Generalising The Diffusion Model To Higher Dimensions

Earlier this year, Professor Philip Smith facilitated a tutorial and gave a research talk for the 2019 Complex Human Data Hub Seminar Series. These events were titled ‘Modelling Speeded Decision Making as Diffusions in Circles and Hyperspheres’ and they presented work that generalises the diffusion model to higher dimensions.

The study of decision making is fundamental to Cognitive Science, as decision making hinges upon the cognitive and neural processes involved in translating perception into action. The diffusion decision model is an evidence-accumulation model of decision making that has provided a unified theory of the response time and accuracy data from a wide variety of experimental tasks.

The first event was a tutorial that provided a deep dive into Professor Smith’s 2016 paper titled 'Diffusion Theory Of Decision Making In Continuous Report'. This tutorial demonstrated an application of a 2D version of the model that models continuous-outcome decisions as diffusions on the interior of a circle. The model provides a successful account of data from an eye-movement decision task about the hues of noisy colour patches, including the decision biases associated with nameable colours.

The second event was a research talk on a new application of the 2016 model and an account of the results from a recent paper he wrote with Dr Elaine Corbett. Here, he presented a 4D generalisation of the model that models decisions as diffusions on the interior of a hypersphere. The model provides a successful account of performance in a double-target detection task, in which people identified the presence of one or two target stimuli in brief four-element displays. Together, these applications represent a significant generalisation of the diffusion model and highlight its utility as a unifying framework for speeded simple decisions.

This was a valuable talk on a very useful model, and it gave rise to an interesting discussion. We thank Professor Smith for his presentation.


Smith, P. L. (2016). Diffusion theory of decision making in continuous report. Psychological Review, 123, 425-451.

Smith, P. L., & Corbett, E. A. (2019). Speeded multielement decision-making as diffusion in a hypersphere: Theory and application to double-target detection. Psychonomic Bulletin & Review