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We show that if among the tested hypotheses the number of true hypotheses is not equal to the number of false hypotheses, then Neyman-Pearson theory of testing hypotheses does not warrant minimal epistemic reliability (the feature of driving to true conclusions more often than to false ones). We also argue that N-P does not protect from the possible negative effects of the pragmatic value-laden unequal setting of error probabilities on N-P’s epistemic reliability. Most importantly, we argue that in the case (...) |
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In statistics, there are two main paradigms: classical and Bayesian statistics. The purpose of this article is to investigate the extent to which classicists and Bayesians can agree. My conclusion is that, in certain situations, they cannot. The upshot is that, if we assume that the classicist is not allowed to have a higher degree of belief in a null hypothesis after he has rejected it than before, then he has to either have trivial or incoherent credences to begin with (...) |
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Bayesian confirmation theory is a leading theory to decide the confirmation/refutation of a hypothesis based on probability calculus. While it may be much discussed in philosophy of science, is it actually practiced in terms of hypothesis testing by scientists? Since the assignment of some of the probabilities in the theory is open to debate and the risk of making the wrong decision is unknown, many scientists do not use the theory in hypothesis testing. Instead, they use alternative statistical tests that (...) |
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The paper examines the claim that significance testing violates the Principle of Total Evidence. I argue that p-values violate PTE for two-sided tests but satisfy PTE for one-sided tests invoking a sufficient test statistic independent of the preferred theory of evidence. While the focus of the paper is to evaluate a particular claim about the relationship of significance testing and PTE, I clarify the reading of this methodological principle along the way. |
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The Jeffreys–Lindley paradox exposes a rift between Bayesian and frequentist hypothesis testing that strikes at the heart of statistical inference. Contrary to what most current literature suggests, the paradox was central to the Bayesian testing methodology developed by Sir Harold Jeffreys in the late 1930s. Jeffreys showed that the evidence for a point-null hypothesis $${\mathcal {H}}_0$$ H 0 scales with $$\sqrt{n}$$ n and repeatedly argued that it would, therefore, be mistaken to set a threshold for rejecting $${\mathcal {H}}_0$$ H 0 (...) |
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This article discusses the dual interpretation of the Jeffreys-Lindley paradox associated with Bayesian posterior probabilities and Bayes factors, both as a differentiation between frequentist and Bayesian statistics and as a pointer to the difficulty of using improper priors while testing. I stress the considerable impact of this paradox on the foundations of both classical and Bayesian statistics. While assessing existing resolutions of the paradox, I focus on a critical viewpoint of the paradox discussed by Spanos in Philosophy of Science. |
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