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jack-vanlightly.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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jaberkow.wordpress.com
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| | | | | Lately I have been making use of a continuous relaxation of discrete random variables proposed in two recent papers: The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables and Categorical Reparameterization with Gumbel-Softmax. I decided to write a blog post with some motivation of the method, as well as providing some minor clarification on... | |
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opguides.info
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| | | | | 10 - Probability/Stats # Seeing Theory: A visual Introduction to probability and statistics Why, where are these used, etc. bring up music things, part failure rates, tolerances, etc. Basics # For the following, Ill be using a die roll example, where the events are the total of two die. The Sample Space of this is \(S = \{2,3,4,5,6,7,8,9,10,11,12\}\) Note, that 1 isnt possible as the lowest is both die being 1. | |
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errorstatistics.com
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| | | The following is the February stop of our leisurely cruise (meeting 6 from my 2020 Seminar at the LSE). There was a guest speaker, Professor David Hand. Slides and videos are below. Ship StatInfasSt may head back to port or continue for an additional stop or two. Leisurely Cruise February 25: Power, shpower, severity, positive... | ||
