: As well as antibiotic prophylaxis being a generally effective intervention for preventing postoperative wound infection, the level of this effectiveness would appear to be reasonably independent of what type of surgery is being considered. Therefore, the general prevailing attitude that antibiotic prophylaxis should be assumed to be ineffective unless its effectiveness has been experimentally proven beyond doubt for the specific type of surgery being considered, perhaps should be revised. In particular, perhaps a sensible philosophy would be to assume that antibiotic prophylaxis is effective in reducing the risk of wound infection for all types of surgery, even ones where no clinical trial data exists and make exceptions to this rule if, for certain types of surgery, it can be proved to the contrary.

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The aim of this paper is to firmly establish subjective fiducial inference as a rival to the more conventional schools of statistical inference, and to show that Fisher's intuition concerning the importance of the fiducial argument was correct. In this regard, a methodology outlined in an earlier paper is modified, enhanced and extended to deal with general inferential problems in which various parameters are unknown. As part of this, an analytical method or the Gibbs sampler is used to construct the joint fiducial distribution of all the parameters of the model concerned on the basis of first determining the full conditional fiducial distributions for these parameters. Although the resulting theory is classified as being 'subjective', it is maintained that this is simply due to the argument that all probability statements made about fixed but unknown parameters must be inherently subjective. In particular, a systematic framework is used to reason that, in general, there is no need to place a great emphasis on the difference between the fiducial probabilities that can be derived using this theory and objective probabilities. Some important examples of the application of this theory are presented.

This paper is motivated by the questions of how to give the concept of probability an adequate real-world meaning, and how to explain a certain type of phenomenon that can be found, for instance, in Ellsberg's paradox. It attempts to answer these questions by constructing an alternative theory to one that was proposed in earlier papers on the basis of various important criticisms that were raised against this earlier theory. The conceptual principles of the corresponding definition of probability are laid out and explained in detail. In particular, what is required to fully specify a probability distribution under this definition is not just the distribution function of the variable concerned, but also an assessment of the internal and/or the external strength of this function relative to other distribution functions of interest. This way of defining probability is applied to various examples and problems including, perhaps most notably, to a long-running controversy concerning the distinction between Bayesian and fiducial inference. The characteristics of this definition of probability are carefully evaluated in terms of the issues that it sets out to address.

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