About this topic
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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Bayesian Reasoning, Misc
  1. Laith Al-Shawaf & David Buss (2011). Evolutionary Psychology and Bayesian Modeling. Behavioral and Brain Sciences 34 (4):188-189.
    The target article provides important theoretical contributions to psychology and Bayesian modeling. Despite the article's excellent points, we suggest that it succumbs to a few misconceptions about evolutionary psychology (EP). These include a mischaracterization of evolutionary psychology's approach to optimality; failure to appreciate the centrality of mechanism in EP; and an incorrect depiction of hypothesis testing. An accurate characterization of EP offers more promise for successful integration with Bayesian modeling.
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  2. Casper J. Albers, Barteld P. Kooi & Willem Schaafsma (2005). Trying to Resolve the Two-Envelope Problem. Synthese 145 (1):89 - 109.
    After explaining the well-known two-envelope paradox by indicating the fallacy involved, we consider the two-envelope problem of evaluating the factual information provided to us in the form of the value contained by the envelope chosen first. We try to provide a synthesis of contributions from economy, psychology, logic, probability theory (in the form of Bayesian statistics), mathematical statistics (in the form of a decision-theoretic approach) and game theory. We conclude that the two-envelope problem does not allow a satisfactory solution. An (...)
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  3. Max Albert (2005). Should Bayesians Bet Where Frequentists Fear to Tread? Philosophy of Science 72 (4):584-593.
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  4. J. McKenzie Alexander (2009). Social Deliberation: Nash, Bayes, and the Partial Vindication of Gabriele Tarde. Episteme 6 (2):164-184.
    At the very end of the 19th century, Gabriele Tarde wrote that all society was a product of imitation and innovation. This view regarding the development of society has, to a large extent, fallen out of favour, and especially so in those areas where the rational actor model looms large. I argue that this is unfortunate, as models of imitative learning, in some cases, agree better with what people actually do than more sophisticated models of learning. In this paper, I (...)
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  5. Ronald J. Allen (2001). Artificial Intelligence and the Evidentiary Process: The Challenges of Formalism and Computation. [REVIEW] Artificial Intelligence and Law 9 (2-3):99-114.
    The tension between rule and judgment is well known with respect to the meaning of substantive legal commands. The same conflict is present in fact finding. The law penetrates to virtually all aspects of human affairs; irtually any interaction can generate a legal conflict. Accurate fact finding about such disputes is a necessary condition for the appropriate application of substantive legal commands. Without accuracy in fact finding, the law is unpredictable, and thus individuals cannot efficiently accommodate their affairs to its (...)
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  6. Mair Allen-Williams & Nicholas R. Jennings (2009). Bayesian Learning for Cooperation in Multi-Agent Systems. In. In L. Magnani (ed.), Computational Intelligence. 321--360.
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  7. Peter Allmark (2005). Bayes and Health Care Research. Medicine, Health Care and Philosophy 7 (3):321-332.
    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 (...)
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  8. Paul Anand (2005). Bayes's Theorem (Proceedings of the British Academy, Vol. 113), Edited by Richard Swinburne, Oxford University Press, 2002, 160 Pages. [REVIEW] Economics and Philosophy 21 (1):139-142.
  9. Barton L. Anderson (2011). The Myth of Computational Level Theory and the Vacuity of Rational Analysis. Behavioral and Brain Sciences 34 (4):189-190.
    I extend Jones & Love's (J&L's) critique of Bayesian models and evaluate the conceptual foundations on which they are built. I argue that: (1) the part of Bayesian models is scientifically trivial; (2) theory is a fiction that arises from an inappropriate programming metaphor; and (3) the real scientific problems lie outside Bayesian theorizing.
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  10. Herbert Hoijtink Anouck Kluytmans, Rens van de Schoot, Joris Mulder (2012). Illustrating Bayesian Evaluation of Informative Hypotheses for Regression Models. Frontiers in Psychology 3.
    In the present paper we illustrate the Bayesian evaluation of informative hypotheses for regression models. This approach allows psychologists to more directly test their theories than they would using conventional statis- tical analyses. Throughout this paper, both real-world data and simulated datasets will be introduced and evaluated to investigate the pragmatical as well as the theoretical qualities of the approach. We will pave the way from forming informative hypotheses in the context of regression models to interpreting the Bayes factors that (...)
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  11. Arthur Isak Applbaum (2014). Bayesian Inference and Contractualist Justification on Interstate 95. In Andrew I. Cohen & Christopher H. Wellman (eds.), Contemporary Debates in Applied Ethics. Wiley Blackwell. 219.
