In his highly influential book ‘Wonderful Life’, Harvard paleontologist Stephen Jay Gould proposed that evolution is an unpredictable process that can be characterized as “a staggeringly improbable series of events, sensible enough in retrospect and subject to rigorous explanation, but utterly unpredictable and quite unrepeatable. Wind back the tape of life to the early days of the Burgess Shale; let…

With apologies to Bertrand Russell. John Tukey famously stated that the collective noun for a group of statisticians is a quarrel, and I. J. Good argued that there are at least 46,656 qualitatively different interpretations of Bayesian inference (Good, 1971). With so much Bayesian quarrelling, outsiders may falsely conclude that the field is in disarray. In order to provide a…

Tl;dr In 1847, Augustus De Morgan suggested that researchers could avoid overselling their work if, every time they made a key claim, they reminded the reader (and themselves) of how confident they were in making that claim. In 1971, Eric Minturn went further and proposed that such confidence could be expressed as a wager, with beneficial side-effects: “Replication would be…

“Anything is fair in love and war” — this saying also applies to the eternal struggle between frequentists (those who draw conclusions based on the performance of their procedures in repeated use) and Bayesians (those who quantify uncertainty for the case at hand). One argument that frequentists have hurled at the Bayesian camp is that “Bayesian procedures do not control…

Over the past year or so I’ve been working on a book provisionally titled “Bayesian bedtime stories”. Below is a part of the preface. This post continues the cooking analogy from the previous post. Like cooking, reasoning under uncertainty is not always easy, particularly when the ingredients leave something to be desired. But unlike cooking, reasoning under uncertainty can be…

Over the past year or so I’ve been working on a book provisionally titled “Bayesian bedtime stories”. Below is a part of the preface. The next post continues the cooking analogy by introducing the frequentist chef. Even though the book [Bayesian Bedtime Stories] addresses a large variety of questions, the method of reasoning is always based on the same principle:…

if there could be any mortal who could observe with his mind the interconnection of all causes, nothing indeed would escape him. For he who knows the causes of things that are to be necessarily knows all the things that are going to be. (…) For the things which are going to be do not come into existence suddenly, but…