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Oversells Bayes and Undersells frequentism
First off, the writing is excellent and despite my low overall rating, I do recommend this book overall for increasing thinking about probability, statistics, philosophy, and science.
How does the author oversell Bayes?
The book simply doesn't mention any problems with priors, false confidence, brittle priors, pretends questionable research practices only occur in frequentism, assumes Bayesian P(H) is the same as P(H|beliefs) or Belief(H), assumes that just because one can assign or compute P(H) that therefore H is well-tested, portrays Bayes Theorem as inherently "Bayesian" when it is in fact fully in the frequentist statistics domain, didn't mention Cox theorems had a counterexample that needed to be patched up, and presents Jaynes as a major figure in probability/statistics.
How does the author undersell frequentism?
The book omits reams of positive uses of frequentism in science, omits many important frequentist contributions (equivalence testing, confidence distributions, severity, sequential analysis, jackknife, bootstrap, survey sampling, quality control, meta analysis, permutation tests, adaptive tests, nonparametric statistics, machine learning, tests for nonrandomness, MCMC (which makes Bayesian estimation work), and model checking), and dismisses flexibility in solving problems as "ad hoc". The book also omits ASA's newly updated guidance on p-values, which is pro-p-values, although that omission is not a fault of the author.
Variations of the phrase "what we really want is P(H|D)" is something you'll read a lot in this book. This "what we really want to know (or say), is X" has been called "The Statistician's Fallacy" by Lakens. This is where a statistician is saying what all researchers supposedly want to know, and not coincidentally the answer, X, is aligned 100% with the statistician's philosophy of statistics and science.
One could of course argue the other way, that we never can know P(H), so what we really want is to know the distance what we observe is away from what we expect under a model, or that Bayesians really want to say that their procedures have good long-term performance, good coverage, be free from as much subjectivity as possible, or not be confined to having to try and solve all problems using the same tool.
August 2021 · Books · verified purchase