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Summary Bayesian Reasoning includes issues related to: 1. the probabilistic logic of evidential support for hypotheses;  2. the logic of comparative belief, belief strengths, and belief updating as represented by classical probability functions; 3. the logic of decision as represented in terms of utilities, probabilities, and expected utility maximization, including ways in which this logic may represent comparative preferences among acts or states of affairs; 4. Bayesian probabilistic treatments of causal influence (e.g. via Bayes nets); 5. studies of relationships between human performance and models of reasoning and decision of a Bayesian kind (as described in 1-4 above).
Key works

Bayesian reasoning includes a wide variety of topics and issues. For introductory overviews of Bayesian confirmation theory and decision theory, among the best texts available are Skyrms 1966 and Hacking 2001; at a somewhat more advanced level Howson & Urbach 1993 is essential reading. Key sources for Bayesian probability and decision theory include Ramsey 2010Savage 1954Jeffrey 1983, and Joyce 1999. The classic treatment of Bayes nets is Pearl 1988Chater & Oaksford 2008 is an excellent collection of articles on Bayesian modeling of natural human reasoning. Also see the Stanford Encyclopedia of Philosophy (online, Zalta 2004) for helpful articles on various aspects of Bayesian reasoning: e.g. on Bayes' Theorem, Bayesian Epistemology, Inductive Logic, Decision Theory, etc.

Introductions Hájek 2008; Joyce 2008; Hawthorne 2011; Talbott 2008; Vineberg 2011; Weirich 2009; Hitchcock 2008.
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  1. Peter Achinstein (1963). Confirmation Theory, Order, and Periodicity. Philosophy of Science 30 (1):17-35.
    This paper examines problems of order and periodicity which arise when the attempt is made to define a confirmation function for a language containing elementary number theory as applied to a universe in which the individuals are considered to be arranged in some fixed order. Certain plausible conditions of adequacy are stated for such a confirmation function. By the construction of certain types of predicates, it is proved, however, that these conditions of adequacy are violated by any confirmation function defined (...)
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  2. Peter Achinstein (1963). Variety and Analogy in Confirmation Theory. Philosophy of Science 30 (3):207-221.
    Confirmation theorists seek to define a function that will take into account the various factors relevant in determining the degree to which an hypothesis is confirmed by its evidence. Among confirmation theorists, only Rudolf Carnap has constructed a system which purports to consider factors in addition to the number of instances, viz. the variety manifested by the instances and the amount of analogy between the instances. It is the purpose of this paper to examine the problem which these additional factors (...)
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  3. Daniel Acuna & Paul Schrater (2008). Bayesian Modeling of Human Sequential Decision-Making on the Multi-Armed Bandit Problem. In B. C. Love, K. McRae & V. M. Sloutsky (eds.), Proceedings of the 30th Annual Conference of the Cognitive Science Society. Cognitive Science Society. 100--200.
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  4. Ernest W. Adams (1988). Confirming Inexact Generalizations. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:10 - 16.
    I suppose that 'ravens are black' is an inexact generalization having a degree of truth measured by the proportion of ravens that are black, and a probability measured by its expected degree of truth in different 'possible worlds.' Given this, 'ravens are black' differs in truth, probability, and confirmation from 'non-black things are not ravens', and this suggests a new approach to Hempel's Paradox as well as to other aspects of confirmation. Basic concepts of a formal theory developing this approach (...)
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  5. P. M. Ainsworth (2012). In Defence of Objective Bayesianism. Analysis 72 (4):832-843.
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  6. Jean Aitchison (1995). Free or Ensnared? The Hidden Nets Of. In E. Barker (ed.), Lse on Freedom. Lse Books. 75.
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  7. Nilufa Ali, Anne Schlottman, Abigail Shaw, Nick Chater, & Oaksford & Mike (2010). Causal Discounting and Conditional Reasoning in Children. In Mike Oaksford & Nick Chater (eds.), Cognition and Conditionals: Probability and Logic in Human Thinking. Oup Oxford.
