A central idea in modern cognitive science is that the brain performs something like Bayesian inference: combining prior beliefs with sensory information to make decisions under uncertainty. This connects closely to the distinction popularised by Daniel Kahneman between fast intuitive reasoning and slower deliberative reasoning.
While Bayesian models often provide 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.
The project sits at the interface of applied mathematics, statistics and cognitive science, and will involve mathematical modelling, computational work, and interpretation of experimentally motivated problems.
---The group project will introduce the core mathematical and modelling ideas underlying Bayesian inference in cognition. Students will work together to develop a shared understanding of how probabilistic models are used to describe perception and decision-making.
By the end of the group project we will have:
The individual project will build on the group work, allowing students to explore a specific aspect of Bayesian modelling in more depth. There is flexibility in the balance between theory, computation and application.
Possible directions include:
Students will be encouraged to develop their own direction within the topic.
---Group Project:
The group project will operate through guided reading, collaborative problem-solving, and computational exploration. Students will work together to understand core concepts and apply them to structured examples.
Understanding will be demonstrated through group discussions, shared written work, problem-solving exercises, and a clear presentation of the underlying ideas and models.
Individual Project:
The individual 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.
---There is also scope to connect with ideas from mathematical biology and network dynamics. For example, reaction–diffusion systems or Hodgkin–Huxley-type models on networks describe how local dynamics interact through coupling. Similar structures arise in models of neural inference, where interacting components exchange information across a network.
The distinction between fast and slow reasoning also suggests a modelling perspective in which slower processes update the priors or internal models that guide faster intuitive decisions, providing a mathematical framework for learning and adaptation.
---If you are interested in this project or would like to discuss it further, please get in touch.