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Bayes' theorem

Stanford Encyclopedia of Philosophy (2008)

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  1. (4 other versions)The Logic of Scientific Discovery.Karl Popper - 1959 - Studia Logica 9:262-265.
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  • Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference.J. Pearl, F. Bacchus, P. Spirtes, C. Glymour & R. Scheines - 1988 - Synthese 104 (1):161-176.
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  • (1 other version)A Treatise on Probability.J. M. Keynes - 1989 - British Journal for the Philosophy of Science 40 (2):219-222.
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  • (2 other versions)Decision Theory as Philosophy.Mark Kaplan - 1998 - Philosophical Quarterly 48 (192):406-408.
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  • (2 other versions)Decision Theory as Philosophy.Mark Kaplan - 1997 - Mind 106 (424):787-791.
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  • (5 other versions)Philosophical Explanations. [REVIEW]Robert Nozick - 1981 - Ethics 94 (2):326-327.
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  • The Scientific Image.William Demopoulos & Bas C. van Fraassen - 1982 - Philosophical Review 91 (4):603.
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  • (2 other versions)An Introduction to Confirmation Theory.Mark Pastin & Richard Swinburne - 1975 - Philosophical Review 84 (1):122.
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  • (1 other version)Rational Decision and Causality.Ellery Eells - 2009 - Cambridge University Press.
    First published in 1982, Ellery Eells' original work on rational decision making had extensive implications for probability theorists, economists, statisticians and psychologists concerned with decision making and the employment of Bayesian principles. His analysis of the philosophical and psychological significance of Bayesian decision theories, causal decision theories and Newcomb's paradox continues to be influential in philosophy of science. His book is now revived for a new generation of readers and presented in a fresh twenty-first-century series livery, including a specially commissioned (...)
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  • (1 other version)A Primer of Probability Logic.Ernest Wilcox Adams - 1996 - Center for the Study of Language and Inf.
    This book is meant to be a primer, that is, an introduction, to probability logic, a subject that appears to be in its infancy. Probability logic is a subject envisioned by Hans Reichenbach and largely created by Adams. It treats conditionals as bearers of conditional probabilities and discusses an appropriate sense of validity for arguments such conditionals, as well as ordinary statements as premisses. This is a clear well-written text on the subject of probability logic, suitable for advanced undergraduates or (...)
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  • (1 other version)The Emergence of Probability: A Philosophical Study of Early Ideas About Probability, Induction and Statistical Inference.Ian Hacking - 1975 - Cambridge University Press.
    Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. Ian Hacking presents a philosophical critique of early ideas about probability, induction, and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth, and seventeenth centuries. Hacking invokes a wide intellectual framework involving the growth of science, economics, and the theology of the period. He argues that the (...)
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  • Betting on Theories.Patrick Maher - 1993 - Cambridge, New York and Melbourne: Cambridge University Press.
    This book is a major contribution to decision theory, focusing on the question of when it is rational to accept scientific theories. The author examines both Bayesian decision theory and confirmation theory, refining and elaborating the views of Ramsey and Savage. He argues that the most solid foundation for confirmation theory is to be found in decision theory, and he provides a decision-theoretic derivation of principles for how many probabilities should be revised over time. Professor Maher defines a notion of (...)
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  • The Foundations of Causal Decision Theory.James M. Joyce - 1999 - Cambridge University Press.
    This book defends the view that any adequate account of rational decision making must take a decision maker's beliefs about causal relations into account. The early chapters of the book introduce the non-specialist to the rudiments of expected utility theory. The major technical advance offered by the book is a 'representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general conditional decision theory. The book solves (...)
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  • (1 other version)A Bayesian Account of Independent Evidence with Applications.Branden Fitelson - 2001 - Philosophy of Science 68 (S3):S123-S140.
    A Bayesian account of independent evidential support is outlined. This account is partly inspired by the work of C. S. Peirce. I show that a large class of quantitative Bayesian measures of confirmation satisfy some basic desiderata suggested by Peirce for adequate accounts of independent evidence. I argue that, by considering further natural constraints on a probabilistic account of independent evidence, all but a very small class of Bayesian measures of confirmation can be ruled out. In closing, another application of (...)
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  • Philosophical Theories of Probability.Donald Gillies - 2000 - New York: Routledge.
    The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. _Philosophical Theories of Probability_ is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.
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  • (3 other versions)Philosophical Investigations.Ludwig Wittgenstein - 1953 - New York, NY, USA: Wiley-Blackwell. Edited by G. E. M. Anscombe.
    Editorial preface to the fourth edition and modified translation -- The text of the Philosophische Untersuchungen -- Philosophische untersuchungen = Philosophical investigations -- Philosophie der psychologie, ein fragment = Philosophy of psychology, a fragment.
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  • Problems of Old Evidence†.Ellery Eells - 2017 - Pacific Philosophical Quarterly 66 (3-4):283-302.
