TITLE:
Maximum Entropy and Bayesian Inference for the Monty Hall Problem
AUTHORS:
Jennifer L. Wang, Tina Tran, Fisseha Abebe
KEYWORDS:
The Monty Hall Problem, Conditional Probability, Nash Equilibrium, Bayesian Inference, Maximum Entropy Principle
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.7,
July
11,
2016
ABSTRACT: We devise an approach to Bayesian statistics and their applications in the analysis of the Monty Hall problem. We combine knowledge gained through applications of the Maximum Entropy Principle and Nash equilibrium strategies to provide results concerning the use of Bayesian approaches unique to the Monty Hall problem. We use a model to describe Monty’s decision process and clarify that Bayesian inference results in an “irrelevant, therefore invariant” hypothesis. We discuss the advantages of Bayesian inference over the frequentist inference in tackling the uneven prior probability Monty Hall variant. We demonstrate that the use of Bayesian statistics conforms to the Maximum Entropy Principle in information theory and Bayesian approach successfully resolves dilemmas in the uneven probability Monty Hall variant. Our findings have applications in the decision making, information theory, bioinformatics, quantum game theory and beyond.