Thanks for the link to this article. I do not agree with the assertion that "But the Bayesian approach is much less helpful when there is no consensus about what the prior probabilities should be." especially as the authors of the article use this assertion to claim that in such circumstances Fisher's approach works best. For a start in order to use Fisher's approach there are not only already numerous prior assumptions but you also need plenty of data. If you do not have plenty of data then those committed to Fisher have to effectively 'give up' whereas a Bayesian approach at least enables us to draw some conclusions with minimal data. The fact that different experts have different priors is not a problem because you can use Bayes to show the conclsuons that can be drawn from the different expert priors - in fact this is an approach we have recommended in the legal context where it is usually impossible to get agreement on the priors (most lawyers atually hate the idea of even thinking about priors). For example, in a medical negligence case we were involved in and described here (and mentioned in Chapter 13 of the book):
we had to use various fragmented data to determine which of two medical pathways was most risky (in terms of probability of death/permanent damage). The conclusions depended on the accuracy of the different medical tests that were used in the different pathways. The experts for the claimant and the experts for the defence had very different priors for the accuracy of the relevant tests. So what we did was run a Bayesian network based analysis in which we first used the claimant priors and then used the defence priors. It turned out that in BOTH cases the results decisively pointed to the same pathway being more risky than the other.
Thank you so much for your response. As an aside, I have been enjoying reading your book. It is well written, and you have made a topic that could be dreary very enjoyable. It is actually my current "leisure" reading book, fitting it in between work and other obligations.