Sequential Sampling Models in Cognitive Neuroscience: Advantages, Applications and Extensions

(Forstmann, Ratcliff, & Wagenmakers, 2016)

The article by Forstmann, Ratcliff and Wagenmakers (2016) is a comprehensive and very easy-to-read article that captures the history leading up to the current popularity of the drift diffusion model (DDM), a subset of sequential sampling models. Sequential sampling models are models in which evidence is built up over time (comprising a sequence of trials) favouring one response over another. The research in this field remains largely dichotomous in nature, with experiments tracking the choice of one option over another – the random dot kinematogram (RDK) being a common type of experiment used to track decision-making choices.

The authors track the theories and approaches adopted by researchers over the years starting with Turing and his use of sequential analysis to break the German enigma codes and incorporating Feller’s ‘gambler’s ruin’ experiment (1968), a random walk sequential model. Psychologists that have explored the random walk models include Stone (1960), Laming (1968) and Link & Heath (1975).

In 1948, Wald proposed the sequential probability ratio test (SPRT), in which each incoming datum is transformed into a log likelihood ratio that quantifies the relative evidence for one hypothesis over another. The SPRT has proven optimal in producing the fastest mean time for a given accuracy. However, earlier models did not account for relative speed-of-error reaction times (RTs) across experiments. As a result, the DDM was put forward to account for ‘noise’ data accumulation from a starting point to a decision threshold associated with a particular choice. Because of the noisy nature of the DDM, choices tend to be error prone and RTs variable. Forstmann et al also link the DDM with signal-detection theory (SDT). In SDT, the focus is on a single sample of information, while in the DDM, the decision maker draws on a sequence of samples.

The DDM has four key parameters, namely the drift rate (the average amount of evidence accumulated per unit time); the boundary separation – the point where a decision is made (the closer the separation, the faster the response, but the greater the number of errors); the starting point which reflects priori bias or preference; and non-decision time that is an additive lag time for peripheral stimulus encoding, transforming the stimulus representation into a decision-related representation, and executing a response. Thus the total RT is the time to diffuse from starting point to boundary, plus non-decision time. Forstmann et al also highlight across-trial variabilities in drift rate, starting point and non-decision time and explain each of these. They also draw on the literature to argue for the robustness of the DDM, the many parameters notwithstanding.

Forstman et al then move on to discuss the advantages of the DDM in the analysis of choice behaviour from the perspectives of aging, working memory, IQ and clinical contexts and argue the robustness of the model in each of these cases. Their article also discusses the neural firing rates (in monkeys) and suggest that decision-related information flows from the lateral intraparietal cortex (LIP) to the frontal eye field (FEF) and then to the superior colliculus (SC).

They further discuss methods for measuring human brain activity namely fMRI and EEG. The problem with EEG is the noisy nature of these signals, but using event-related potentials more meaningful data can be extracted from EEG data. As far as the use of EEG is concerned, Forstmann suggests that the extent of research into brain activity using EEG is likely to expand in the near future.

Finally, Forstmann explains how the DDM framework has been extended to address issues on multi-alternative decisions, confidence judgements, sequential sampling models for confidence, value-based judgements, changes of mind and dynamic thresholds.

Forstmann, B.U., Ratcliff, R. and Wagenmakers, E.J. 2016. Sequential Sampling Models in Cognitive Neuroscience: Advantages, Applications and Extensions. Annual Review of Psychology, 67, pp. 641–666.