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ryantolsma.com | ||
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danieltakeshi.github.io
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| | | | | In my STAT 210A class, we frequently have to deal with the minimum of asequence of independent, identically distributed (IID) random variables. Thishappens b... | |
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www.randomservices.org
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| | | | | [AI summary] The text presents a comprehensive overview of the beta-Bernoulli process and its related statistical properties. Key concepts include: 1) The Bayesian estimator of the probability parameter $ p $ based on Bernoulli trials, which is $ rac{a + Y_n}{a + b + n} $, where $ a $ and $ b $ are parameters of the beta distribution. 2) The stochastic process $ s{Z} = rac{a + Y_n}{a + b + n} $, which is a martingale and central to the theory of the beta-Bernoulli process. 3) The distribution of the trial number of the $ k $th success, $ V_k $, which follows a beta-negative binomial distribution. 4) The mean and variance of $ V_k $, derived using conditional expectations. 5) The connection between the beta distribution and the negative binomial distributi... | |
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austinrochford.com
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| | | | | While preparing the first in an upcoming series of posts on multi-armed bandits, I realized that a post diving deep on a simple Monte Carlo estimate of $\pi$ would be a useful companion, so here it is | |
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www.mit.edu
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