论文标题
基于蒙蒂大厅难题的可能性解决方案和相关的三囚犯悖论
Likelihood-based solution to the Monty Hall puzzle and a related 3-prisoner paradox
论文作者
论文摘要
Monty Hall难题已通过多种方式解决和解剖，但始终使用概率论点，因此被认为是概率难题。在本文中，难题是作为一个正统统计问题，涉及未知参数，概率模型和观察结果。这意味着我们可以计算一个可能性函数，而切换的决定对应于选择最大似然解决方案。基于可能性的解决方案的优点是，推理适用于单个游戏，不受主机未来计划的影响。我还用三名囚犯来描述一个早期版本的难题：两个要处决，一个被释放。与山羊和汽车不同，这些囚犯有意识，因此他们可以考虑交换惩罚。但是，当他们两个这样做时，我们有一个悖论，这对双方互相交换彼此的惩罚是有利的。总体而言，难题和悖论是统计思维的有用例子，因此它们是出色的教学主题。
The Monty Hall puzzle has been solved and dissected in many ways, but always using probabilistic arguments, so it is considered a probability puzzle. In this paper the puzzle is set up as an orthodox statistical problem involving an unknown parameter, a probability model and an observation. This means we can compute a likelihood function, and the decision to switch corresponds to choosing the maximum likelihood solution. One advantage of the likelihood-based solution is that the reasoning applies to a single game, unaffected by the future plan of the host. I also describe an earlier version of the puzzle in terms of three prisoners: two to be executed and one released. Unlike the goats and the car, these prisoners have consciousness, so they can think about exchanging punishments. When two of them do that, however, we have a paradox, where it is advantageous for both to exchange their punishment with each other. Overall, the puzzle and the paradox are useful examples of statistical thinking, so they are excellent teaching topics.
