The statistics of optimal decision making: Exploring the relationship between signal detection theory and sequential analysis

Griffith, Thom, Baker, Sophie-Anne and Lepora, Nathan F. 2021. The statistics of optimal decision making: Exploring the relationship between signal detection theory and sequential analysis. Journal of Mathematical Psychology 103 , 102544. 10.1016/j.jmp.2021.102544

PDF - Published Version Available under License Creative Commons Attribution. Download (1MB)

Abstract

Signal detection theory (SDT) and the sequential probability ratio test (SPRT) are two leading models for binary perceptual decision-making in psychology and neuroscience. For initiates in this research area, the foundational relationship between SDT and the SPRT, or between statistical inference models and their mechanistic counterparts, can be unclear because many decision-making models in use today are much extended versions of the original, simpler models that contain the essence of these models’ claims to optimality. For those familiar with the models, it would be useful to have a quantitative comparison between their performance as multi-sample hypothesis tests. In this tutorial review of SDT and the SPRT, we emphasize that SDT and the SPRT differ only in their sampling procedures and so can be viewed as static and dynamic variants from the same family of hypothesis tests. Furthermore, we map the sample efficiency gains of using the SPRT over a multi-sample version of SDT by a novel construction of ROC curves. The goal of this paper is to provide a compact treatise on the statistical underpinnings of SDT and the SPRT, how they relate to the drift–diffusion model (DDM), and what these models imply for the physical implementation of evidence gathering and optimal decision making in biological systems.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Psychology
Publisher:	Elsevier
ISSN:	0022-2496
Date of First Compliant Deposit:	2 September 2025
Date of Acceptance:	21 April 2021
Last Modified:	02 Sep 2025 09:00
URI:	https://orca.cardiff.ac.uk/id/eprint/180766

Actions (repository staff only)

Edit Item