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.
Highlights
Perceptual decision making is the process by which agents use sensory information to make inferences about the world and select discrete actions
The leading decision-making models that have a statistical basis in psychology and neuroscience are signal detection theory (SDT) and the sequential probability ratio test (SPRT) (Bogacz et al, 2006; Dayan & Daw, 2008; Gold & Shadlen, 2007)
Understanding the implications of the formalism is important because, despite recent single-neuron studies advancing our understanding of perceptual decision making at the neural level, a complete account of how decision making is implemented biologically remains unfinished (Churchland et al, 2008; Hanks & Summerfield, 2017) and will depend on the mathematics of the theory. We explore these issues by examining the relationship between Signal detection theory (SDT) and SPRT from a mathematical viewpoint that bears in mind how biology might implement these methods
Summary
Perceptual decision making is the process by which agents use sensory information to make inferences about the world and select discrete actions. The leading decision-making models that have a statistical basis in psychology and neuroscience are signal detection theory (SDT) and the sequential probability ratio test (SPRT) (Bogacz et al, 2006; Dayan & Daw, 2008; Gold & Shadlen, 2007) These methods are routinely employed to explain behavioural data (Laming, 1968; Ratcliff & McKoon, 2008; Stone, 1960), the mathematical relationship between these two theories has some subtleties that are key to understanding their implications. We emphasize that the essential difference between fixed sample testing (nSDT) and SPRT is in their sampling method and so they can be viewed as static and dynamic variants from the same family of hypothesis tests (Gottlieb & Oudeyer, 2018)
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