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jonathanweisberg.org | ||
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cgad.ski
[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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www.randomservices.org
[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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danieltakeshi.github.io
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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extremal010101.wordpress.com
With Alexandros Eskenazis we posted a paper on arxiv "Learning low-degree functions from a logarithmic number of random queries" exponentially improving randomized query complexity for low degree functions. Perhaps a very basic question one asks in learning theory is as follows: there is an unknown function $latex f : \{-1,1\}^{n} \to \mathbb{R}$, and we are... |
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