Subjective confidence

An individual's expressed certainty in a judgment. Its relation to objective correctness is measured separately from the certainty itself. Metacognitive calibration concerns numerical agreement with outcomes; metacognitive sensitivity concerns discrimination between better and worse performance.

A computation that evaluates an action using partially shared evidence about the action-producing system. First-order decisions and confidence need not have identical internal samples; calling the computation second order does not imply conscious verbal reasoning.^[ref]

Confidence inferred from agreement among sampled representations supporting a response. Internally consistent evidence can systematically favour a wrong answer, separating confidence from correctness.^[ref]

The ability of confidence to distinguish a person's correct from incorrect responses, or to rank items by later success. It is distinct from metacognitive calibration. A type 2 receiver operating characteristic measures discrimination in a binary-correctness task; other metamemory designs may need other measures.

The first-order sensitivity index that, in a fitted signal detection theory model, would generate the observed confidence discrimination. Model assumptions and sampling uncertainty matter; raw confidence–accuracy association alone does not estimate it.^[ref]

A model-based comparison of meta-d-prime with first-order discrimination, often their ratio. Interpretation becomes unstable when the denominator is close to zero. Efficiency, metacognitive calibration and overall confidence are different quantities.

If confidence $C$ is replaced by a strictly increasing function $g(C)$, the attainable threshold partitions have the same ordering and ties. Consequently the type 2 receiver operating characteristic and its area under the ROC curve are unchanged. Equivalently, $P(C_{\mathrm{correct}}>C_{\mathrm{error}})+\frac{1}{2}P(C_{\mathrm{correct}}=C_{\mathrm{error}})$ is invariant. Calibration need not be preserved: adding a positive constant to probabilities within their allowed range changes their absolute values while preserving ranks. A merely nondecreasing transformation can merge distinct reports and requires additional care.

A receiver operating characteristic treating high confidence as a prediction that a first-order answer was correct. Varying confidence threshold $t$ traces the false-positive and true-positive probabilities in the displayed expression. Raw discrimination can depend on first-order task performance; it is not automatically a performance-independent measure of monitoring quality.

For correctness indicator function $Y$ and stated probability $C$, ideal calibration means that answers assigned confidence $c$ are correct with conditional probability $c$. Overall overconfidence is $\mathbb{E}[C-Y]>0$; a zero overall difference does not establish calibration at every confidence level. Estimated calibration depends on sample size and how reports are grouped.

Confidence evaluated after making a response. It may use evidence, further processing and information about the action that were not all available at the moment of the response.

A normative Bayesian inference model of retrospective confidence. For two exhaustive alternatives with equal prior probabilities, let $L=\log [p(E\mid H_1)/p(E\mid H_0)]$ be the log-likelihood ratio. Bayes' theorem gives posterior odds $e^L$. Choosing the alternative with the larger posterior yields $P(\text{correct}\mid E)=(1+e^{-|L|}{)}^{-1}$. Unequal priors add prior log odds; choosing a different action changes which posterior probability is appropriate. This calculation does not establish that an observer knows the true likelihoods.