This page gives an overview of my current research interests and areas of expertise for potential students or those looking for consulting services.
Students and Supervision. I’m always happy to discuss potential PhD and MPhil projects with motivated students. The topics below are a good guide to the problems I’m working on at the moment and potential topics, but I’m open to anything as long as they fall within my general areas of interest. For a list of past and present students and their projects see my researcher profile
Overview
My research lies at the intersection of stochastic modelling, mathematical biology, computational Bayesian statistics and Monte-Carlo methods. The thing that connects all of these topics is the use of probability and stochastic processes for understanding the world and solving interesting problems. Increasingly, much of what I do comes under the banner of data science.
Epidemic modelling and inference
I have particular expertise in mathematical epidemiology and stochastic epidemic modelling. I was contracted by the Australian government to advise on these topics and provide modelling to support the initial public health interventions for the covid19 pandemic.
Although recently in vogue, household models and pandemic preparedness are a long standing interests. Households are an easy unit to surveil for data, but their size require stochastic models of the transmission process. Data is still fairly sparse and corrupted by noise which makes this more challenging. Much of my interest in Bayesian computational methods has been spurred by particular problems arising from this research. My work in this area formed the basis for the analysis of data collected for the first FFX project in Australia .
Computational Bayesian statistics
Bayesian statistics is the natural framework for tacking inference problems for time series where we have an underlying probabilistic or mechanistic model.
A particular challenge with inference for epidemic models is that that likelihood itself is often intractable. Hence developing new computational techniques and algorithms to fit these models is an active research interest. Most of the best techniques are currently based on sequential Monte Carlo, particle filters and importance sampling techniques.
I am also interested in using machine learning methods to increase the efficiency of Bayesian approaches (which are often computationally intensive), for example in learning optimal proposals for importance sampling algorithms. A current student is investigating the use of normalising flows and neural likelihood estimation for developing new inference methods.
Evolution of multicellularity
Another long term project is investigating the evolution of multicellularity from unicellular ancestors—one of the so-called major transitions in evolution. My interest is in building mathematical models that can capture the dynamics of this transitions and to try and better understand it from a mechanistic point of view.
The challenging part of this is to understand the very earliest stages of the transition, especially how early groups of cells came to possess Darwinian characteristics needed for natural selection to act at the level of groups. In modelling this phenomena, the basic concepts that we normally rely on when doing evolutionary analysis, such as defined modes of reproduction, now must themselves be explained, rather than being assumed in the model.
In collaboration with Paul Rainey and Pierrick Bourrat , we have advocated a solution to the problem called “Ecological Scaffolding”. This is discussed in detail in our paper Ecological scaffolding and the evolution of individuality, but the basic idea is that Darwinian properties can be scaffolded by the environment which causes cells to participate in the process or evolution as if they were members of multicellular collectives.
The perspective of ecological scaffolding changes the problem from an abstract one of understanding levels of selection to a more concrete problem of understanding the ecological conditions that can create scaffolded populations. For example, a new preprint by recent PhD student Cody Nitschke looks at how bottleneck size effects the evolutionary dynamics of nested Darwinian populations.