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  12. Horacio Arló-Costa (2001). Bayesian Epistemology and Epistemic Conditionals: On the Status of the Export-Import Laws. Journal of Philosophy 98 (11):555-593.
    Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use.
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  13. Horacio Arlo-Costa, Bayesian Epistemology and Epistemic Conditionals: On the Status of the Export-Import Laws.
    The notion of probability occupies a central role in contemporary epistemology and cognitive science. Nevertheless, the classical notion of probability is hard to reconcile with the central notions postulated by the epistemological tradition.
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  14. Frank Arntzenius, Adam Elga & and John Hawthorne (2004). Bayesianism, Infinite Decisions, and Binding. Mind 113 (450):251-283.
    We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as ‘Trumped’ (Arntzenius and McCarthy 1997), ‘Rouble trouble’ (Arntzenius and Barrett 1999), ‘The airtight Dutch book’ (McGee 1999), and ‘The two envelopes puzzle’ (Broome 1999). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...)
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  15. David Atkinson & Jeanne Peijnenburg (2008). Reichenbach's Posits Reposited. Erkenntnis 69 (1):93 - 108.
    Reichenbach’s use of ‘posits’ to defend his frequentistic theory of probability has been criticized on the grounds that it makes unfalsifiable predictions. The justice of this criticism has blinded many to Reichenbach’s second use of a posit, one that can fruitfully be applied to current debates within epistemology. We show first that Reichenbach’s alternative type of posit creates a difficulty for epistemic foundationalists, and then that its use is equivalent to a particular kind of Jeffrey conditionalization. We conclude that, under (...)
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  16. Joseph L. Austerweil & Thomas L. Griffiths (2011). Seeking Confirmation Is Rational for Deterministic Hypotheses. Cognitive Science 35 (3):499-526.
    The tendency to test outcomes that are predicted by our current theory (the confirmation bias) is one of the best-known biases of human decision making. We prove that the confirmation bias is an optimal strategy for testing hypotheses when those hypotheses are deterministic, each making a single prediction about the next event in a sequence. Our proof applies for two normative standards commonly used for evaluating hypothesis testing: maximizing expected information gain and maximizing the probability of falsifying the current hypothesis. (...)
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  17. Peter C. Austin, Lawrence J. Brunner & Janet E. Hux Md Sm (2002). Bayeswatch: An Overview of Bayesian Statistics. Journal of Evaluation in Clinical Practice 8 (2):277-286.
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  18. Peter C. Austin, C. David Naylor & Jack V. Tu (2001). A Comparison of a Bayesian Vs. A Frequentist Method for Profiling Hospital Performance. Journal of Evaluation in Clinical Practice 7 (1):35-45.
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  19. Bengt Autzen (2011). Constraining Prior Probabilities of Phylogenetic Trees. Biology and Philosophy 26 (4):567-581.
    Although Bayesian methods are widely used in phylogenetic systematics today, the foundations of this methodology are still debated among both biologists and philosophers. The Bayesian approach to phylogenetic inference requires the assignment of prior probabilities to phylogenetic trees. As in other applications of Bayesian epistemology, the question of whether there is an objective way to assign these prior probabilities is a contested issue. This paper discusses the strategy of constraining the prior probabilities of phylogenetic trees by means of the Principal (...)
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  20. A. J. Ayer (1972). Probability and Evidence. [London]Macmillan.
  21. Andrew Backe (1999). The Likelihood Principle and the Reliability of Experiments. Philosophy of Science 66 (3):361.
    The likelihood principle of Bayesian statistics implies that information about the stopping rule used to collect evidence does not enter into the statistical analysis. This consequence confers an apparent advantage on Bayesian statistics over frequentist statistics. In the present paper, I argue that information about the stopping rule is nevertheless of value for an assessment of the reliability of the experiment, which is a pre-experimental measure of how well a contemplated procedure is expected to discriminate between hypotheses. I show that, (...)
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  22. Irina Baetu, Itxaso Barberia, Robin A. Murphy & A. G. Baker (2011). Maybe This Old Dinosaur Isn't Extinct: What Does Bayesian Modeling Add to Associationism? Behavioral and Brain Sciences 34 (4):190-191.
