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gregorygundersen.com | ||
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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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cgad.ski
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| | | | | [AI summary] This article explores the asymptotic growth of the central binomial coefficient using Laplace's method to analyze random walks on integer lattices. | |
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extremal010101.wordpress.com
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| | | | | Suppose we want to understand under what conditions on $latex B$ we have $latex \begin{aligned} \mathbb{E} B(f(X), g(Y))\leq B(\mathbb{E}f(X), \mathbb{E} g(Y)) \end{aligned}$holds for all test functions, say real valued $latex f,g$, where $latex X, Y$ are some random variables (not necessarily all possible random variables!). If $latex X=Y$, i.e., $latex X$ and $latex Y$ are... | |
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ewulczyn.github.io
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| | | Data Scientist @ WMF | ||
