Understanding how people rate their confidence is critical for characterizing a wide range of perceptual, memory, motor, and cognitive processes. To enable the continued exploration of these processes, we created a large database of confidence studies spanning a broad set of paradigms, participant populations, and fields of study. The data from each study are structured in a common,

6Much work has explored the possibility that the drift diffusion model, a model of response times and choices, could 7 be extended to account for confidence reports. Many methods for making predictions from such models exist, 8 although these methods either assume that stimuli are static over the course of a trial, or are computationally 9 expensive, making it difficult to capitalise on trial-by-trial variability in dynamic stimuli. Using the framework of 10 the drift diffusion model with time-dependent thresholds, and the idea of a Bayesian confidence readout, we derive 11 expressions for the probability distribution over confidence reports. In line with current models of confidence, 12 the derivations allow for the accumulation of "pipeline" evidence which has been received but not processed 13 by the time of response, the effect of drift rate variability, and metacognitive noise. The expressions are valid 14 for stimuli which change over the course of a trial with normally distributed fluctuations in the evidence they 15 provide. A number of approximations are made to arrive at the final expressions, and we test all approximations 16 via simulation. The derived expressions only contain a small number of standard functions, and only require 17evaluating once per trial, making trial-by-trial modelling of confidence data in dynamic stimuli tasks more feasible. 18 We conclude by using the expressions to gain insight into the confidence of optimal observers, and empirically 19 observed patterns.

Visual search, the task of detecting or locating target items amongst distractor items in a visual scene, is an important function for animals and humans. Different theoretical accounts make differing predictions for the effects of distractor statistics. Here we use a task in which we parametrically vary distractor items, allowing for a simultaneously fine-grained and comprehensive study of distractor statistics. We found effects of target-distractor similarity, distractor variability, and an interaction between the two, although the effect of the interaction on performance differed from the one expected. To explain these findings, we constructed computational process models that make trial-by-trial predictions for behaviour based on the full set of stimuli in a trial. These models, including a Bayesian observer model, provided excellent accounts of both the qualitative and quantitative effects of distractor statistics, as well as of the effect of changing the statistics of the environment (in the form of distractors being drawn from a different distribution). We conclude with a broader discussion of the role of computational process models in the understanding of visual search. claim that Treisman and Gelade (1980) only explored part of the stimulus space spanned by targetdistractor similarity and distractor variability; the appearance of a dichotomy would then stem from the use of stimuli drawn from two distinct clusters in this space.While Duncan and Humphreys (1989) made a valuable contribution in suggesting that performance likely lies on a continuum, their exploration of this claim was necessarily limited by the stimuli that they used. Using letters and joined lines, they could not parametrically vary properties of these stimuli along an easily quantified dimension. Therefore, it could be that Duncan and Humphreys (1989), while describing performance in a larger area of stimulus space than Treisman and Gelade (1980), missed areas of the space, along with distinctive qualitative effects.Other visual search researchers have used stimuli that can easily be parametrically varied (Palmer,

The drift diffusion model (DDM) provides an excellent account of decisions and response times. It also features the optimal property of tracking the difference in evidence between two options. However, the DDM struggles to account for human confidence reports, because responses are triggered when the difference in evidence reaches a set value, suggesting confidence in all decisions should be equal. Previously considered extensions to the DDM fall short of providing an adequate quantitative account of confidence. Possibly because of this, much confidence research has used non-normative models of the decision mechanism. Motivated by the idea that perceptual decision-making will reflect optimal computation, we consider 9 variants of the DDM. Motivated by the idea that the brain will not duplicate the representation of evidence, in all model variants confidence is read out from the decision mechanism. We compare the models to benchmark results, and make 4 qualitative predictions which we verify in a preregistered study. Modelling confidence on a trial-by-trial basis, we find that a subset of model variants provide an excellent account of the precise quantitative effects observed in confidence data. Specifically, models in which confidence reflects a miscalibrated Bayesian readout perform best. These results support the claim that confidence is based on the decision mechanism, which is itself optimal. Therefore, there is no need to abandon the idea that the implementation of perceptual decision-making will reflect optimal computation.