    We agree with Jones & Love (J&L) that much of Bayesian modeling has taken a fundamentalist approach to cognition; but we do not believe in the potential of Bayesianism to provide insights into psychological processes. We discuss the advantages of associative explanations over Bayesian approaches to causal induction, and argue that Bayesian models have added little to our understanding of human causal reasoning.
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  23. Arnold Baise, 20. “Objective Bayesian Probability”.
    The objective theory of probability of Richard von Mises has been criticized by Crovelli (2009), who defends a subjective approach. This paper attempts to clarify the different meanings of ‘objective’ and ‘subjective’ when applied to probability, and then argues for an objective Bayesian theory of probability, as exemplified in the writings [...].
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  24. Alexandru Baltag & Sonja Smets (2008). Probabilistic Dynamic Belief Revision. Synthese 165 (2):179 - 202.
    We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief (...)
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  25. Greg Bamford (1999). What is the Problem of Ad Hoc Hypotheses? Science and Education 8 (4):375 - 86..
    The received view of an ad hochypothesis is that it accounts for only the observation(s) it was designed to account for, and so non-ad hocness is generally held to be necessary or important for an introduced hypothesis or modification to a theory. Attempts by Popper and several others to convincingly explicate this view, however, prove to be unsuccessful or of doubtful value, and familiar and firmer criteria for evaluating the hypotheses or modified theories so classified are characteristically available. These points (...)
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  26. Prasanta S. Bandyopadhayay, Robert J. Boik & Prasun Basu (1996). The Curve Fitting Problem: A Bayesian Approach. Philosophy of Science 63 (3):272.
    In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes' theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory's goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the relationship (...)
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  27. Prasanta S. Bandyopadhyay & Robert J. Boik (1999). The Curve Fitting Problem: A Bayesian Rejoinder. Philosophy of Science 66 (3):402.
    In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit pull in opposite directions. To solve this problem, two proposals, the first one based on Bayes's theorem criterion (BTC) and the second one advocated by Forster and Sober based on Akaike's Information Criterion (AIC) are discussed. We show that AIC, which is frequentist in spirit, is logically equivalent to BTC, provided that a suitable choice of priors is made. We evaluate the charges against Bayesianism and contend that AIC approach (...)
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  28. Prasanta S. Bandyopadhyay & Malcolm Forster (eds.) (forthcoming). Philosophy of Statistics, Handbook of the Philosophy of Science, Volume 7. Elsevier.
  29. Jean Baratgin & Guy Politzer (2011). Updating: A Psychologically Basic Situation of Probability Revision. Thinking and Reasoning 16 (4):253-287.
    The Bayesian model has been used in psychology as the standard reference for the study of probability revision. In the first part of this paper we show that this traditional choice restricts the scope of the experimental investigation of revision to a stable universe. This is the case of a situation that, technically, is known as focusing. We argue that it is essential for a better understanding of human probability revision to consider another situation called updating (Katsuno & Mendelzon, 1992), (...)
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  30. Jean Baratgin & Guy Politzer (2007). The Psychology of Dynamic Probability Judgment: Order Effect, Normative Theories, and Experimental Methodology. Mind and Society 6 (1):53-66.
    The Bayesian model is used in psychology as the reference for the study of dynamic probability judgment. The main limit induced by this model is that it confines the study of revision of degrees of belief to the sole situations of revision in which the universe is static (revising situations). However, it may happen that individuals have to revise their degrees of belief when the message they learn specifies a change of direction in the universe, which is considered as changing (...)
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  31. Jean Baratgin & Guy Politzer (2006). Is the Mind Bayesian? The Case for Agnosticism. Mind and Society 5 (1):1-38.
    This paper aims to make explicit the methodological conditions that should be satisfied for the Bayesian model to be used as a normative model of human probability judgment. After noticing the lack of a clear definition of Bayesianism in the psychological literature and the lack of justification for using it, a classic definition of subjective Bayesianism is recalled, based on the following three criteria: an epistemic criterion, a static coherence criterion and a dynamic coherence criterion. Then it is shown that (...)
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  32. David James Barnett (2013). What's the Matter with Epistemic Circularity? Philosophical Studies:1-29.
    If the reliability of a source of testimony is open to question, it seems epistemically illegitimate to verify the source’s reliability by appealing to that source’s own testimony. Is this because it is illegitimate to trust a questionable source’s testimony on any matter whatsoever? Or is there a distinctive problem with appealing to the source’s testimony on the matter of that source’s own reliability? After distinguishing between two kinds of epistemically illegitimate circularity—bootstrapping and self-verification—I argue for a qualified version of (...)
