Posts Tagged ‘ probability ’

Odds and Probability: Commonly Misused Terms in Statistics – An Illustrative Example in Baseball

Odds and Probability: Commonly Misused Terms in Statistics – An Illustrative Example in Baseball

Yesterday, all 15 home teams in Major League Baseball won on the same day – the first such occurrence in history.  CTV News published an article written by Mike Fitzpatrick from The Associated Press that reported on this event.  The article states, “Viewing every game as a 50-50 proposition independent of all others, STATS figured the […]

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How Predictable is the English Premier League?

May 19, 2015
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How Predictable is the English Premier League?

The reason why football is so exciting is uncertainty. The outcome of any match or league is unknown, and you get to watch the action unfold without knowing what’s going to happen. Watching matches where you know the score is never exciting. This weekend the English Premier League season will conclude with little fanfare. Bar […]

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I still think you can manufacture an unfair coin

April 13, 2015
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In Gelman and Nolan’s paper “You Can Load a Die, But You Can’t Bias a Coin” The American Statistician, November 2002, Vol. 56, No. 4 it is argued you can’t easily produce a coin that is biased when flipped (and caught). A numb...

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Machine Learning Books Suggested by Michael I. Jordan from Berkeley

December 30, 2014
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Machine Learning Books Suggested by Michael I. Jordan from Berkeley

There has been a Machine Learning (ML) reading list of books in hacker news for a while, where Professor Michael I. Jordan recommend some books to start on ML for people who are going to devote many decades of their lives to the field, and who want to get to the research frontier fairly quickly. […]

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Mathematical Statistics Lesson of the Day – Complete Statistics

Mathematical Statistics Lesson of the Day – Complete Statistics

Filed under: Mathematical Statistics, Mathematics, Probability, Statistics, Statistics Lesson of the Day Tagged: almost surely, complete statistic, completeness, estimation, mathematical statistics, point estimation, probability, probability density function, probability mass function, statistics, unbiased estimation, unbiased estimator

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Mathematics and Mathematical Statistics Lesson of the Day – Convex Functions and Jensen’s Inequality

Mathematics and Mathematical Statistics Lesson of the Day – Convex Functions and Jensen’s Inequality

Consider a real-valued function that is continuous on the interval , where and are any 2 points in the domain of .  Let be the midpoint of and .  Then, if then is defined to be midpoint convex. More generally, let’s consider any point within the interval .  We can denote this arbitrary point as where . […]

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Mathematical Statistics Lesson of the Day – The Glivenko-Cantelli Theorem

Mathematical Statistics Lesson of the Day – The Glivenko-Cantelli Theorem

In 2 earlier tutorials that focused on exploratory data analysis in statistics, I introduced the conceptual background behind empirical cumulative distribution functions (empirical CDFs) how to plot  empirical cumulative distribution functions in 2 different ways in R There is actually an elegant theorem that provides a rigorous basis for using empirical CDFs to estimate the true CDF – and […]

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Mathematical and Applied Statistics Lesson of the Day – The Motivation and Intuition Behind Chebyshev’s Inequality

Mathematical and Applied Statistics Lesson of the Day – The Motivation and Intuition Behind Chebyshev’s Inequality

In 2 recent Statistics Lessons of the Day, I introduced Markov’s inequality. explained the motivation and intuition behind Markov’s inequality. Chebyshev’s inequality is just a special version of Markov’s inequality; thus, their motivations and intuitions are similar. Markov’s inequality roughly says that a random variable is most frequently observed near its expected value, .  Remarkably, it quantifies just […]

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Mathematical Statistics Lesson of the Day – Chebyshev’s Inequality

Mathematical Statistics Lesson of the Day – Chebyshev’s Inequality

The variance of a random variable is just an expected value of a function of .  Specifically, . Let’s substitute into Markov’s inequality and see what happens.  For convenience and without loss of generality, I will replace the constant with another constant, . Now, let’s substitute with , where is the standard deviation of . […]

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Exercices de probabilités, et rappels de statistique

September 3, 2014
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Exercices de probabilités, et rappels de statistique

Vendredi, je commencerais les rappels de probabilités et statistiques. Le plan de cours est maintenant en ligne. J’ai ajouté quelques exercices de calcul de probabilités, histoire de s’entraîner. Un petit quizz sera organisé dans dix j...

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