Subjective Bayesianism is a major school of uncertain reasoning and statistical inference. It is often criticized for a lack of objectivity: (i) it opens the door to the influence of values and biases, (ii) evidence judgments can vary substantially between scientists, (iii) it is not suited for informing policy decisions. My paper rebuts these concerns by connecting the debates on scientific objectivity and statistical method. First, I show that the above concerns arise equally for standard frequentist inference with null hypothesis significance tests (NHST). Second, the criticisms are based on specific senses of objectivity with unclear epistemic value. Third, I show that Subjective Bayesianism promotes other, epistemically relevant senses of scientific objectivity—most notably by increasing the transparency of scientific reasoning.
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This means that p(X) = 0 ⇔ q(X) = 0; a property known as absolute continuity of probability measures. Notably, the convergence is uniform, that it, it holds simultaneously for all elements of the probability space.
Sometimes, meta-analysis is supposed to fill this gap, e.g., failure to find significant evidence against the null in a series of experiments counts as evidence for the null. But first, this move does not provide a systematic, principled theory of statistical evidence, and second, it fails to answer the important question how data support the null hypothesis in a single experiment.
Of course, the problem is more general: for both Bayesians and frequentists, the choice of a statistical test demands a lot of subjective judgment. Often, these choices are nontrivial even in simple problems, e.g., in deciding whether to analyze a contingency table with Fisher’s exact test, Pearson’s χ2-test or yet another method.
The use of default priors in Bayesian inference raises a number of interesting philosophical questions (e.g., Sprenger 2012) which go beyond the scope of this paper. That said, for the given (Binomial) dataset, the chosen approach looks adequate.
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Sprenger, J. The objectivity of Subjective Bayesianism. Euro Jnl Phil Sci 8, 539–558 (2018). https://doi.org/10.1007/s13194-018-0200-1
- Statistical inference
- Heather Douglas
- Value-free ideal