19,083 research outputs found
Statistical Inference and the Plethora of Probability Paradigms: A Principled Pluralism
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 âsubjectiveâ and âobjectiveâ interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an âobjectiveâ probability
The Problem of Confirmation in the Everett Interpretation
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
The paper investigates measures of explanatory power and how to define the inference schema âInference to the Best Explanationâ. It argues that these measures can also be used to quantify the systematic power of a hypothesis and the inference schema âInference to the Best Systematizationâ 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 Fraassenâs famous criticism of IB
Approaches for the Joint Evaluation of Hypothesis Tests: Classical Testing, Bayes Testing, and Joint Confirmation
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 â traditional classical testing, Bayes testing, joint confirmation â 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.
Bayesâ rule shows how one might rationally change oneâs 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. Frequentismâs 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.
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The Logic of Experimental Tests, Particularly of Everettian Quantum Theory
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
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
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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