Overall, it's an interesting book which I regard as basically correct and a fruitful approach for future research, and Richard Carrier is a good guy whose work should be supported.
On the other hand, so far it's not quite as awesome as I was hoping it'd be when I was writing http://www.gwern.net/Death%20Note%20script recently - I think lukeprog was right in this review that Carrier does his case a disservice by trying to expound Bayesian ideas in a New Testament context where, half the point of Bayesian ideas is to point out how useless the evidence is! That's... not a good way to either demonstrate Bayes is good in history nor to convince people of his overarching claims like 'all correct historical inference is Bayesian inference'.
The way to introduce a new paradigm is to start with its successes, where Bayesian methods led to a correct prediction or retrodiction of an issue where decisive evidence surfaced while before the issue was settled, conventional methods were confused, wrong, or underconfident; and then argue that its practical success combined with your philosophical arguments about Bayesian reasoning being the only correct reasoning is a convincing synthesis, maybe then work out verdicts/predictions/retrodictions on a non-controversial area so the experts can see how they like the conclusions, and only then extend it to highly controversial and difficult (scarce or low-quality evidence) material.
I understand how he would come to write it that way since that's what he was paid to do and Biblical material has become his specialty but I can still regret that the outcome wasn't as good as it could've been.
(Copied over my review from GoodReads.)
I recently received an advance review copy of historian and philosopher Richard Carrier's new book, Proving History: Bayes' Theorem and the Quest for the Historical Jesus.
The book belongs to a two-volume work on the Historical Jesus that argues for two major claims:
Claim #1 might provoke a yawning "Yes, of course..." from many scientists and philosophers, but both claims are currently heretical in the field of Jesus Studies, which shows many signs of being an unsound research program in general. The book is written for a mass audience, but is also aimed at historians in general. It is, as far as I know, the first book to lay out the detailed case for why historians should be using Bayesian methods. (For an overview of the other methods historians typically use, see Justifying Historical Descriptions.)
Though the Bayesian revolution of the sciences has already slammed into archaeology and a few other fields of historical inquiry, it has not yet overwhelmed mainstream historical inquiry. Carrier's book may be seen as the first salvo in that attack, but this makes me wish his case had not been presented in the context of such a parochial and disreputable sub-field of history as Jesus Studies. No chapter in the book discusses the evidence concerning the historicity of Jesus in much detail, and it clearly isn't necessary to make Carrier's points, so why poison the presentation of such a clear and powerful case (in favor of Bayesian historical methods) by marinating it in such a disreputable field (Jesus Studies), and with anticipation of a startling conclusion almost everyone disagrees with (Jesus myth theory)? (For the record, I take Jesus myth theory pretty seriously, but most people don't.)
Chapter 3 is a tutorial on Bayes' Theorem, similar to Carrier's Skepticon IV talk. Chapter 4 provides an analysis of non-Bayesian methods of historical analysis, showing that they are wrong in exactly the degree to which they depart from the Bayesian method. Chapter 5 provides a similar analysis of typical "Historicity Criteria" used in Jesus Studies, e.g. "multiple attestation." The final chapter tackles some more detailed issues with the application of Bayes' Theorem, for example the interaction between frequentism and Bayesianism.
At first, the contents of Proving History seemed too obvious and underwhelming for me to strongly recommend it. Then I remembered that no other book I've read on historical methodology or the Historical Jesus had correctly used probability theory to justify its judgments. Which means that Proving History may actually be the best book yet written in either field.