Quantum probability updating from zero priors (by-passing Cromwell's rule)
Quantum probability updating from zero priors (by-passing Cromwell's rule)
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DOI：
10.1016/j.jmp.2016.08.005
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发表时间：
2017-04-01
影响因子：
1.8
通讯作者：
Busemeyer, Jerome
中科院分区：
文献类型：
--
作者：
Basieva, Irina;Pothos, Emmanuel;Busemeyer, Jerome
克伦威尔规则（英语：Cromwell's rule）（也被称为零先验悖论）是指经典概率论的一个约束，如果一个假设的先验概率为0或1，那么后验概率也必须为0或1（这是贝叶斯规则的直接含义）。与此相关的是，如果没有大量的新证据来支持它们（或使其他可能性变得非常不可能），先验非常低的假设就不能更新为具有非常高的后验。克伦威尔的规则似乎与我们对人类如何更新概率的直觉不一致。在这项工作中，我们报告了两个简单的决策实验，这似乎是不符合克伦威尔的规则。量子概率论是量子力学的数学形式体系中如何分配概率的规则，它为概率推理提供了另一种框架。量子概率论的一个优点是它不受克伦威尔规则的约束，它可以适应从零或非常小的先验到显著的后验的变化。我们概述了一个模型的决策，量子理论的基础上，它可以容纳从先验到后验的变化，在我们的实验中观察到的。(C)2016 Elsevier Inc. All rights reserved.
Cromwell's rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a straightforward implication of how Bayes' rule works). Relatedly, hypotheses with a very low prior cannot be updated to have a very high posterior without a tremendous amount of new evidence to support them (or to make other possibilities highly improbable). Cromwell's rule appears at odds with our intuition of how humans update probabilities. In this work, we report two simple decision making experiments, which seem to be inconsistent with Cromwell's rule. Quantum probability theory, the rules for how to assign probabilities from the mathematical formalism of quantum mechanics, provides an alternative framework for probabilistic inference. An advantage of quantum probability theory is that it is not subject to Cromwell's rule and it can accommodate changes from zero or very small priors to significant posteriors. We outline a model of decision making, based on quantum theory, which can accommodate the changes from priors to posteriors, observed in our experiments. (C) 2016 Elsevier Inc. All rights reserved.