First the conclusion: this is a well researched and important book. My rating is a strong buy, and Bernoulli’s Fallacy is already influencing how I approach my work.
My initial “judge the book by its back cover” impression of Bernoulli’s Fallacy was negative. The back cover writes some very large checks that I was initially (and wrongly) doubtful that “its fists could cash.” The thesis is that frequentist statistics (the dominant statistical practice) is far worse than is publicly admitted, and that Bayesian methods are the fix. However, other reviews and the snippets by people I respect (such as Andrew Gelman and Persi Diaconis) convinced me to buy and read the book. And I am glad that I read it. The back cover was, in my revised opinion, fully justified.
Read on for John’s full review of a book that is quite critical of frequentist statistics in favor of Bayesian statistics—so that already makes the book a winner for me.