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ryantolsma.com | ||
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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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bldavies.com
I derive the posterior variance-minimizing sample size when observations have constant marginal cost. |
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austinrochford.com
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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qchu.wordpress.com
This is a post I wanted to write some time ago; I've forgotten why, but it was short and cute enough to finish. Our starting point is the following observation: Theorem 1: Universal lossless compression is impossible. That is, there is no function which takes as input finite strings (over some fixed alphabet) and always... |
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