# Posts Tagged ‘ mathematics ’

## Sequential Analysis

December 11, 2015
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We here at Win-Vector LLC been working through an ad-hoc series about A/B testing combining elements of both operations research and statistical points of view. A dynamic programming solution to A/B test design Why does designing a simple A/B test seem so complicated? A clear picture of power and significance in A/B tests Bandit Formulations … Continue reading Sequential Analysis

## 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 […]

## 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 […]

## Mathematical Statistics Lesson of the Day – Basu’s Theorem

$Mathematical Statistics Lesson of the Day – Basu’s Theorem$

Today’s Statistics Lesson of the Day will discuss Basu’s theorem, which connects the previously discussed concepts of minimally sufficient statistics, complete statistics and ancillary statistics.  As before, I will begin with the following set-up. Suppose that you collected data in order to estimate a parameter .  Let be the probability density function (PDF) or probability […]

## Mathematical Statistics Lesson of the Day – Basu’s Theorem

$Mathematical Statistics Lesson of the Day – Basu’s Theorem$

Today’s Statistics Lesson of the Day will discuss Basu’s theorem, which connects the previously discussed concepts of minimally sufficient statistics, complete statistics and ancillary statistics.  As before, I will begin with the following set-up. Suppose that you collected data in order to estimate a parameter .  Let be the probability density function (PDF) or probability […]

## A dynamic programming solution to A/B test design

July 6, 2015
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Our last article on A/B testing described the scope of the realistic circumstances of A/B testing in practice and gave links to different standard solutions. In this article we will be take an idealized specific situation allowing us to show a particularly beautiful solution to one very special type of A/B test. For this article … Continue reading A dynamic programming solution to A/B test design →

## Mathematical Statistics Lesson of the Day – An Example of An Ancillary Statistic

$Mathematical Statistics Lesson of the Day – An Example of An Ancillary Statistic$

Consider 2 random variables, and , from the normal distribution , where is unknown.  Then the statistic has the distribution . The distribution of does not depend on , so is an ancillary statistic for . Note that, if is unknown, then is not ancillary for .Filed under: Mathematical Statistics, Statistics, Statistics Lesson of the […]

## Mathematical Statistics Lesson of the Day – An Example of An Ancillary Statistic

$Mathematical Statistics Lesson of the Day – An Example of An Ancillary Statistic$

Consider 2 random variables, and , from the normal distribution , where is unknown.  Then the statistic has the distribution . The distribution of does not depend on , so is an ancillary statistic for . Note that, if is unknown, then is not ancillary for .Filed under: Mathematical Statistics, Statistics, Statistics Lesson of the […]

## Mathematics and Applied Statistics Lesson of the Day – Contrasts

$Mathematics and Applied Statistics Lesson of the Day – Contrasts$

A contrast is a linear combination of a set of variables such that the sum of the coefficients is equal to zero.  Notationally, consider a set of variables . Then the linear combination is a contrast if . There is a reason for why I chose to use as the symbol for the variables in […]

## Mathematics and Applied Statistics Lesson of the Day – Contrasts

$Mathematics and Applied Statistics Lesson of the Day – Contrasts$

A contrast is a linear combination of a set of variables such that the sum of the coefficients is equal to zero.  Notationally, consider a set of variables . Then the linear combination is a contrast if . There is a reason for why I chose to use as the symbol for the variables in […]