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Bayesians often assume, suppose, or conjecture that for any reasonable explication of the notion of simplicity a prior can be designed that will enforce a preference for hypotheses simpler in just that sense. But it is shown here that there are simplicity-driven approaches to curve-fitting problems that cannot be captured within the orthodox Bayesian framework. |
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Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and long-standing problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test's (pre-data) error probabilities are to be used for (post-data) inductive inference as opposed to inductive behavior. We argue that the relevance of error probabilities (...) |
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The sample space of the chance distribution at a given time is a class of possible worlds. Thanks to this connection between chance and modality, one’s views about modal space can have significant consequences in the theory of chance and can be evaluated in part by how plausible these implications are. I apply this methodology to evaluate certain forms of modal contingentism, the thesis that some facts about what is possible are contingent. Any modal contingentist view that meets certain conditions (...) |
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Four experiments investigated uncertainty about a premise in a deductive argument as a function of the expertise of the speaker and of the conversational context. The procedure mimicked everyday reasoning in that participants were not told that the premises were to be treated as certain. The results showed that the perceived likelihood of a conclusion was greater when the major or the minor premise was uttered by an expert rather than a novice (Experiment 1). The results also showed that uncertainty (...) |
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Bayesians often assume, suppose, or conjecture that for any reasonable explication of the notion of simplicity a prior can be designed that will enforce a preference for hypotheses simpler in just that sense. Further, it is often claimed that the Bayesian framework automatically implements Occam's razor—that conditionalizing on data consistent with both a simple theory and a complex theory more or less inevitably favours the simpler theory. But it is shown here that there are simplicity-driven approaches to curve-fitting problems that (...) |
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