Although no consensus on the issue exists yet, some evidence indicates that people are typically overprecise in their inferences. In particular, subjective confidence intervals are often too narrow when compared with Bayesian ones. This paper uses a quasi-Bayesian theory and lab experiments to explore overprecision when people learn about the empirical frequency $\theta$ of some random event. Motivated by the literature on limited attention, we hypothesize that, when there is a large number of potential values of $\theta ,$ individuals mentally operate with simplified representations of the objective state space. Their mental models are however sophisticated in that they co-move with the signals observed, focusing on the values of $\theta$ most consistent with the evidence available. As a result, they elaborate accurate point estimates of $\theta ,$ but also become too confident about them, as they hardly reflect on those values of $\theta$ that would call more into doubt their conclusions. In this line, subjects in our experiment almost exclusively report overly narrow confidence intervals, but also unbiased point estimates of $\theta$ (except when $\theta$ takes extreme values, i.e., close to 0 or 1). Indirect evidence suggests that subjects often consider about 1/5 of the objective state space.

尽管在此问题上尚无共识，但一些证据表明人们的推论通常过于精确。特别是，与贝叶斯相比较，主观置信区间通常太窄。本文使用准贝叶斯理论和实验室实验来探索人们了解经验频率时的超精确度$\theta$一些随机事件。根据有限关注的文献，我们假设，当存在大量潜在价值时，$\theta ，$个人在心理上以客观状态空间的简化表示进行操作。然而，他们的思维模式十分精巧，因为它们与观察到的信号共同移动，专注于$\theta$最符合现有证据。结果，他们详细阐述了$\theta ，$ 但也对它们变得过于自信，因为它们几乎无法反映出 $\theta$这将使人们更加怀疑他们的结论。在这条线中，我们实验中的对象几乎专门报告了过窄的置信区间，但也无偏点估计$\theta$ （除非 $\theta$取极值，即接近0或1）。间接证据表明，受试者通常会考虑客观状态空间的约1/5。