“Bayesian reasoning in science”

That is the title of this commentary by Colin Howson and Peter Urbach published in the journal Nature on 4 April 1991. (Howson and Urbach also published a book with the title “Scientific Reasoning: The Bayesian Approach”; see the image of their book cover below.) Their dense 1991 paper offers a concise overview of Bayesian methods, provides a powerful critique of alternative statistical methods, and has shaped our work as well (in which we apply Bayesian methods to litigation). We shall thus review the main points and insights of “Bayesian reasoning in science” in this and the next few blog posts.

Let’s begin at the beginning, shall we? Howson and Urbach start out by acknowledging that “ours is uncertain world” and by noting how gamblers use odds to measure numerically the likely outcomes of future events. (This method of expressing probabilities is especially common in sports betting. For example, prior to the running of this year’s Kentucky Derby, the odds that California Chrome would win the race were 5 to 2, meaning that a \$2 wager on this horse finishing in first place would pay out a total of \$7 in winnings–i.e. a profit of \$5, plus the bettor’s original \$2 wager.) The authors also identify a major problem with this familiar system of gambling odds: “Because odds are ratios the odds scale starts at 0 and is unbounded to the right (infinite odds).” The solution to this problem is to transform the odds scale into a finite probability scale (ranging from 0 to 1) by restating the probability of an event p using the formula p = odds divided by 1 + odds. In other words, we want to express probabilities using a uniform and finite space (i.e. from 0 to 1) in order to make probability problems tractable and easier to solve. “Stay tuned” … for we shall review the remaining parts of this important paper over the next few days.