Sanborn Adam N, Beierholm Ulrik R
Department of Psychology, University of Warwick, Coventry, United Kingdom.
Department of Psychology, Durham University, Durham, United Kingdom.
PLoS Comput Biol. 2016 Apr 12;12(4):e1004859. doi: 10.1371/journal.pcbi.1004859. eCollection 2016 Apr.
Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates.
许多日常估计任务都具有内在的离散性质，无论该任务是对物体进行计数（例如，油漆桶的数量）还是估计离散化的连续变量（例如，粉刷一个房间所需的油漆桶数量）。虽然贝叶斯推理常用于对沿连续尺度做出的估计进行建模，但离散数值估计尽管在日常生活中很常见，却没有受到同等程度的关注。通过两项任务，即数量任务和面积估计任务，我们运用贝叶斯决策理论来描述人们如何学习离散数值分布并进行数值估计。在针对新刺激分布的三项实验中，我们发现参与者在将其不确定表征转换为反应的两种常见决策函数之间：从其后验分布中抽取样本以及取其后验分布的最大值。虽然这与先前使用连续估计任务的研究中发现的决策函数一致，但令人惊讶的是，我们实验中的参与者所学习的先验分布适应性更强：在进行连续估计时，参与者需要数千次试验才能学习到双峰先验，但在我们的任务中，参与者在几百次试验内就学习到了离散双峰甚至离散四峰先验。这使得离散数值估计任务成为研究人们如何学习和进行估计的良好试验平台。
