Earlier this year I rekindled an interest in probability theory. In my classes, Bayes' theorem was little more than a footnote, and we drilled frequentist techniques. Browsing a few books led me to question this. In particular, though parts of Jaynes' "Probability Theory: The Logic of Science" sounded like a conspiracy theory at first, I was soon convinced that the author’s militant condemnation of frequentism was justified.
Today, I had the pleasure of reading a Nature article about a paper by Valen E. Johnson directly comparing Bayesian and frequentist methods in scientific publications, who suggests the latter is responsible for a plague of irreproducible findings. I felt vindicated; or rather, I felt I had several more decibels of evidence for the hypothesis that Bayesian methods produce far better results than frequentist methods when compared against the hypothesis that the two methods produce equivalent results!
This post explains it well. In short, frequentist methods have led to bad science.
An apologist might retort that it’s actually the fault of bad scientists, who are misusing the methods due to insufficient understanding of the theory. There may be some truth here, but I still argue that Bayesian probability should be taught instead. I need only look at my undergraduate probability and statistics textbook. On page 78, I see the 0.05 P-value convention castigated by Johnson, right after recipe-like instructions for computing a P-value. If other textbooks are similar, no wonder scientists are robotically misapplying frequentist procedures and generating garbage.
Johnson’s recommended fix of using 0.005 instead 0.05 is curious. I doubt it has firm theoretical grounding, but perhaps the nature of data that most scientists collect mean that this rule of thumb will usually work well enough. Though perhaps striving for the arbitrary 0.005 standard may require excessive data: a Bayesian method might yield similar results with less input. I guess it’s an expedient compromise. Those with poor understanding of statistical inference can still obtain decent results, at the cost of gathering more data than necessary.
The above post also mentions a paper describing how even a correctly applied frequentist technique leads to radically different inferences from a Bayesian one. The intriguing discussion within is beyond me, but I’m betting Bayesian is better; or rather, the prior I’d assign to the probability that Bayesian inference will one day shown to be better is extremly close to one!