Belief Movement, Uncertainty Reduction, and Rational Updating
研究了贝叶斯学习者在获取新信息时信念变动与不确定性降低的关系，提出两者期望相等的度量及统计检验，并模拟检验对四种常见心理偏见的检测能力，最后应用于个体、算法和市场信念数据。
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.