Shownotes Transcript
After Laplace
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After Laplace
Before Bayes’ resurgence, the “central limit theorem” stole the show, and authorities started collecting data on everything, the opinion that probability could be subjective sounded specious and non-rigorous. John Stuart Mill argued that probability was ignorance, coined into science.
However, some scientists still used it. Once such person was Joseph Louis François Bertrand (1822–1900), a French mathematician with contributions to many scientific fields, from economics to thermodynamics. Bertrand devised a method, based on Bayes, for artillery firings. The method dealt with uncertainties, such as the wind, or the enemy’s position, in order to optimize the firings.
The French polymath Henri Poincaré (1854–1912) intervened in the famous Dreyfus Affair, proffering Bayes’ theorem in court as evidence that Lieutenant Alfred Dreyfus wasn’t a traitor. It was one of the most famous trials in modern French history and Bayes’ theorem saved Dreyfus from life imprisonment in what was then French Guinea. Bayes’ theorem is arguably the only sensible way to treat evidence in court, and Poincaré recognized this, in spite of him being a frequentist.
It is deeply unfortunate that a court in England in 2011 ruled that Bayes’ theorem can no longer be used in trials. [3] It might seem odd for a mathematical theory (or lack thereof) to have such a bearing on—for example—cases of first-degree murder. But that’s exactly what happened to Sally Clark in 1999, when she was wrongfully convicted of smothering her two infant sons; the jurors and judges erroneously rested their decision on the statistical unlikelihood of two siblings dying of cot death. In fact, it was far more statistically rare for a mother to willfully kill both her children, and Clark’s sentence was overturned and she was finally freed in 2003. It might sometimes be difficult to grasp the intuition behind it, but Bayes theorem is very powerful.