Kiani, R. and Shadlen, M. N.
Science, 324:759–764, 2009
DOI, Google Scholar
The degree of confidence in a decision provides a graded and probabilistic assessment of expected outcome. Although neural mechanisms of perceptual decisions have been studied extensively in primates, little is known about the mechanisms underlying choice certainty. We have shown that the same neurons that represent formation of a decision encode certainty about the decision. Rhesus monkeys made decisions about the direction of moving random dots, spanning a range of difficulties. They were rewarded for correct decisions. On some trials, after viewing the stimulus, the monkeys could opt out of the direction decision for a small but certain reward. Monkeys exercised this option in a manner that revealed their degree of certainty. Neurons in parietal cortex represented formation of the direction decision and the degree of certainty underlying the decision to opt out.
The authors used a 2AFC-task with an option to waive the decision in favour of a choice which provides low, but certain reward (the sure option) to investigate the representation of confidence in LIP neurons. Behaviourally the sure option had the expected effect: it was increasingly chosen the harder the decisions were, i.e., the more likely a false response was. Trials in which the sure option was chosen, thus, may be interpreted as those in which the subject was little confident in the upcoming decision. It is important to note that task difficulty here was manipulated by providing limited amounts of information for a limited amount of time, i.e., this was not a reaction time task.
The firing rates of the recorded LIP neurons indicate that selection of the sure option is associated with an intermediate level of activity compared to that of subsequent choices of the actual decision options. For individual trials the authors found that firing rates closer to the mean firing rate (in a short time period before the sure option became available) more frequently lead to selection of the sure option than firing rates further away from the mean, but in absolute terms the activity in this time window could predict choice of the sure option only weakly (probability of 0.4). From these results the authors conclude that the LIP neurons which have previously been found to represent evidence accumulation also encode confidence in a decision. They suggest a simple drift-diffusion model with fixed diffusion parameter to explain the results. Additional to standard diffusion models they define confidence in terms of the log-posterior odds which they compute from the state of the drift-diffusion model. They define posterior as p(S_i|v), the probability that decision option i is correct given that the drift-diffusion state (the decision variable) is v. They compute it from the corresponding likelihood p(v|S_i), but don’t state how they obtained that likelihood. Anyway, the sure option is chosen in the model, when the log-posterior odds is below a certain level. I don’t see why the detour via the log-posterior odds is necessary. You could directly define v as the posterior for decision option i and still be consistent with all the findings in the paper. Of course, then v could not be governed by a linear drift anymore, but why should it in the first place? The authors keenly promote the Bayesian brain, but stop just before the finishing line. Why?