Posts Tagged ‘ Probability and Statistics ’

Quantile-quantile plots and powers of 3/2

April 2, 2017
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Quantile-quantile plots and powers of 3/2

This post serves two purposes. It will empirically explore a question in number theory and demonstrate quantile-quantile (q-q) plots. It will shed light on a question raised in the previous post. And if you’re not familiar with q-q plots, it will serve as an introduction to such plots. The previous post said that for almost all x > […]

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Freudian hypothesis testing

March 23, 2017
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Freudian hypothesis testing

In his paper Mindless statistics, Gerd Gigerenzer uses a Freudian analogy to describe the mental conflict researchers experience over statistical hypothesis testing. He says that the “statistical ritual” of NHST (null hypothesis significance testing) “is a form of conflict resolution, like compulsive hand washing.” In Gigerenzer’s analogy, the id represents Bayesian analysis. Deep down, a […]

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Big data and the law

February 2, 2017
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Big data and the law

Excerpt from the new book Big Data of Complex Networks: Big Data and data protection law provide for a number of mutual conflicts: from the perspective of Big Data analytics, a strict application of data protection law as we know it today would set an immediate end to most Big Data applications. From the perspective of […]

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Subjectivity in statistics

December 15, 2016
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Andrew Gelman on subjectivity in statistics: Bayesian methods are often characterized as “subjective” because the user must choose a prior distribution, that is, a mathematical expression of prior information. The prior distribution requires information and user input, that’s for sure, but I don’t see this as being any more “subjective” than other aspects of a […]

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Interim analysis, futility monitoring, and predictive probability

October 19, 2016
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Interim analysis, futility monitoring, and predictive probability

An interim analysis of a clinical trial is an unusual analysis. At the end of the trial you want to estimate how well some treatment X works. For example, you want to how likely is it that treatment X works better than the control treatment Y. But in the middle of the trial you want to know something more subtle. It’s […]

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Uncertainty in a probability

September 20, 2016
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Uncertainty in a probability

Suppose you did a pilot study with 10 subjects and found a treatment was effective in 7 out of the 10 subjects. With no more information than this, what would you estimate the probability to be that the treatment is effective in the next subject? Easy: 0.7. Now what would you estimate the probability to be […]

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Insufficient statistics

September 12, 2016
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Experience with the normal distribution makes people think all distributions have (useful) sufficient statistics [1]. If you have data from a normal distribution, then the sufficient statistics are the sample mean and sample variance. These statistics are “sufficient” in that the entire data set isn’t any more informative than those two statistics. They effectively condense […]

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Mittag-Leffler function and probability distribution

July 17, 2016
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Mittag-Leffler function and probability distribution

The Mittag-Leffler function is a generalization of the exponential function. Since k!= Γ(k + 1), we can write the exponential function’s power series as and we can generalize this to the Mittag=Leffler function which reduces to the exponential function when α = β = 1. There are a few other values of α and β for […]

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Continuum between anecdote and data

March 4, 2016
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Continuum between anecdote and data

The difference between anecdotal evidence and data is overstated. People often have in mind this dividing line where observations on one side are worthless and observations on the other side are trustworthy. But there’s no such dividing line. Observations are data, but some observations are more valuable than others, and there’s a continuum of value. I believe […]

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The empty middle: why no one is average

February 20, 2016
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The empty middle: why no one is average

In 1945, a Cleveland newspaper held a contest to find the woman whose measurements were closest to average. This average was based on a study of 15,000 women by Dr. Robert Dickinson and embodied in a statue called Norma by Abram Belskie. Out of 3,864 contestants, no one was average on all nine factors, and fewer than 40 […]

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