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www.athenopolis.net | ||
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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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liorsinai.github.io
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| | | | | Quantifying how likely each birthday is present (covered) in some large group of people. | |
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thirdorderscientist.org
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| | | | | [AI summary] The article explains how to determine the number of samples needed to estimate a success probability with a specific confidence level by using Hoeffding's Inequality for Bernoulli random variables. | |
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www.seascapemodels.org
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| | | [AI summary] A tutorial explaining the basics of General Linear Models using statistical concepts like linear equations, R programming simulations, and assumption checking for biological sciences. | ||
