Response by Thomas J. Loredo
The choice of alternatives relevant for inference, and not the use of priors, is the fundamental distinguishing feature of Bayesian inference. Nevertheless, priors play an important role in inference, and I welcome Prof. West’s discussion of their influence on Bayesian results. Much can be said about this issue. Here I will only note that my paper discusses parameter estimation calculations, which are often very insensitive to prior information, whereas West discusses a model comparison calculation (deciding between models with and without the parameter s) which is more sensitive; in fact, such calculations use information about the prior range of parameters to implement an objective posterior, “Ockham’s razor,” for which there is only a meager and subjective frequentist counterpart (see, e.g., W.H. Jefferys and J.O. Berger, American Scientist 80. 64–72, 1992). A more extensive discussion of priors and of many of the examples in my paper can be found in the original longer draft, which I will gladly provide to interested readers.