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The Bayesian sampler: Generic Bayesian inference causes incoherence in human probability judgments.
Psychological Review ( IF 5.4 ) Pub Date : 2020-03-19 , DOI: 10.1037/rev0000190 Jian-Qiao Zhu 1 , Adam N Sanborn 1 , Nick Chater 2
Psychological Review ( IF 5.4 ) Pub Date : 2020-03-19 , DOI: 10.1037/rev0000190 Jian-Qiao Zhu 1 , Adam N Sanborn 1 , Nick Chater 2
Affiliation
Human probability judgments are systematically biased, in apparent tension with Bayesian models of cognition. But perhaps the brain does not represent probabilities explicitly, but approximates probabilistic calculations through a process of sampling, as used in computational probabilistic models in statistics. Naïve probability estimates can be obtained by calculating the relative frequency of an event within a sample, but these estimates tend to be extreme when the sample size is small. We propose instead that people use a generic prior to improve the accuracy of their probability estimates based on samples, and we call this model the Bayesian sampler. The Bayesian sampler trades off the coherence of probabilistic judgments for improved accuracy, and provides a single framework for explaining phenomena associated with diverse biases and heuristics such as conservatism and the conjunction fallacy. The approach turns out to provide a rational reinterpretation of “noise” in an important recent model of probability judgment, the probability theory plus noise model (Costello & Watts, 2014, 2016a, 2017; Costello & Watts, 2019; Costello, Watts, & Fisher, 2018), making equivalent average predictions for simple events, conjunctions, and disjunctions. The Bayesian sampler does, however, make distinct predictions for conditional probabilities and distributions of probability estimates. We show in 2 new experiments that this model better captures these mean judgments both qualitatively and quantitatively; which model best fits individual distributions of responses depends on the assumed size of the cognitive sample.
中文翻译:
贝叶斯采样器:通用贝叶斯推理导致人类概率判断不一致。
人类的概率判断是有系统的偏见,与贝叶斯认知模型明显紧张。但也许大脑并没有明确表示概率,而是通过抽样过程来近似概率计算,如统计学中的计算概率模型中所使用的那样。可以通过计算样本内事件的相对频率来获得朴素概率估计,但当样本量较小时,这些估计往往会变得极端。相反,我们建议人们使用通用先验来提高基于样本的概率估计的准确性,我们称这种模型为贝叶斯采样器。贝叶斯采样器权衡概率判断的一致性以提高准确性,并提供了一个单一的框架来解释与各种偏见和启发式相关的现象,例如保守主义和合取谬误。事实证明,该方法在最近一个重要的概率判断模型(概率论加噪声模型)中提供了对“噪声”的理性重新解释(Costello & Watts,2014、2016a、2017;Costello & Watts,2019;Costello、Watts & Fisher,2018 年),对简单事件、连词和析取进行等效的平均预测。然而,贝叶斯采样器确实对条件概率和概率估计的分布做出了不同的预测。我们在 2 个新实验中表明,该模型在定性和定量方面都能更好地捕捉这些平均判断;
更新日期:2020-03-19
中文翻译:
贝叶斯采样器:通用贝叶斯推理导致人类概率判断不一致。
人类的概率判断是有系统的偏见,与贝叶斯认知模型明显紧张。但也许大脑并没有明确表示概率,而是通过抽样过程来近似概率计算,如统计学中的计算概率模型中所使用的那样。可以通过计算样本内事件的相对频率来获得朴素概率估计,但当样本量较小时,这些估计往往会变得极端。相反,我们建议人们使用通用先验来提高基于样本的概率估计的准确性,我们称这种模型为贝叶斯采样器。贝叶斯采样器权衡概率判断的一致性以提高准确性,并提供了一个单一的框架来解释与各种偏见和启发式相关的现象,例如保守主义和合取谬误。事实证明,该方法在最近一个重要的概率判断模型(概率论加噪声模型)中提供了对“噪声”的理性重新解释(Costello & Watts,2014、2016a、2017;Costello & Watts,2019;Costello、Watts & Fisher,2018 年),对简单事件、连词和析取进行等效的平均预测。然而,贝叶斯采样器确实对条件概率和概率估计的分布做出了不同的预测。我们在 2 个新实验中表明,该模型在定性和定量方面都能更好地捕捉这些平均判断;