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The Misconception Posterior Bayes factors are a good idea: they provide a measure of evidence but are relatively unaffected by the shape of the prior distribution. The Correction Posterior Bayes factors use the data twice, effectively biasing the outcome in favor of the more complex model. The Explanation The standard Bayes factor is the ratio of predictive performance between two…

Summary Einstein confused his students with a riddle about probability – or was it Einstein himself who was confused? Albert Einstein disliked the idea that the laws of nature were inherently probabilistic. ‘God does not play dice with the universe,’ he stated famously and repeatedly. Yet, physicists like Niels Bohr strongly advocated the idea –based on the ‘Copenhagen interpretation’ of…

Cicero eloquently summarized the philosophical position that the universe is deterministic – all events are preordained, either by nature or by divinity. Although “ignorance of causes” may create the illusion of Fortune, in reality there is only Necessity. Cicero Citatus, Glans Inflatus? The male academic who cites Cicero generally lacks the insight that, instead of imbuing his writing with gravitas,…

Summary: When Bayesians speak of probability, they mean plausibility. The famous Matrix trilogy is set in a dystopic future where most of mankind has been enslaved by a computer network, and the few rebels that remain find themselves on the brink of extinction. Just when the situation seems beyond salvation, a messiah –called Neo– is awakened and proceeds to free…

This post is based on the example discussed in Wagenmakers et al. (in press). The Misconception Bayes factors are a measure of absolute goodness-of-fit or absolute pre- dictive performance. The Correction Bayes factors are a measure of relative goodness-of-fit or relative predictive performance. Model A may outpredict model B by a large margin, but this does not imply that model…

This post is inspired by Morey et al. (2016), Rouder and Morey (in press), and Wagenmakers et al. (2016a). The Misconception Bayes factors may be relevant for model selection, but are irrelevant for parameter estimation. The Correction For a continuous parameter, Bayesian estimation involves the computation of an infinite number of Bayes factors against a continuous range of different point-null…

“By seeking and blundering we learn.” – Johann Wolfgang von Goethe Bayesian methods have never been more popular than they are today. In the field of statistics, Bayesian procedures are mainstream, and have been so for at least two decades. Applied fields such as psychology, medicine, economy, and biology are slow to catch up, but in general researchers now view…