Then Steve discussed some very influential mathematicians and probabilists who helped contributed to some important ideas in statistics such as 'The Rule of Three'. A brief summary would be if the following relationships holds

\[ \frac{A}{B} = \frac{C}{D} \]

and you know any of the three out of the four (A, B, C, D), then you can easily solve for the fourth. In 1855, Charles Darwin is even quoted saying, "I have no faith in anything short of actual measurement and the Rule of Three". Karl Pearson suggested this be the motto of the journal

*Biometrika*. For a full description of the story, see the publication Stigler (2012) in

*Biometrika*.

Interestingly, Francis Galton made the discovery that if data were perfectly correlated then the Rule of Three is true. When data is not perfectly correlated, then the idea of a conditional distribution must be introduced. The example that led to this discovery was an anthropologist was studying skeletons in a grave site. He let $T$ = length of a man's thigh bone and $H$ = man's height. After measuring several complete skeletons, he averaged $m_T$ = mean of thigh bones and $m_H$ = mean of heights. Then anthropologist wanted to infer heights from thigh bone lengths. He made the assumption that

\[ \frac{m_T}{m_H} = \frac{T}{H} \]

What Galton discovered is that if the data were perfectly correlated, then this formula would work. Because this assumption did not hold, Galton stumbled on to what we now call correlation. This led to the idea of expectations of conditional distributions, and hence the regression line! Very interesting story.

Steve ended his talk with some encouraging words about the Statistics Department at Rice. He showed this picture which was taken at Rice when Emile Borel visited.

The night ended with a nice dinner in Duncan Hall hall with pictures, awards and a lovely cake.

Congratulations to the Department of Statistics at Rice! I'm excited to see what the next 25 years has to hold.

Didn't Steve say that the Rule of Three was actually discovered by the number Two?

ReplyDeleteI miss big JT, yo.

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