Subjectivity and Scientific Judgment
Claims of the subjectivity of Bayesian inference have been much debated, and I am under no illusion that I can resolve them here. But I will repeat my point made at the outset of this discussion that Bayesian probability, like frequentist probability, is except in the simplest of examples a model-based activity that is mathematically anchored by physical randomization at one end and calibration to a reference set at the other. I will also repeat the familiar, but true, argument that most of the power of a Bayesian inference typically comes from the likelihood, not the prior, and a person who is really worried about subjective model-building might profitably spend more effort thinking about assumptions inherent in additive models, logistic regressions, proportional hazards models, and the like. Even the Wilcoxon test is based on assumptions! To put it another way, I will accept the idea of subjective Bayesianism when this same subjectivity is acknowledged for other methods of inference. Until that point, I prefer to speak not of “subjectivity” but of “assumptions” and “scientific judgment. -- Bayesian Statistical Pragmatism, Andrew Gelman
