A Bayesian Reformulation of the Extended Drift-Diffusion Model in Perceptual Decision Making

Abstract

Perceptual decision making can be described as a process of accumulating evidence to a bound which has been formalized within drift-diffusion models (DDMs). Recently, an equivalent Bayesian model has been proposed. In contrast to standard DDMs, this Bayesian model directly links information in the stimulus to the decision process. Here, we extend this Bayesian model further and allow inter-trial variability of two parameters following the extended version of the DDM. We derive parameter distributions for the Bayesian model and show that they lead to predictions that are qualitatively equivalent to those made by the extended drift-diffusion model (eDDM). Further, we demonstrate the usefulness of the extended Bayesian model (eBM) for the analysis of concrete behavioral data. Specifically, using Bayesian model selection, we find evidence that including additional inter-trial parameter variability provides for a better model, when the model is constrained by trial-wise stimulus features. This result is remarkable because it was derived using just 200 trials per condition, which is typically thought to be insufficient for identifying variability parameters in DDMs. In sum, we present a Bayesian analysis, which provides for a novel and promising analysis of perceptual decision making experiments.

Deep Active Inference and Scene Construction

“…Subsequent theory attempted to model the process underlying perceptual decisions as the dynamics of a decision variable whose instantaneous value is related to the amount of evidence currently available to discriminate a stimulus’ identity - hence the term evidence accumulation (Ratcliff & Rouder, 1998; Bogacz, Brown, Moehlis, Holmes, & Cohen, 2006; Ratcliff & McKoon, 2008b). Properties of the decision variable’s dynamics have been related to experimental parameters like stimulus strength and the prior beliefs of the decision-maker about stimulus preponderance, among others (Bitzer, Park, Blankenburg, & Kiebel, 2014; Fard, Park, Warkentin, Kiebel, & Bitzer, 2017). Upon reaching an ‘evidence-bound’ or decision threshold, the decision variable then triggers the perceptual recognition or decision, which is often measured as the choice of one out of a discrete set of response options, with each option reporting recognition of a particular stimulus.…”

Personalizing Human-Agent Interaction Through Cognitive Models

“…All these paradigms allow for free parameters that govern individual model behavior and, hence, allow for personalization by parameter fitting. Moreover, the paradigms have soft boundaries, and mathematical representations of specific cognitive processes overlap (Roe et al, 2001;Fard et al, 2017). The number of free parameters in cognitive models can, however, cause overfitting as discussed in Section "Application Examples and Pitfalls. "…”

“…All these paradigms allow for free parameters that govern individual model behavior and, hence, allow for personalization by parameter fitting. Moreover, the paradigms have soft boundaries, and mathematical representations of specific cognitive processes overlap ( Roe et al, 2001 ; Fard et al, 2017 ). The number of free parameters in cognitive models can, however, cause overfitting as discussed in Section “Application Examples and Pitfalls.” Therefore, we advise readers to approach the selection of cognitive modeling paradigms driven by their research question’s underlying theory: Assuming interest in whether human choices satisfy criteria of rationality, juxtaposing a Bayesian model as a proxy for computational rationality against a heuristic model of violations against computational rationality is a suitable approach.…”

Rats strategically manage learning during perceptual decision making

“…Because of its simplicity, like the standard DDM, it is not meant to quantitatively describe all aspects of behavior. We instead use it to investigate qualitative features of decision making strategy, and expect that these features would be preserved in other related models of perceptual decision making [9,[36][37][38][39][40][41][42][43][44][45][46][47][48].…”