Abstract

When a Bayesian learns new information and changes her beliefs, she must on average become concomitantly more certain about the state of the world. Consequently, it is rare for a Bayesian to frequently shift beliefs substantially while remaining relatively uncertain, or, conversely, become very confident with relatively little belief movement. We formalize this intuition by developing specific measures of movement and uncertainty reduction given a Bayesian’s changing beliefs over time, showing that these measures are equal in expectation and creating consequent statistical tests for Bayesianess. We then show connections between these two core concepts and four common psychological biases, suggesting that the test might be particularly good at detecting these biases. We provide support for this conclusion by simulating the performance of our test and other martingale tests. Finally, we apply our test to data sets of individual, algorithmic, and market beliefs.

中文翻译：

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信念运动，减少不确定性和合理更新*

摘要

当贝叶斯人学到新信息并改变信念时，平均而言，她必须同时更加确定世界的状况。因此，贝叶斯很少会在保持相对不确定性的同时频繁地大量转移信念，或者相反，在相对较少的信念运动下变得非常有信心。考虑到贝叶斯的信念随着时间的推移不断变化，我们通过制定运动和不确定性减少的具体度量来对这种直觉进行形式化，表明这些度量在期望上是相等的，并因此对贝叶斯性进行了统计检验。然后，我们展示了这两个核心概念与四个常见的心理偏见之间的联系，这表明该测试可能特别擅长于发现这些偏见。我们通过模拟测试和其他and测试的性能来为该结论提供支持。最后，我们将测试应用于个人，算法和市场信念的数据集。