Paper:
A Bayesian Framework for Modeling Confidence in Perceptual Decision Making
The degree of confidence in one's choice or decision is a critical aspect of perceptual decision making. Attempts to quantify a decision maker's confidence by measuring accuracy in a task have yielded limited success because confidence and accuracy are typically not equal. In this paper, we introduce a Bayesian framework to model confidence in perceptual decision making. We show that this model, based on partially observable Markov decision processes (POMDPs), is able to predict confidence of a decision maker based only on the data available to the experimenter. We test our model on two experiments on confidence-based decision making involving the well-known random dots motion discrimination task.
In both experiments, we show that our model's predictions closely match experimental data. Additionally, our model is also consistent with other phenomena such as the hard-easy effect in perceptual decision making.

Review:
The authors' model confidence data from two experiments (conducted by others and previously published in the scientific literature) using a POMDP. In both experiments, subjects saw a random-dot kinematogram on each trial and made a binary choice about the dominant motion direction. The first experiment used monkeys as subjects and stimuli had a fixed duration. The second experiment used people as subjects and stimuli continued until a subject made a response. The paper reports that the POMDP model does a good job of fitting the experimental data, both the accuracy data and the confidence data.I should start by stating that I know a bit about perceptual decision making and a (small) bit about POMDPs but I am unfamiliar with the application of POMDPs to perceptual decision making. The paper reports that this is the first time that a POMDP has been used to model confidence data in a perceptual decision making task. I'll take the authors' word on this.Taken as a whole, I have a positive opinion of this manuscript. I very much like the problem studied here (modeling confidence data in perceptual decision making) and I like the idea of applying a POMDP to this data. The fit to the experimental data is qualitatively good (though quantitatively mediocre).A significant shortcoming of this paper is the lack of a literature review section providing context for the work provided here. Other researchers have previously applied POMDPs to perceptual decision making. Did they only model accuracy data? Did they model reaction time data too? How does the POMDP studied here relate to the POMDPs presented in these earlier papers? Is it largely the same or is it substantially different? If the latter , how (and why) is it different? If the current paper is the first to apply POMDPs to confidence data in a perceptual decision making task, how did researchers model confidence data previously? Without answers to these questions, there is no way to evaluate the novelty and significance of the contribution made by the current paper.