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  • Bayes or Bust?: A Critical Examination of Bayesian Confirmation Theory.John Earman - 1992 - MIT Press.
    There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes’s original paper to contemporary formal learning theory.In (...)
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  • The Foundations of Statistics.Leonard Savage - 1954 - Wiley Publications in Statistics.
    Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.
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  • (1 other version)The theory of probability.Hans Reichenbach - 1949 - Berkeley,: University of California Press.
    We must restrict to mere probability not only statements of comparatively great uncertainty, like predictions about the weather, where we would cautiously ...
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  • (1 other version)Logical foundations of probability.Rudolf Carnap - 1950 - Chicago]: Chicago University of Chicago Press.
    APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...)
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  • (7) law and causality.Frank Ramsey - 1961 - In John Langshaw Austin (ed.), Philosophical Papers. Oxford, England: Clarendon Press. pp. 140-163.
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  • Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference.Judea Pearl - 1988 - Morgan Kaufmann.
    The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.
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  • (1 other version)Gambling with truth.Isaac Levi - 1967 - Cambridge,: MIT Press.
    This comprehensive discussion of the problem of rational belief develops the subject on the pattern of Bayesian decision theory. The analogy with decision theory introduces philosophical issues not usually encountered in logical studies and suggests some promising new approaches to old problems."We owe Professor Levi a debt of gratitude for producing a book of such excellence. His own approach to inductive inference is not only original and profound, it also clarifies and transforms the work of his predecessors. In short, the (...)
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  • Philosophical explanations.Robert Nozick - 1981 - Cambridge: Harvard University Press.
    Nozick analyzes fundamental issues, such as the identity of the self, knowledge and skepticism, free will, the foundations of ethics, and the meaning of life.
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  • (1 other version)The direction of time.Hans Reichenbach - 1956 - Mineola, N.Y.: Dover Publications. Edited by Maria Reichenbach.
    The final work of a distinguished physicist, this remarkable volume examines the emotive significance of time, the time order of mechanics, the time direction of thermodynamics and microstatistics, the time direction of macrostatistics, and the time of quantum physics. Coherent discussions include accounts of analytic methods of scientific philosophy in the investigation of probability, quantum mechanics, the theory of relativity, and causality. "[Reichenbach’s] best by a good deal."—Physics Today. 1971 ed.
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  • Scientific reasoning: the Bayesian approach.Peter Urbach & Colin Howson - 1993 - Chicago: Open Court. Edited by Peter Urbach.
    Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...
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  • Laws and symmetry.Bas C. Van Fraassen - 1989 - New York: Oxford University Press.
    Metaphysicians speak of laws of nature in terms of necessity and universality; scientists, in terms of symmetry and invariance. In this book van Fraassen argues that no metaphysical account of laws can succeed. He analyzes and rejects the arguments that there are laws of nature, or that we must believe there are, and argues that we should disregard the idea of law as an adequate clue to science. After exploring what this means for general epistemology, the author develops the empiricist (...)
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  • Milne's measure of confirmation.Stephen Pollard - 1999 - Analysis 59 (4):335–338.
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  • Probabilities for two properties.Patrick Maher - 2000 - Erkenntnis 52 (1):63-91.
    Let R(X, B) denote the class of probability functions that are defined on algebra X and that represent rationally permissible degrees of certainty for a person whose total relevant background evidence is B. This paper is concerned with characterizing R(X, B) for the case in whichX is an algebra of propositions involving two properties and B is empty. It proposes necessary conditions for a probability function to be in R(X, B), some of which involve the notion of statistical dependence. The (...)
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  • Bayesian confirmation: Paradise regained.R. D. Rosenkrantz - 1994 - British Journal for the Philosophy of Science 45 (2):467-476.
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  • Subjective and objective confirmation.Patrick Maher - 1996 - Philosophy of Science 63 (2):149-174.
    Confirmation is commonly identified with positive relevance, E being said to confirm H if and only if E increases the probability of H. Today, analyses of this general kind are usually Bayesian ones that take the relevant probabilities to be subjective. I argue that these subjective Bayesian analyses are irremediably flawed. In their place I propose a relevance analysis that makes confirmation objective and which, I show, avoids the flaws of the subjective analyses. What I am proposing is in some (...)
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  • In defense of the Popper-Miller argument.Donald Gillies - 1986 - Philosophy of Science 53 (1):110-113.
    In their 1983 article, Popper and Miller present an argument against inductive probability. This argument is criticized by Redhead in his 1985 article. The aim of the present note is to state one form of the Popper-Miller argument, and defend it against Redhead's criticisms.
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  • The plurality of bayesian measures of confirmation and the problem of measure sensitivity.Branden Fitelson - 1999 - Philosophy of Science 66 (3):378.
    Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of (...)
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  • Putting the irrelevance back into the problem of irrelevant conjunction.Branden Fitelson - 2002 - Philosophy of Science 69 (4):611-622.
