19,083 research outputs found

    Statistical Inference and the Plethora of Probability Paradigms: A Principled Pluralism

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    The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability

    The Problem of Confirmation in the Everett Interpretation

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    I argue that the Oxford school Everett interpretation is internally incoherent, because we cannot claim that in an Everettian universe the kinds of reasoning we have used to arrive at our beliefs about quantum mechanics would lead us to form true beliefs. I show that in an Everettian context, the experimental evidence that we have available could not provide empirical confirmation for quantum mechanics, and moreover that we would not even be able to establish reference to the theoretical entities of quantum mechanics. I then consider a range of existing Everettian approaches to the probability problem and show that they do not succeed in overcoming this incoherence

    On the role of explanatory and systematic power in scientific reasoning

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    The paper investigates measures of explanatory power and how to define the inference schema “Inference to the Best Explanation”. It argues that these measures can also be used to quantify the systematic power of a hypothesis and the inference schema “Inference to the Best Systematization” is defined. It demonstrates that systematic power is a fruitful criterion for theory choice and IBS is truth-conducive. It also shows that even radical Bayesians must admit that systemic power is an integral component of Bayesian reasoning. Finally, the paper puts the achieved results in perspective with van Fraassen’s famous criticism of IB

    Approaches for the Joint Evaluation of Hypothesis Tests: Classical Testing, Bayes Testing, and Joint Confirmation

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    The occurrence of decision problems with changing roles of null and alternative hypotheses has increased interest in extending the classical hypothesis testing setup. Particularly, confirmation analysis has been in the focus of some recent contributions in econometrics. We emphasize that confirmation analysis is grounded in classical testing and should be contrasted with the Bayesian approach. Differences across the three approaches – traditional classical testing, Bayes testing, joint confirmation – are highlighted for a popular testing problem. A decision is searched for the existence of a unit root in a time-series process on the basis of two tests. One of them has the existence of a unit root as its null hypothesis and its non-existence as its alternative, while the roles of null and alternative are reversed for the other hypothesis test.Confirmation analysis, Decision contours, Unit roots

    Bayes and health care research.

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    Bayes’ rule shows how one might rationally change one’s beliefs in the light of evidence. It is the foundation of a statistical method called Bayesianism. In health care research, Bayesianism has its advocates but the dominant statistical method is frequentism. There are at least two important philosophical differences between these methods. First, Bayesianism takes a subjectivist view of probability (i.e. that probability scores are statements of subjective belief, not objective fact) whilst frequentism takes an objectivist view. Second, Bayesianism is explicitly inductive (i.e. it shows how we may induce views about the world based on partial data from it) whereas frequentism is at least compatible with non-inductive views of scientific method, particularly the critical realism of Popper. Popper and others detail significant problems with induction. Frequentism’s apparent ability to avoid these, plus its ability to give a seemingly more scientific and objective take on probability, lies behind its philosophical appeal to health care researchers. However, there are also significant problems with frequentism, particularly its inability to assign probability scores to single events. Popper thus proposed an alternative objectivist view of probability, called propensity theory, which he allies to a theory of corroboration; but this too has significant problems, in particular, it may not successfully avoid induction. If this is so then Bayesianism might be philosophically the strongest of the statistical approaches. The article sets out a number of its philosophical and methodological attractions. Finally, it outlines a way in which critical realism and Bayesianism might work together. </p

    The Logic of Experimental Tests, Particularly of Everettian Quantum Theory

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    Claims that the standard methodology of scientific testing is inapplicable to Everettian quantum theory, and hence that the theory is untestable, are due to misconceptions about probability and about the logic of experimental testing. Refuting those claims by correcting those misconceptions leads to various simplifications, notably the elimination of everything probabilistic from fundamental physics (stochastic processes) and from the methodology of testing ('Bayesian' credences)

    On Universal Prediction and Bayesian Confirmation

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    The Bayesian framework is a well-studied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard statistical guidelines for choosing the model class and prior are not always available or fail, in particular in complex situations. Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. We discuss in breadth how and in which sense universal (non-i.i.d.) sequence prediction solves various (philosophical) problems of traditional Bayesian sequence prediction. We show that Solomonoff's model possesses many desirable properties: Strong total and weak instantaneous bounds, and in contrast to most classical continuous prior densities has no zero p(oste)rior problem, i.e. can confirm universal hypotheses, is reparametrization and regrouping invariant, and avoids the old-evidence and updating problem. It even performs well (actually better) in non-computable environments.Comment: 24 page

    Risk Objectivism and Risk Subjectivism: When Are Risks Real

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    Typically, those who discuss Risk management envision a two-step process wherein, first, Risk is more or less objectively appraised and, second, the acceptability of those Risks is subjectively evaluated. This paper questions the philosophical foundations of that approach
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