We introduce a new approach to modelling decision confidence, with the aim of enabling computationally cheap predictions while taking into account, and thereby exploiting, trial-by-trial variability in stochastically fluctuating stimuli. Using the framework of the drift diffusion model of decision making, along with time-dependent thresholds and the idea of a Bayesian confidence readout, we derive expressions for the probability distribution over confidence reports. In line with current models of confidence, the derivations allow for the accumulation of “pipeline” evidence that has been received but not processed by the time of response, the effect of drift rate variability, and metacognitive noise. The expressions are valid for stimuli that change over the course of a trial with normally-distributed fluctuations in the evidence they provide. A number of approximations are made to arrive at the final expressions, and we test all approximations via simulation. The derived expressions contain only a small number of standard functions, and require evaluating only once per trial, making trial-by-trial modelling of confidence data in stochastically fluctuating stimuli tasks more feasible. We conclude by using the expressions to gain insight into the confidence of optimal observers, and empirically observed patterns.

我们引入了一种新的决策置信度建模方法，目的是在考虑并从而利用随机波动刺激中逐次试验的可变性的同时，实现计算成本低廉的预测。使用决策漂移扩散模型的框架，以及时间相关阈值和贝叶斯置信度读数的思想，我们推导出置信度报告的概率分布表达式。根据当前的置信度模型，推导允许积累已收到但未根据响应时间、漂移率变异性的影响和元认知噪声进行处理的“管道”证据。这些表达式对于在试验过程中变化的刺激有效，并且它们提供的证据呈正态分布波动。为了得到最终的表达式，我们进行了许多近似，并且我们通过模拟来测试所有近似。导出的表达式仅包含少量标准函数，并且每次试验仅需要评估一次，使得随机波动刺激任务中的置信数据的逐次试验建模更加可行。最后，我们使用表达式来深入了解最佳观察者的置信度和经验观察到的模式。