    Naive deductive accounts of confirmation have the undesirable consequence that if E confirms H, then E also confirms the conjunction H & X, for any X—even if X is utterly irrelevant to H (and E). Bayesian accounts of confirmation also have this property (in the case of deductive evidence). Several Bayesians have attempted to soften the impact of this fact by arguing that—according to Bayesian accounts of confirmation— E will confirm the conjunction H & X less strongly than E confirms (...)
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  • Measuring confirmation.David Christensen - 1999 - Journal of Philosophy 96 (9):437-461.
    The old evidence problem affects any probabilistic confirmation measure based on comparing pr(H/E) and pr(H). The article argues for the following points: (1) measures based on likelihood ratios also suffer old evidence difficulties; (2) the less-discussed synchronic old evidence problem is, in an important sense, the most acute; (3) prominent attempts to solve or dissolve the synchronic problem fail; (4) a little-discussed variant of the standard measure avoids the problem, in an appealing way; and (5) this measure nevertheless reveals a (...)
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  • On inductive logic.Rudolf Carnap - 1945 - Philosophy of Science 12 (2):72-97.
    Among the various meanings in which the word ‘probability’ is used in everyday language, in the discussion of scientists, and in the theories of probability, there are especially two which must be clearly distinguished. We shall use for them the terms ‘probability1’ and ‘probability2'. Probability1 is a logical concept, a certain logical relation between two sentences ; it is the same as the concept of degree of confirmation. I shall write briefly “c” for “degree of confirmation,” and “c” for “the (...)
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  • (4 other versions)The Logic of Scientific Discovery.K. Popper - 1959 - British Journal for the Philosophy of Science 10 (37):55-57.
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  • (4 other versions)Probability and Evidence.Paul Horwich - 1985 - Erkenntnis 23 (2):213-219.
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  • The Evidential Foundations of Probabilistic Reasoning.David A. Schum - 1994 - New York, NY, USA: Wiley-Interscience.
    A detailed treatment regarding the diverse properties and uses of evidence and the judgmental tasks they entail. Examines various processes by which evidence may be developed or discovered. Considers the construction of arguments made in defense of the relevance and credibility of individual items and masses of evidence as well as the task of assessing the inferential force of evidence. Includes over 100 numerical examples to illustrate the workings of diverse probabilistic expressions for the inferential force of evidence and the (...)
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  • Inference, Method and Decision.David Miller - 1980 - Philosophical Quarterly 30 (120):264.
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  • The uncertain reasoner's companion: a mathematical perspective.J. B. Paris - 1994 - New York: Cambridge University Press.
    Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject, and formalising within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of the (...)
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  • The logic of induction.Halina Mortimer - 1988 - New York: Halsted Press. Edited by I. Craig & A. G. Cohn.
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  • Studies in the logic of confirmation.Carl A. Hempel - 1983 - In Peter Achinstein (ed.), The concept of evidence. New York: Oxford University Press. pp. 1-26.
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  • Probabilities for multiple properties: The models of Hesse and Carnap and Kemeny. [REVIEW]Patrick Maher - 2001 - Erkenntnis 55 (2):183-215.
    In 1959 Carnap published a probability model that was meant to allow forreasoning by analogy involving two independent properties. Maher (2000)derived a generalized version of this model axiomatically and defended themodel''s adequacy. It is thus natural to now consider how the model mightbe extended to the case of more than two properties. A simple extension waspublished by Hess (1964); this paper argues that it is inadequate. Amore sophisticated one was developed jointly by Carnap and Kemeny in theearly 1950s but never (...)
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  • Bayesianism and diverse evidence.Andrew Wayne - 1995 - Philosophy of Science 62 (1):111-121.
    A common methodological adage holds that diverse evidence better confirms a hypothesis than does the same amount of similar evidence. Proponents of Bayesian approaches to scientific reasoning such as Horwich, Howson and Urbach, and Earman claim to offer both a precise rendering of this maxim in probabilistic terms and an explanation of why the maxim should be part of the methodological canon of good science. This paper contends that these claims are mistaken and that, at best, Bayesian accounts of diverse (...)
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  • Inductive logic and the ravens paradox.Patrick Maher - 1999 - Philosophy of Science 66 (1):50-70.
    Hempel's paradox of the ravens arises from the inconsistency of three prima facie plausible principles of confirmation. This paper uses Carnapian inductive logic to (a) identify which of the principles is false, (b) give insight into why this principle is false, and (c) identify a true principle that is sufficiently similar to the false one that failure to distinguish the two might explain why the false principle is prima facie plausible. This solution to the paradox is compared with a variety (...)
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  • The relevance criterion of confirmation.J. L. Mackie - 1969 - British Journal for the Philosophy of Science 20 (1):27-40.
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  • (1 other version)On confirmation.Janina Hosiasson-Lindenbaum - 1940 - Journal of Symbolic Logic 5 (4):133-148.
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  • Studies in the logic of confirmation (I.).Carl Gustav Hempel - 1945 - Mind 54 (213):1-26.
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