This dense and meticulously reasoned argument explains why the author recommends that Bayes’ Theorem be the basic technique for the analysis of hypotheses in history, both for our general education and in preparation for his second volume, On the Historicity of Jesus. I’m no expert, and I mostly used Bayes’ Theorem for demonstrations of medical diagnostic problems about 30 years ago, and then gradually more and more as a replacement of more common frequentist type statistics in everyday work as it became easier to do with computer software and better understood. From my point of view, so distant from Professor Carrier, this method acts as a way to check and compare your data, your assumptions, and your hypotheses, but, frankly, it’s hard for me to imagine thinking this way ab initio. Perhaps it comes with practice. Also, I must admit that regardless of the statistical analysis used, many of the problems that I had or was consulted about in my career mostly benefited in a similar way, i.e. the statistics confirmed why the researchers were correct in their assumptions and hypotheses, either graphically or numerically, but weren’t really necessary for them to know this initially. The great value of these techniques was always in those uncommon cases where the findings could be shown to be counter-intuitive. The classic Bayesian example that most doctors have seen, but probably never really understand, is looking for a rare disease with a sensitive test. The great majority of positive tests are false positives. I think that all of these factors are evident in Carrier’s discussion. I especially liked the flowchart in the appendix that shows the non-numerical use of Bayes’ theorem for the analysis of historical hypotheses. ( )

The book Proving History: Bayes's Theorem and the Quest for the Historical Jesus gives an introduction to Bayesian statistical analysis and arguments for changing how historical truths are validated. Richard Carrier uses the book length exposition to argue that methods used to authenticate historical evidence should always contain Bayesian methods.
Carrier wants the reader to conclude by the end of the book that Bayesian approaches should always be used to resolve questions of historical accuracy for past events. Carrier has a steep hill to climb to prove his case. He has taken on in this book to explain Bayesian analysis to non-Bayesian scholars, to explain how Bayesian methods can effectively replace all other historical authenticity methods, why Bayesian approaches are the same as frequentist approaches and how Bayesian approaches are useful for addressing questions about biblical historical accuracy.
My view of the target audience for this book can be expressed in a form of interlocking Venn diagrams. It would contain people who have been exposed to college level statistics 101. The people should be interested in learning about Bayesian methods. They should be familiar with academic scholarship. They should be interested in learning about historical scholarship. They should have some exposure to Christian biblical information. And additionally they should be interested in assessments of Christian biblical evidence. My opinion is, that with the target action that matches the overlapped Venn diagrams, that Carrier does a fairly good job making his arguments. He adequately explains Bayes techniques for people comfortable with statistical ideas and conditional probability. He makes strong arguments for adopting his approach to historical research. I was not completely able to accept his complete argument on historical evidence. I intuitively felt he might be correct, but I was not able to follow his argument enough to be persuaded by the presentation. He uses the entire book to attack the credibility of evidence in the Bible. I agree with his arguments, but don’t think everyone would agree. So I think people who fit the target audience could enjoy the book, but I would not recommend the book for people outside of the target audience.
I would be more interested in a different goal for a future similar scholarly effort. I would like to see a Bayesian approach to why the history of Christianity led to the most successful mythic construct in human history. The value of statistical analysis is comparing human constructs and producing numerical results that represent how normal or unusual are event occurrences. A review of the statistical accuracy employed in the book is at: Review of Proving History