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  8. Nilufa Ali, Anne Schlottmann, Abigail Shaw, Nick Chater & Mike Oaksford (2010). Causal Discounting and Conditional Reasoning in Children. In M. Oaksford & N. Chater (eds.), Cognition and Conditionals: Probability and Logic in Human Thought. Oxford University Press.
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  9. Jerrold L. Aronson (1989). The Bayesians and the Raven Paradox. Noûs 23 (2):221-240.
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  10. J. Austerweil & T. Griffiths (2008). A Rational Analysis of Confirmation with Deterministic Hypotheses. In B. C. Love, K. McRae & V. M. Sloutsky (eds.), Proceedings of the 30th Annual Conference of the Cognitive Science Society. Cognitive Science Society. 1041--1046.
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  11. Peter C. Austin (2009). Are (the Log‐Odds of) Hospital Mortality Rates Normally Distributed? Implications for Studying Variations in Outcomes of Medical Care. Journal of Evaluation in Clinical Practice 15 (3):514-523.
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  12. Patricia Baillie (1969). That Confirmation May yet Be a Probability. British Journal for the Philosophy of Science 20 (1):41-51.
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  13. A. Balakrishnan & A. K. Shanmukham (1968). Equipment for Calibration of Bathythermograph and Preparation of Grids. In Peter Koestenbaum (ed.), Proceedings. [San Jose? Calif.. 38--334.
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  14. David Barber (2002). Bayesian Methods for Supervised Neural Networks. In M. Arbib (ed.), The Handbook of Brain Theory and Neural Networks. Mit Press.
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  15. Daniel Barker (forthcoming). Seeing the Wood for the Trees: Philosophical Aspects of Classical, Bayesian and Likelihood Approaches in Statistical Inference and Some Implications for Phylogenetic Analysis. Biology and Philosophy:1-21.
    The three main approaches in statistical inference—classical statistics, Bayesian and likelihood—are in current use in phylogeny research. The three approaches are discussed and compared, with particular emphasis on theoretical properties illustrated by simple thought-experiments. The methods are problematic on axiomatic grounds (classical statistics), extra-mathematical grounds relating to the use of a prior (Bayesian inference) or practical grounds (likelihood). This essay aims to increase understanding of these limits among those with an interest in phylogeny.
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  16. H. B. Barlow (1991). Need for Prior Probabilities in Learning. In A. Gorea (ed.), Representations of Vision. Cambridge University Press. 319.
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  17. G. A. Barnard (1972). The Logic of Statistical Inference. British Journal for the Philosophy of Science 23 (2):123-132.
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  18. Jeffrey A. Barrett (2014). Description and the Problem of Priors. Erkenntnis 79 (6):1343-1353.
    Belief-revision models of knowledge describe how to update one’s degrees of belief associated with hypotheses as one considers new evidence, but they typically do not say how probabilities become associated with meaningful hypotheses in the first place. Here we consider a variety of Skyrms–Lewis signaling game (Lewis in Convention. Harvard University Press, Cambridge, 1969; Skyrms in Signals evolution, learning, & information. Oxford University Press, New York, 2010) where simple descriptive language and predictive practice and associated basic expectations coevolve. Rather than (...)
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  19. Lee R. Beach & James A. Wise (1969). Subjective Probability Revision and Subsequent Decisions. Journal of Experimental Psychology 81 (3):561.
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  20. A. Berman (1939). The Relation of Time Estimation to Satiation. Journal of Experimental Psychology 25 (3):281.
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  21. William Bevan & Edward D. Turner (1964). Assimilation and Contrast in the Estimation of Number. Journal of Experimental Psychology 67 (5):458.
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  22. Lukáš Bielik (2011). Havraní paradox, logika a metódy testovania. Organon F 18 (2):213-225.
