As regular readers of this blog already know, Bayes factors rule! In practice, however, the calculation of Bayes factors is seriously hampered by computational difficulties. In a new paper, we revive two theorems put forth by Alan Turing and Jack Good and propose a step-by-step approach to use them as a check for the calculation of Bayes factors. According to Good, the first theorem was proposed by Turing during their work on deciphering German naval Enigma messages during World War II (for the movie lovers among you, The Imitation Game is a great way to learn how mathematics (and Bayes theore ..read more

I am thrilled to report that, after considerable discussion, the University of Amsterdam has agreed to ban the teaching of p-values for first-year students at the Faculty of Social and Behavioural Sciences. The new policy will take effect at the start of the new academic year, and its introduction was facilitated by the fact that I am taking over from Ingmar Visser as Director of Teaching at the Psychology Department starting September 1st 2024. I have discussed the drawbacks of p-values many times in this blog. For students, the main problem with the p-value is that it is a difficult measure ..read more

Inspired by a recent article on Ockham’s razor, this post shows how a simple set of polyhedral dice can clarify the basic idea underlying Bayes factors (or likelihood ratios).  The ideas may be used in a classroom demonstration, and each of the lessons below could be discovered by the students themselves. Meet the Family Our polyhedral dice are a family of four. Below you see the D3, the D6 (this is the common six-sided die), the D12, and the D60.   The Setup You may assume each die is fair. I will first toss the D3 in order to select either the D6, the D12, or the D60. (if th ..read more

Klaas Sijtsma is an experienced psychometrician and former rector magnificus of Tilburg University. In “Never waste a good crisis”, Sijtsma discusses academic fraud (and in particular the infamous Stapel case, the fallout of which he had to deal with as dean of the School of Social and Behavioral Sciences at Tilburg University) and questionable research practices (henceforth QRPs). Importantly, Sijtsma also offer some refreshingly direct suggestions on how the reliability of psychological science may be improved. Solicit Statistical Advice! Before outlining the contents of the book, I would li ..read more

In the previous post I asked the following question: Here is a test of your Bayesian intuition: Suppose you assign a binomial chance parameter θ a beta(2,2) prior distribution. You anticipate collecting two observations. What is your expected posterior distribution? NB. ChatGPT 3.5, Bard, and the majority of my fellow Bayesians get this wrong. The answer will be revealed in the next post. The incorrect answer often goes a little something like this: under a beta(2,2) prior for θ, the expected number of successes equals 1 (and hence the expected number of failures also equals 1). Hence, the e ..read more

Since 2017, Dora Matzke and I have been teaching the master course “Bayesian Inference for Psychological Science”. Over the years, the syllabus for this course matured into a book (and an accompanying book of answers) titled “Bayesian inference from the ground up: The theory of common sense”. The current plan is to finish the book in the next few months, and share the pdf publicly online. For now, you can click here or on the cover page below to read the first 320 pages [67 MB!]. Today we are adding three chapters: “Haldane’s Rule of Succession” (with Sandy Zabell and Quentin Gronau), “Jeffrey ..read more

Dear František Bartoš: I’m Xu Rui, an employee of Zhejiang Science and Technology Museum, which is located in Hangzhou, Zhejiang province, China, a city not far from Shanghai. I’m writing this letter to sincerely invite you to attend the 12th “Pineapple Science Award”. We find your research <Fair coins tend to land on the same side they started: Evidence from 350,757 flips> very interesting. We hope you can accept the award in the math category. This was the start of an email that reached us on November 1st. One week later I was on a plane to Whenzou, China. The research that Rui refer ..read more

In my research master course “Bayesian Inference for Psychological Science” (co-taught with Dora Matzke), students are asked to specify a beta distribution on the probability θ that I will bake a bacon pancake rather than a standard “vanilla” pancake. So θ is my “bacon proclivity” that students are unsure about. The chapter “The pancake puzzle” from our free course book discusses the results from four pancake forecasters: Tabea, Sandra, Elise, and Vukasin. The chapter first presents their individual beta prior distributions, and then, after observing 3 bacon pancakes and 5 vanilla pancakes, it ..read more

Since 2017, Dora Matzke and I have been teaching the master course “Bayesian Inference for Psychological Science”. Over the years, the syllabus for this course matured into a book (and an accompanying book of answers) titled “Bayesian inference from the ground up: The theory of common sense”. The current plan is to finish the book in the next few months, and share the pdf publicly online. For now, you can click here or on the cover page below to read the first 271 pages [62 MB!]. Today we are adding two chapters: “A Crack in the Laplacean Edifice”, and “Wrinch and Jeffreys to the Rescue”. Thes ..read more

Today I came across the recently published article “A model-independent redundancy measure for human versus ChatGPT authorship discrimination using a Bayesian probabilistic approach” by Bozza and colleagues. As the title suggests, Bozza et al. use Bayes factors to quantify the evidence for texts being generated by humans versus ChatGPT. This seems exactly the right approach, and I am generally a fan of the authors’ Bayesian work in forensics. And the paper itself presents some promising results! However, browsing the paper left me with three gripes.  My first gripe is that the author ..read more