A friend from Elba surprised me by sending the interesting paper and discussion of Dennis Lindley (2000), “The Philosophy of Statistics,” which I hadn’t seen in years. She suggested, as especially apt, J. Nelder’s remarks; I recommend the full article and discussion:
(from) Comments by J. Nelder:
Recently (Nelder,1999) I have argued that statistics should be called statistical science, and that probability theory should be called statistical mathematics (not mathematical statistics). I think that Professor Lindley's paper should be called the philosophy of statistical mathematics, and within it there is little that I disagree with. However, my interest is in the philosophy of statistical science, which I regard as different. Statistical science is not just about the study of uncertainty but rather deals with inferences about scientific theories from uncertain data. An important quality about theories is that they are essentially open ended; at anytime someone may come along and produce a new theory outside the current set. This contrasts with probability where to calculate a specific probability it is necessary to have a bounded universe of possibilities over which the probabilities are defined. When there is intrinsic open-endedness it is not enough to have a residual class of all the theories that I have not thought of yet. The best that we can do is to express relative likelihoods of different parameter values, without any implication that one of them is true. Although Lindley stresses that probabilities are conditional I do not think that this copes with the open-endedness problem. I follow Fisher in distinguishing between inferences about specific events, such as that it will rain here tomorrow and inferences about theories. .…
