Keynote speakers in 2026: Dale Barr and Lisa DeBruine.

A common disease in academia is that for any position X there is an academic with an opposing position not-X. It's just how academics are. One can't just blindly follow one or another person's recommendation, but develop a good understanding of it oneself, and draw one's own conclusions.

I guess then we should also recommend against using p-values because they are sensitive to the likelihood function assumed? :) Who was it that gave this recommendation? I'm guessing SIngmann but maybe I'm wrong.

Because this is a frequently asked question in summer schools I teach, I am thinking about adding a video lecture on this in my online materials for the book. Do also read the online chapter from our book on this topic:

bruno.nicenboim.me/bayescogsci/...

Also:

Cumming, G. (2014). The new statistics: Why and how. Psychological science, 25(1), 7-29.

Kruschke, J. K. (2011). Bayesian assessment of null values via parameter estimation and model comparison. Perspectives on Psychological Science, 6(3), 299-312.

epub.ub.uni-muenchen.de/74222/

Some other books to read:

Royall, R. (2017). Statistical evidence: a likelihood paradigm. Routledge.

Spiegelhalter, D. (2024). The art of uncertainty: how to navigate chance, ignorance, risk and luck. Random House.

Spiegelhalter, D. J., Abrams, K. R., & Myles, J. P. (2004). Bayesian approaches to clinical trials and health-care evaluation. John Wiley & Sons.

You can use the credible interval to think about whether the pattern is consistent with the predicted effect. Even better if you can compare that interval to a model's a priori predicted interval. Read Spiegelhalter's 2004 book:

That's what the likelihood ratio test (aka anova) does, you compare likelihoods under the null and non-null to decide whether to reject the null. Bayes factors compare marginal likelihoods but the idea is the same. See our BF chapter.

E.g., if my data point is 0, the likelihood of mu being 0 (assuming sd=1) is dnorm(0,0,1). The lik. of mu being 10 is dnorm(0,10,1), which is much smaller than that of dnorm(0,0,1). So I'd favor mu=0 over mu=10. If the data point were 10, the lik. of mu=10 is much higher, and I would reject mu=0.

So with Bayes factors you'd compute the marginal likelihoods under the two models and compare them.

To make a discovery claim, I would have to set up two models, m0 where the effect is 0, and mfull, where it is not. Then I can talk about the relative evidence assuming a null or a non-null effect. 2/2

I would say that both credible intervals in my example are *consistent* with the effect being positive, but I would not go so far as to make a discovery claim. 1/2

Also see: pure.uva.nl/ws/files/636...

Just a quick question first: If the Bayesian 95% Credible interval is [0.0000001,100] you would reject the null, and if it is [-0.0000001,99], would you fail to reject or even accept the null?