A computational framework for the study of confidence in humans and animals

Abstract

Confidence judgements, self-assessments about the quality of a subject's knowledge, are considered a central example of metacognition. Prima facie, introspection and self-report appear the only way to access the subjective sense of confidence or uncertainty. Contrary to this notion, overt behavioural measures can be used to study confidence judgements by animals trained in decision-making tasks with perceptual or mnemonic uncertainty. Here, we suggest that a computational approach can clarify the issues involved in interpreting these tasks and provide a much needed springboard for advancing the scientific understanding of confidence. We first review relevant theories of probabilistic inference and decision-making. We then critically discuss behavioural tasks employed to measure confidence in animals and show how quantitative models can help to constrain the computational strategies underlying confidence-reporting behaviours. In our view, post-decision wagering tasks with continuous measures of confidence appear to offer the best available metrics of confidence. Since behavioural reports alone provide a limited window into mechanism, we argue that progress calls for measuring the neural representations and identifying the computations underlying confidence reports. We present a case study using such a computational approach to study the neural correlates of decision confidence in rats. This work shows that confidence assessments may be considered higher order, but can be generated using elementary neural computations that are available to a wide range of species. Finally, we discuss the relationship of confidence judgements to the wider behavioural uses of confidence and uncertainty.

Figure 1.

Behavioural tasks for studying confidence in animals. (a) In uncertain option tasks, there are three choices, the two categories, A and B, and the uncertain option. (b) In decline option or opt-out tasks, there is first a choice between taking the test or declining it, then taking the test and answering A or B. In a fraction of trials, the option to decline is omitted. (c) In post-decision wagering, for every trial there is first a two-category discrimination, A or B, and then a confidence report, such as low or high options.

Figure 2.

Leaving decision tasks for studying confidence in animals. (a) Schematic of the behavioural paradigm. To start a trial, the rat enters the central odour port and after a pseudorandom delay of 0.2–0.5 s an unequal mixture of two odours is delivered. Rats respond by moving to the A or B choice port, where a drop of water is delivered after a 0.5–8 s (exponentially distributed) waiting period for correct decisions. In catch trials (approx. 10% of correct choices), the rat is not rewarded and no feedback is provided. Therefore, the waiting time can be measured (from entry into choice ports until withdrawal) for all error and a subset of correct choices. (b) Psychometric function for an example rat. (c) Choice accuracy as a function of waiting time. For this plot, we assumed that the distribution of waiting times for correct catch trials is a representative sample for the entire correct waiting time distribution. (d) Mean waiting time as a function of odour mixture contrast and trial outcome (correct/error) for an example rat.

Figure 3.

Computational models for choice and confidence. (a–c) Bayesian signal detection theory model. (a) The two stimulus distributions, A and B. (b) Psychometric function. (c) Predictions for confidence estimate as a function of observables. (d,e) Dual integrator, race model. (d) Schematic showing the accumulation of evidence in two integrators up to a threshold. Blue line denotes evidence for A and purple line denotes evidence for B. (e) Calibration of ‘balance of evidence’ yields veridical confidence estimate. (f) Prediction for confidence estimate as a function of observables.

Figure 4.

Neural correlates of decision confidence in rat orbitofrontal cortex. (a–d) Analyses of firing rate for a single neuron rat in OFC after the animal made its choice and before it received feedback. (a) Tuning curve as a function of stimulus and outcome (red, error; green, correct). (b) Firing rate conditional accuracy function. (c) Psychometric function conditioned of firing rate (blue, low rates; orange, high rates). (d) Regression analysis of firing rate based on reward history. Coefficient α₁ is an offset term, α₂ is stimulus difficulty and β coefficients represent outcomes (correct/error) divided by left/right choice side and a function of recent trial history (current trial = 0). Note that the largest coefficients are for the current trial and beyond the past trial the coefficients are not significantly different from zero (unfilled circles).