Really good. Bayesian reasoning isn’t as complicated as it sounds—it’s an approach, not a standardized equation. It is a way of calculating the odds of something happening when you don’t know much about it, and learning as you go.
Bayes himself, part of the 18th century Scottish Enlightenment, used the example of dropping a ball on a random spot on a flat table, and finding out blind where it is. Have a friend drop other balls at random and report whether they are to the left or right of the original ball. With each drop, you learn more and can use that to better suss out where the original ball is. For example, if every dropped ball is to the original’s left, then you know it is somewhere on the far right of the table.
This way of thinking turns out to have many applications, from population censuses to deciphering codes to finding lost airplanes and submarines, to making more accurate cancer diagnoses, to the autocorrect in your smartphone, to Google’s language translators and targeted advertisements.
It also has enormous implications for certainty in quantitative reasoning—it is often more useful to have an approximate answer to the right question than a precise answer to the wrong question. But this lack of pure certainty has led many quantitative analysts to reject Bayesian reasoning, to the point where his name has until recently been almost unmentionable in polite circles. This mindset is similar to the Nirvana Fallacy in economics.
Besides putting this old boys’ club mentality its proper place, McGrayne tells the stories of Bayes and Simon LaPlace, the French Enlightenment mathematician who independently discovered Bayesian reasoning and probably deserves most of the credit.
She also introduces and humanizes many of the other major and minor personalities involved in Bayesian reasoning’s long and treacherous history, from Alan Turing, who cracked the Enigma code during World War II, to some of the more tradition-minded scientists who preferred precision at accuracy’s expense.
But she keeps in mind that Bayesianism is one useful tool among many in the scientist’s toolkit. Bayesianism is not gospel, and there is a need for human judgment too, a point Stephen Ziliak and Deirdre McCloskey make in their book The Cult of Statistical Significance.