Polya’s Urn and the Martingale Convergence Theorem
نویسنده
چکیده
This paper is about Polya’s Urn and the Martingale Convergence Theorem. I will start with the formal definition, followed by a simple example of martingale and the basic properties of martingale. Then I will explain the Polya’s Urn model and how it contributes to proving the Martingale Convergence Theorem. Finally, I will give a full proof of the Martingale Convergence Theorem.
منابع مشابه
Polya’s Urn and the Beta-bernoulli Process
The Polya’s Urn model is notable within statistics because it generalizes the binomial, hypergeometric, and beta-Bernoulli (beta-binomial) distributions through a single formula. In addition, Polya’s Urn is a multivariate distribution whose variables are exchangeable but not independent. This paper introduces basic probability and Bayesian concepts in order to prove these properties.
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