A central idea in modern cognitive science is that the brain performs something like Bayesian inference: combining prior beliefs with incoming sensory data to make decisions under uncertainty. This idea is closely related to the distinction popularised by Daniel Kahneman in Thinking, Fast and Slow, between intuitive, fast reasoning and slower, more deliberative processes. Bayesian models provide a mathematical framework for understanding when these processes should be optimal—and when they are not.
While Bayesian models often give an elegant account of perception and decision-making, experimental evidence shows a more nuanced picture: in some settings humans behave close to Bayes optimal, while in others they deviate systematically. A key aim of this project is to understand that boundary.
Consider a simple medical test scenario. Suppose a disease is rare (say 1% prevalence), and a test is highly accurate. A Bayesian calculation shows that even after a positive test, the probability of actually having the disease may still be relatively low. However, many people intuitively overestimate this probability—this is known as base-rate neglect.
This mismatch between optimal inference and human judgement is typical: in some contexts humans appear highly efficient statistical learners, while in others they rely on heuristics that systematically bias their decisions.
The project will focus on developing and testing Bayesian models in experimentally grounded settings, particularly tasks that are natural or intuitive, where human performance may be expected to align more closely with optimal inference. In many cases these models can be expressed as graphical models (networks of interacting variables), providing a natural bridge between probabilistic inference and network-based representations.
The project may involve a combination of:
There is flexibility to tailor the balance between theory, computation and experiment depending on the student’s interests. A further direction is to explore how such inference might be implemented in practice: for example, how networks (whether abstract graphical models or neural systems) could perform or approximate Bayesian reasoning.
This project builds on a summer research programme in collaboration with Dr Ulrik Beierholm in the Department of Psychology. It sits at the interface between mathematics, statistics, computational modelling and cognitive science.
Students will have the opportunity to see how ideas from Bayesian inference, inverse problems and statistical modelling translate directly into questions about real human behaviour, and to engage with how cognitive experiments are designed and interpreted.
The project connects to several areas of mathematics, including:
There is also scope to connect this project with ideas from mathematical biology and network dynamics. For example, reaction–diffusion systems and Hodgkin–Huxley-type models on networks provide familiar ways of describing how local dynamics interact through coupling. Similar mathematical structures appear in models of neural inference, where beliefs, sensory signals or neural populations interact across a network. This offers a natural route for students with a background in mathematical biology to explore how dynamical systems, networks and Bayesian modelling can meet.
The distinction between fast intuitive judgements and slower reasoning also raises an interesting modelling question: whether slower, more deliberative processes can update the priors or internal models that later guide fast intuition. In this sense, slower reasoning may help to train or reshape fast responses, providing a mathematical route into questions about learning, habit formation, and when human behaviour becomes close to Bayes optimal.
The project will involve a combination of independent reading, mathematical modelling and (optionally) computational implementation. The precise balance will depend on the chosen direction.
Students will demonstrate their understanding through a written report and presentation, which may include theoretical development, model construction, computational results, and critical analysis.
This project is aimed at students with an interest in applied mathematics, statistics, or computational modelling. Experience with probability or statistics is helpful, and some programming experience is desirable, but the most important ingredients are curiosity and an interest in interdisciplinary work.
If you are interested in this project or would like to discuss it further, please get in touch.