Generating and Evaluating Interval Estimates

这项研究考察了不确定性以区间估计的形式表达。例如，房地产经纪人可能会估计一套房子的市场价值在50万美元到52.5万美元之间，价值的不确定性越大(越小)，可能会导致更宽(更窄)的区间。以前的研究表明，人们在报告可信区间时往往过于自信，即CI(例如，我90%相信圣地亚哥的人口在100万到150万之间)。也就是说，X%配置项往往太窄，并且在很多情况下包含的真实值比X%少得多。这可能非常重要。例如，一家领先的美国制造商为了规划一家新工厂的生产能力，从其营销人员那里获得了一个预计的销售范围。结果发现，区间太窄，新工厂无法满足意想不到的需求。我们研究了人们如何产生区间估计，以及与之密切相关的人们如何评价区间估计的问题。在评估任务中，向评估者呈现多个生产者对同一问题报告的区间估计，告诉他们真实价值，并询问哪个估计是最好的。人们倾向于权衡区间的准确性(其中点与真实值的距离有多近)和信息性(它有多窄)。例如，评估者有时发现不包含真实值的区间比包含真实值的区间更好--但只有当前者很窄或信息量很大时。我们提出了一个正式的模型来解释这种行为。假设生产者的主观概率分布是正态的，我们的模型计算每个区间的主观概率密度为真值。在真值处具有最高密度的区间被判定为最优。模型中唯一的自由参数是假设生产者在报告的区间内有多大的置信度(例如，评估者是否将其视为50%CI或90%CI)。初步结果表明，新模型的性能优于竞争模型。因为我们将区间生产和评估视为一枚硬币的两面--区间如何评估可能决定它们是如何产生的--拟议的评估实验的结果将指导关于生产的研究。此外，我们正在进行一系列关于生产的补充研究。我们的出发点是，生产者在很大程度上对主体之间操纵的显性概率不敏感，但他们对主体内部操纵的概率很敏感。我们的实验将揭示受试者对他们的命中率的期望(例如，受试者是否期望他们的90%的CI比他们的50%的CI更频繁地包含真值？)，以及他们对显式概率的敏感性的性质(例如，生产者是对显式概率做出反应，还是他们只是在数字所暗示的方向上扩大和缩小他们的间隔？)。这些实验将回答有关区间生产的基本问题，这些问题既有应用意义，也有理论意义。

This research examines expressions of uncertainty in the form of interval estimates. For example, a realtor might estimate the market value of a home to be between $500,000 and $525,000, and more (less) uncertainty in the value would presumably result in a wider (narrower) interval. Previous research has shown that people tend to be overconfident when reporting confidence intervals, or CIs (e.g., "I'm 90% confident that the population of San Diego is between 1 million and 1.5 million"). That is, X% CIs tend to be much too narrow and contain the true value much less than X% of the time. This can matter a great deal. For example, a leading U.S. manufacturer elicited a projected range of sales from its marketing staff in order to plan the production capacity of a new factory. The range turned out to be too narrow and the new factory was incapable of meeting the unexpected demand.We examine both how people produce interval estimates and the closely related question of how people evaluate them. In evaluation tasks, evaluators are presented with interval estimates reported by multiple producers to the same question, told the true value, and asked which estimate is best. People tend to trade off an interval's accuracy (how close its midpoint is to the true value) and its informativeness (how narrow it is). For example, evaluators sometimes find intervals that do not contain the true value to be superior to those that do -- but only when the former are narrow, or highly informative. We propose a formal model to account for such behavior. Assuming that producers' subjective probability distributions are normal, our model calculates for each interval the subjective probability density at the true value. The interval with the highest density at the true value is judged superior. The only free parameter in the model is how much confidence the producer is assumed to have in the reported interval (e.g., whether the evaluator treats it as a 50% CI or a 90% CI). Preliminary results indicate that the new model outperforms competing models. Because we view interval production and evaluation as two sides of the same coin -- how intervals are evaluated may shape how they are produced -- the results from the proposed evaluation experiments will guide research on production. In addition, we are conducting a complementary line of research on production. Our starting point is the fact that producers are largely insensitive to explicit probabilities manipulated between subjects, but they are sensitive to the probabilities manipulated within subjects. Our experiments will reveal subjects' expectations about their hit rate (e.g., do subjects even expect their 90% CIs to contain the true value more often than their 50% CIs?), and the nature of their within-subject sensitivity to explicit probabilities (e.g., are producers responding to the explicit probabilities, or are they merely widening and narrowing their intervals in the direction implied by the numbers?). These experiments will answer basic questions about interval production that have both applied and theoretical implications.