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From Laplace To Supernova Sn 1987a: Bayesian Inference In Astrophysics
, 1990
"... . The Bayesian approach to probability theory is presented as an alternative to the currently used longrun relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions ..."
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Cited by 52 (2 self)
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. The Bayesian approach to probability theory is presented as an alternative to the currently used longrun relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions to wellposed statistical problems, and is historically the original approach to statistics. The reasons for earlier rejection of Bayesian methods are discussed, and it is noted that the work of Cox, Jaynes, and others answers earlier objections, giving Bayesian inference a firm logical and mathematical foundation as the correct mathematical language for quantifying uncertainty. The Bayesian approaches to parameter estimation and model comparison are outlined and illustrated by application to a simple problem based on the gaussian distribution. As further illustrations of the Bayesian paradigm, Bayesian solutions to two interesting astrophysical problems are outlined: the measurement of wea...
Severe Testing as a Basic Concept in a NeymanPearson Philosophy of Induction
 BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE
, 2006
"... 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 longstanding problems of N–P tests s ..."
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Cited by 36 (14 self)
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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 longstanding problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test’s (predata) error probabilities are to be used for (postdata) inductive inference as opposed to inductive behavior. We argue that the relevance of error probabilities is to ensure that only statistical hypotheses that have passed severe or probative tests are inferred from the data. The severity criterion supplies a metastatistical principle for evaluating proposed statistical inferences, avoiding classic fallacies from tests that are overly sensitive, as well as those not sensitive enough to particular errors and discrepancies.
Inductive influence
 British Journal for the Philosophy of Science
"... Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief 1 to the next raven being black, however many other black ravens have 2 been observed. I argue that this objection can be overcome by appealing to objective Bay ..."
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Cited by 9 (7 self)
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Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief 1 to the next raven being black, however many other black ravens have 2 been observed. I argue that this objection can be overcome by appealing to objective Bayesian nets, a formalism for representing objective Bayesian degrees of belief. Under this account, previous observations exert an inductive influence on the next observation. I show how this approach can be used to capture the JohnsonCarnap continuum of inductive methods, as well as the NixParis continuum, and show how inductive influence can
Objective Bayesianism, Bayesian Conditionalisation
, 2008
"... Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between ..."
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Cited by 9 (7 self)
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Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification fails because diachronic Dutch book arguments are subject to a reductio: in certain circumstances one can Dutch book an agent however she changes her degrees of belief. One may also criticise objective Bayesianism on the grounds that its norms are not compulsory but voluntary, the result of a stance. It is argued that this second objection also misses the mark, since objective
Philosophies of probability: objective Bayesianism and its challenges
 Handbook of the philosophy of mathematics. Elsevier, Amsterdam. Handbook of the Philosophy of Science
, 2004
"... This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. ..."
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Cited by 8 (5 self)
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This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces.
Objective bayesian probabilistic logic
 Journal of Algorithms
"... This paper develops connections between objective Bayesian epistemology—which holds that the strengths of an agent’s beliefs should be representable by probabilities, should be calibrated with evidence of empirical probability, and should otherwise be equivocal—and probabilistic logic. After introdu ..."
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Cited by 6 (4 self)
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This paper develops connections between objective Bayesian epistemology—which holds that the strengths of an agent’s beliefs should be representable by probabilities, should be calibrated with evidence of empirical probability, and should otherwise be equivocal—and probabilistic logic. After introducing objective Bayesian epistemology over propositional languages, the formalism is extended to handle predicate languages. A rather general probabilistic logic is formulated and then given a natural semantics in terms of objective Bayesian epistemology. The machinery of objective Bayesian nets and objective credal nets is introduced and this machinery is applied to provide a calculus for probabilistic logic that meshes with the objective Bayesian semantics.
Philosophy of Statistics
 Philosophy of Science: An Encyclopedia
, 2006
"... Error statistics, as we are using that term, has a dual dimension involving philosophy and methodology. It refers to a standpoint regarding both: 1. a cluster of statistical tools, their interpretation and justification, 2. a general philosophy of science, and the roles probability plays in inductiv ..."
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Cited by 6 (4 self)
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Error statistics, as we are using that term, has a dual dimension involving philosophy and methodology. It refers to a standpoint regarding both: 1. a cluster of statistical tools, their interpretation and justification, 2. a general philosophy of science, and the roles probability plays in inductive inference. To adequately appraise the error statistical approach, and compare it to other philosophies of statistics, requires understanding the complex interconnections between the methodological and philosophical dimensions in (1) and (2) respectively. To make this entry useful while keeping to a manageable length, we restrict our main focus to (1) the error statistical philosophy. We will however aim to bring out enough of the interplay between the philosophical, methodological, and statistical issues, to elucidate longstanding conceptual, technical, and epistemological debates surrounding both these dimensions. Even with this restriction, we are identifying a huge territory marked by generations of recurring controversy about how to specify and interpret statistical methods. Understandably, standard explications
Philosophies of probability
 Handbook of the Philosophy of Mathematics, Volume 4 of the Handbook of the Philosophy of Science
"... This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of ..."
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Cited by 3 (2 self)
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This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general.
Evidential probability and objective Bayesian epistemology
 Handbook of the Philosophy of Statistics
, 2009
"... In this chapter we draw connections between two seemingly opposing approaches to probability and statistics: evidential probability on the one hand and objective Bayesian epistemology on the other. ..."
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Cited by 3 (3 self)
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In this chapter we draw connections between two seemingly opposing approaches to probability and statistics: evidential probability on the one hand and objective Bayesian epistemology on the other.
EVIDENTIAL PROBABILITY, OBJECTIVE BAYESIANISM, NONMONOTONICITY AND SYSTEM P
"... Abstract: This paper is a comparison of how firstorder Kyburgian Evidential Probability (EP), secondorder EP, and objective Bayesian epistemology compare as to the KLM systemP rules for consequence relations and the monotonic / nonmonotonic divide. 1 ..."
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Cited by 1 (1 self)
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Abstract: This paper is a comparison of how firstorder Kyburgian Evidential Probability (EP), secondorder EP, and objective Bayesian epistemology compare as to the KLM systemP rules for consequence relations and the monotonic / nonmonotonic divide. 1