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danieltakeshi.github.io | ||
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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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ryantolsma.com
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| | | | | IVF embryo selection is having a moment. Companies like Orchid Health are pitching parents on the promise of optimizing their future kids for IQ, height, disease resistance, and other desirable phenotypes with celebs and politicians (quietly) leaning in. The tech is real and improving, but the actual upside and long-term vision is limited by some pretty basic math. | |
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gregorygundersen.com
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| | | | | [AI summary] The blog post derives the expected value of a left-truncated lognormal distribution, explaining the mathematical derivation and validating it with Monte Carlo simulations. | |
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jeremykun.wordpress.com
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| | | This post is a sequel toFormulating the Support Vector Machine Optimization Problem. The Karush-Kuhn-Tucker theorem Generic optimization problems are hard to solve efficiently. However, optimization problems whose objective and constraints have special structureoften succumb to analytic simplifications. For example, if you want to optimize a linear function subject to linear equality constraints, one can compute... | ||
