Experimental data analyzed in: Signal detection models as contextual bandits

Signal detection theory (SDT) has been widely applied to identify the optimal discriminative decisions of receivers under uncertainty. However, the approach assumes that decision-makers immediately adopt the appropriate acceptance threshold, even though the optimal response must often be learned. Here we recast the classical normal-normal (and power-law) signal detection model as a contextual multi-armed bandit (CMAB). Thus, rather than starting with complete information, decision-makers must infer how the magnitude of a continuous cue is related to the probability that a signaller is desirable, while simultaneously seeking to exploit the information they acquire. We explain how various CMAB heuristics resolve the trade-off between better estimating the underlying relationship and exploiting it. Next, we determined how naïve human volunteers resolve signal detection problems with a continuous cue. As anticipated, a model of choice (accept/reject) that assumed volunteers immediately adop..., The experiment was administered through a web application programmed in R (version 3.6.2) using the RShiny package. Our volunteers (36 in total) were drawn primarily from Biology undergraduate and graduate programs at Carleton University, Ottawa with recruitment by email. Participants accessed the web application via a URL link in the email invitation and were only engaged once. No details of the experimental aims were given at that time, and no information was given concerning a potential relationship between a signaller’s appearance and its true nature. 
 Our volunteers were presented with a series of computer-generated signallers (solid-coloured circles) over a sequence of trials. In any given trial, the signaller was either desirable (“good”) or undesirable (“bad”) and signaller type could be probabilistically inferred from their appearance (their greyness, see below). Participants were told the benefits of a correct acceptance of a desirable signaller (1), the cost of an incorrect ..., We used Stan (https://mc-stan.org/) to fit and compare multi-level models of human choices. Stan was accessed in R via RStan and the models were coded using the ulam function in the rethinking package. All posterior distributions were estimated using Markov Chain Monte Carlo (MCMC) sampling for 4000 iterations in four separate chains. To facilitate model fitting, the RGB values (C) of all signallers were rescaled by dividing C by 255, ensuring a value of perceived appearance (x) between 0 and 1. We provide a full listing of R code as part of this submission.