    The paper presents the logical milieu of the Paradox of ravens, identified by Hempel in his Studies in the Logic of Confirmation. It deals with Hempel’s interpretations of Nicod’s criterion of confirmation as well as with its inadmissible consequences. I, subsequently, suggest an epistemological and semantic specification of empirical properties, i.e., of their identity; then I formulate a criterion of the test of properties expressed by empirical hypothesis. Finally, I propose a procedural conception of confirmation by means of the testing (...)
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  23. Tamás Biró (2013). Towards a Robuster Interpretive Parsing. Journal of Logic, Language and Information 22 (2):139-172.
    The input data to grammar learning algorithms often consist of overt forms that do not contain full structural descriptions. This lack of information may contribute to the failure of learning. Past work on Optimality Theory introduced Robust Interpretive Parsing (RIP) as a partial solution to this problem. We generalize RIP and suggest replacing the winner candidate with a weighted mean violation of the potential winner candidates. A Boltzmann distribution is introduced on the winner set, and the distribution’s parameter $T$ is (...)
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  24. Karen Block & James R. Erickson (1969). Multiple-Choice Probability Learning. Journal of Experimental Psychology 81 (1):72.
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  25. Mark Blokpoel, Johan Kwisthout, T. P. van der Weide & Iris van Rooij (2010). How Action Understanding Can Be Rational, Bayesian and Tractable. In S. Ohlsson & R. Catrambone (eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society. Cognitive Science Society.
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  26. David Botting (2012). The Paradox of Analogy. Informal Logic 32 (1):98-115.
    I will show that there is a type of analogical reasoning that instantiates a pattern of reasoning in confirmation theory that is considered at best paradoxical and at worst fatal to the entire syntactical approach to confirmation and explanation. However, I hope to elaborate conditions under which this is a sound (although not necessarily strong) method of reasoning.
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  27. Luc Bovens & Stephan Hartmann (2007). Special Issue on Bayesian Epistemology Edited by L. Bovens and S. Hartmann. Synthese 156 (3).
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  28. Richard Boyd (1991). Confirmation, Semantics, and the Interpretation of Scientific Theories. In Richard Boyd, Philip Gasper & J. D. Trout (eds.), The Philosophy of Science. Mit Press. 3--35.
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  29. Seamus Bradley & Katie Steele (2014). Uncertainty, Learning, and the “Problem” of Dilation. Erkenntnis 79 (6):1287-1303.
    Imprecise probabilism—which holds that rational belief/credence is permissibly represented by a set of probability functions—apparently suffers from a problem known as dilation. We explore whether this problem can be avoided or mitigated by one of the following strategies: (a) modifying the rule by which the credal state is updated, (b) restricting the domain of reasonable credal states to those that preclude dilation.
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  30. Carl M. Brandauer (1953). A Confirmation of Webb's Data Concerning the Action of Irrelevant Drives. Journal of Experimental Psychology 45 (3):150.
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  31. B. A. Brody (1968). Confirmation and Explanation. Journal of Philosophy 65 (10):282-299.
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  32. Brown (1968). The Use of Multiple Sampling Plankton Nets. BioScience 18 (10):962-962.
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  33. Marc J. Buehner & Patricia W. Cheng (2005). Causal Learning. In K. Holyoak & B. Morrison (eds.), The Cambridge Handbook of Thinking and Reasoning. Cambridge Univ Pr. 143--168.
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  34. Richmond Campbell & Thomas Vinci (1983). Novel Confirmation. British Journal for the Philosophy of Science 34 (4):315-341.
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  35. P. -L. Carle (1986). Sermon de S. Fauste de Riez (Ou de Lérins) Pour la Fête de Pentecôte Sur la Confirmation. Nova Et Vetera 61 (3):90-105.
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  36. Rudolf Carnap (1953). On the Comparative Concept of Confirmation. British Journal for the Philosophy of Science 3 (12):311-318.
  37. Martin Carrier (2003). Smooth Lines in Confirmation Theory. In Paolo Parrini, Wes Salmon & Merrilee Salmon (eds.), Logical Empiricism: Historical and Contemporary Perspectives. Pittsburgh University Pres. 304.
