The use of Bayesian probabilities as the basis of Bayesian inference has been supported by several arguments, such as Cox axioms, the Dutch book argument, arguments based on decision theory and de Finetti's theorem.
A decision-theoretic justification of the use of Bayesian inference (and hence of Bayesian probabilities) was given by Abraham Wald, who proved that every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures.[26] Conversely, every Bayesian procedure is admissible.[27]
Wikipedia: Bayesian Probability – Justification of Bayesian Probabilities
What's the best book on the decision-theoretic justification of bayesian probability? I found a few books on the topic:
- The Bayesian choice – Christian P Robert
- Bayesian Theory – Adrian Smith and José-Miguel Bernardo
- Statistical Decision Theory and Bayesian Analysis – Jim Berger
Which one of these books is the best and most relevant to the topic? Are there any other books that are better than these?
Best Answer
I know the third you mentioned and it is a good textbook, even if my favourite is Box Tiao