Conclusions

• To undertake Bayesian statistical inference, a subjective choice, of beliefs held, before any empirical evidence is examined, must be made, and encoded in a prior probability distribution; this insight is not original to this paper.
• Where a non-Bayesian (or an apparently Bayesian) inference method is claimed to have achieved objectivity, by avoiding any explicit, subjective statement of beliefs held before any empirical evidence is examined, Bayes' theorem can often be used to show that the non-Bayesian method is equivalent to Bayesian inference, with some particular prior probability distribution; the effect of not stating this subjective choice explicitly is to conceal it and to render it immutable, not to eliminate the subjectivity; this insight is not original to this paper.
• To obtain a function for measuring scientific uncertainty and choosing experiments, in Bayesian statistical decision theory, from equation 27, a subjective choice of the outcomes, from policy decisions, which are desirable must be made, and encoded in a loss function; this insight is not original to this paper.
• Where an apparently Bayesian experiment selection method, based on judging the quality of an experiment, by the reduction, which the experiment is expected to produce, in an uncertainty function of the posterior probability distribution, as compared with the same uncertainty function of the prior probability distribution, is claimed to have achieved objectivity, by avoiding any explicit statement of the outcomes, from policy decisions, which are desirable, equation 27 can be used to show that the method is, nevertheless, implicitly associated with such a choice of desirable policy outcomes; this insight is not original to this paper.
• The above features of Bayesian statistics, and Bayesian critiques of non-Bayesian (and some apparently Bayesian) methods, are closely analogous to features of the tradition in social science methodology, known as standpoint epistemology, and to standpoint epistemologists' critiques of certain kinds of positivism; this insight is original to this paper.
• It is, therefore, conjectured that, in many important aspects, standpoint epistemology is an expression in natural-language terms of ideas that Bayesian statistics expresses in algebra; this insight is original to this paper.
• It has been shown, using a toy experiment selection problem, that the subjective choice of prior probability distribution can have a dramatic, non-linear influence on the posterior probability distribution: initial, moderately strong belief in a theory, which makes the experiments that tend to confirm that theory appear to be the most interesting experiments to undertake, leads to the undertaking of those experiments, which leads to ever stronger belief in the theory, even though the theory does not, for experiments in general, correspond more closely to reality than another available theory, belief in which is initially slightly weaker; the quantitative demonstration of this effect, using Bayesian statistics, is original to this paper, although the possibility of theories strengthening belief in themselves in a similar way was raised by Kuhn [40].