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  38. G. Casella & R. Berger (2001). Hypothesis Testing in Statistics. In International Encyclopedia of the Social and Behavioral Sciences. 7118--7121.
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  39. Lorenzo Casini, Phyllis Mckay Illari, Federica Russo & Jon Williamson (2011). Models for Prediction, Explanation and Control. Theoria 26 (1):5-33.
    The Recursive Bayesian Net (RBN) formalism was originally developed for modelling nested causal relationships. In this paper we argue that the formalism can also be applied to modelling the hierarchical structure of mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations is vital for prediction, explanation and control respectively, an RBN can be applied to all these tasks. We show in particular (...)
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  40. Alejandro Cassini (2003). Confirmación Hipotético-Deductiva y Confirmación Bayesiana. Análisis Filosófico 23 (1):41-84.
    En este trabajo hago una comparación sistemática entre las dos teorías de la confirmación más populares en la actualidad: el método hipotético-deductivo y el bayesianismo. En primer lugar, enumero los cinco problemas fundamentales de la teoría hipotético-deductivista. Estos son el problema de las hipótesis estadísticas, el del grado de confirmación, el de la conjunción irrelevante, el del holismo epistemológico y el de las hipótesis alternativas. Luego, hago una presentación general de la epistemología bayesiana y muestro de qué manera estos problemas (...)
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  41. Lin Chao-Tien (1978). Solutions to the Paradoxes of Confirmation, Goodman's Paradox, and Two New Theories of Confirmation. Philosophy of Science 45 (3):415-419.
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  42. Alain Chateauneuf, Thibault Gajdos & Jean-Yves Jaffray (2011). Regular Updating. Theory and Decision 71 (1):111-128.
    We study the Full Bayesian Updating rule for convex capacities. Following a route suggested by Jaffray (IEEE Transactions on Systems, Man and Cybernetics 22(5):1144–1152, 1992), we define some properties one may want to impose on the updating process, and identify the classes of (convex and strictly positive) capacities that satisfy these properties for the Full Bayesian Updating rule. This allows us to characterize two parametric families of convex capacities: ${(\varepsilon,\delta)}$ -contaminations (which were introduced, in a slightly different form, by Huber (...)
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  43. Nick Chater, Joshua B. Tenenbaum & Alan Yuille (2006). Subjective Probability in a Nutshell. Trends in Cognitive Sciences 10 (7):287-291.
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  44. Timothy Childers & Ondrej Majer (2012). Interpreting Probability. Journal of Logic, Language and Information 21 (2):141-144.
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  45. L. Jonathan Cohen (1980). Bayesianism Versus Baconianism in the Evaluation of Medical Diagnoses. British Journal for the Philosophy of Science 31 (1):45-62.
  46. L. Jonathan Cohen (1968). An Argument That Confirmation Functors for Consilience Are Empirical Hypotheses. In Imre Lakatos (ed.), The Problem of Inductive Logic. Amsterdam, North Holland Pub. Co.. 247--250.
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  47. L. Jonathan Cohen (1967). Corrigendum: A Logic for Evidential Support. British Journal for the Philosophy of Science 17 (4):352.
    In my paper ‘A Logic for Evidential Support’ (this Journal, 17 (1966), 21 ff.) the argument on page 25 is illustrated by wrong and misleading examples.1 The argument proceeds by considering statements logically equivalent to a universal hypothesis U1 that are formed by generalising analogously not about the individual elements of U1's domain of discourse, but about pairs, trios, or n-membered classes of these elements, where the domain of U1 has at least n elements. But the generalisations must be understood (...)
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  48. L. Jonathan Cohen (1966). What has Confirmation to Do with Probabilities? Mind 75 (300):463-481.
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  49. Enrico Colombatto (2005). Is" Malinvestment" Enough to Go Bust? Journal of Libertarian Studies 19 (3):3.
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  50. John Oliver Cook & Morton Edward Spitzer (1960). Supplementary Report: Prompting Versus Confirmation in Paired-Associate Learning. Journal of Experimental Psychology 59 (4):275.
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