Maximum Entropy and Bayesian Inference for the Monty Hall Problem
نویسندگان
چکیده
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.
منابع مشابه
Inference of Markov Chain: AReview on Model Comparison, Bayesian Estimation and Rate of Entropy
This article has no abstract.
متن کاملClassical and Bayesian Inference in Two Parameter Exponential Distribution with Randomly Censored Data
Abstract. This paper deals with the classical and Bayesian estimation for two parameter exponential distribution having scale and location parameters with randomly censored data. The censoring time is also assumed to follow a two parameter exponential distribution with different scale but same location parameter. The main stress is on the location parameter in this paper. This parameter has not...
متن کاملDetermination of Maximum Bayesian Entropy Probability Distribution
In this paper, we consider the determination methods of maximum entropy multivariate distributions with given prior under the constraints, that the marginal distributions or the marginals and covariance matrix are prescribed. Next, some numerical solutions are considered for the cases of unavailable closed form of solutions. Finally, these methods are illustrated via some numerical examples.
متن کاملThe Monty Hall Problem as a Bayesian Game
This paper formulates the classic Monty Hall problem as a Bayesian game. Allowing Monty a small amount of freedom in his decisions facilitates a variety of solutions. The solution concept used is the Bayes Nash Equilibrium (BNE), and the set of BNE relies on Monty’s motives and incentives. We endow Monty and the contestant with common prior probabilities (p) about the motives of Monty, and show...
متن کاملIntroduction to Bayesian Inference
These are the write-up of a NIKHEF topical lecture series on Bayesian inference. The topics covered are the definition of probability, elementary probability calculus and assignment, selection of least informative probabilities by the maximum entropy principle, parameter estimation, systematic error propagation, model selection and the stopping problem in counting experiments.
متن کامل