at the same email address.
Keywords
Experimental Design, Stochastic Differential Equations, Filtering, Computational Statistics, Monte Carlo algorithms