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  33. Ernest S. Barratt (1984). Personality Traits: Causation, Correlation, or Neo-Bayesian. Behavioral and Brain Sciences 7 (3):435.
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  34. Jeffrey A. Barrett (1996). Oracles, Aesthetics, and Bayesian Consensus. Philosophy of Science 63 (3):280.
    In order for Bayesian inquiry to count as objective, one might argue that it must lead to a consensus among those who use it and share evidence, but presumably this is not enough. It has been proposed that one should also require that the consensus be reached from very different initial opinions by conditioning only on basic experimental evidence, evidence free from subjective, social, or psychological influence. I will argue here, however, that this notion of objectivity in Bayesian inquiry is (...)
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  35. Lawrence W. Barsalou (2011). Integrating Bayesian Analysis and Mechanistic Theories in Grounded Cognition. Behavioral and Brain Sciences 34 (4):191-192.
    Grounded cognition offers a natural approach for integrating Bayesian accounts of optimality with mechanistic accounts of cognition, the brain, the body, the physical environment, and the social environment. The constructs of simulator and situated conceptualization illustrate how Bayesian priors and likelihoods arise naturally in grounded mechanisms to predict and control situated action.
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  36. Thomas Bartelborth (2013). Sollten wir klassische Überzeugungssysteme durch bayesianische ersetzen? Logos 3:2--68.
    In der neueren Erkenntnistheorie wird der Bayesianismus immer populärer. In diesem Ansatz werden Überzeugungen mit Glaubensgraden versehen. Dazu möchte ich der Frage nachgehen, ob wir den klassischen Ansatz in der Erkennnistheorie mit seinen kategorischen Überzeugungen komplett durch einen bayesianischen mit einem probabilistischen Überzeugungssystem ersetzen könnten. Um das zu klären, rekonstruiere ich zunächst beide Modelle unserer Überzeugungssysteme und vergleiche sie dann im Hinblick darauf, wie leistungsfähig sie jeweils dafür sind, erkenntnistheoretische Probleme zu lösen und als Grundlage für Entscheidungen zu dienen. Dabei (...)
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  37. Thomas Bartelborth (2006). Is the Best Explaining Theory the Most Probable One? Grazer Philosophische Studien 70 (1):1-23.
    Opponents of inference to the best explanation often raise the objection that theories that give us the best explanation of some phenomena need not be the most probable ones. And they are certainly right. But what can we conclude from this insight? Should we ban abduction from theory choice and work instead, for example, with a Bayesian approach? This would be a mistake brought about by a certain misapprehension of the epistemological task. We have to think about the real aims (...)
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  38. Paul Bartha & Christopher Hitchcock (1999). No One Knows the Date or the Hour: An Unorthodox Application of Rev. Bayes's Theorem. Philosophy of Science 66 (3):353.
    Carter and Leslie (1996) have argued, using Bayes's theorem, that our being alive now supports the hypothesis of an early 'Doomsday'. Unlike some critics (Eckhardt 1997), we accept their argument in part: given that we exist, our existence now indeed favors 'Doom sooner' over 'Doom later'. The very fact of our existence, however, favors 'Doom later'. In simple cases, a hypothetical approach to the problem of 'old evidence' shows that these two effects cancel out: our existence now yields no information (...)
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  39. Gordon Belot, Mark J. Schervish, Teddy Seidenfeld, Joseph B. Kadane, Miles MacLeod, Nancy J. Nersessian, Hylarie Kochiras, Bryan W. Roberts, Elay Shech & Richard Healey (2013). 1. Bayesian Orgulity Bayesian Orgulity (Pp. 483-503). Philosophy of Science 80 (4).
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  40. Paola Berchialla, Francesca Foltran, Riccardo Bigi & Dario Gregori (2012). Integrating Stress‐Related Ventricular Functional and Angiographic Data in Preventive Cardiology: A Unified Approach Implementing a Bayesian Network. Journal of Evaluation in Clinical Practice 18 (3):637-643.
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  41. Hans Van Den Berg, Dick Hoekzema & Hans Radder (1990). Accardi on Quantum Theory and the "Fifth Axiom" of Probability. Philosophy of Science 57 (1):149 - 157.
    In this paper we investigate Accardi's claim that the "quantum paradoxes" have their roots in probability theory and that, in particular, they can be evaded by giving up Bayes' rule, concerning the relation between composite and conditional probabilities. We reach the conclusion that, although it may be possible to give up Bayes' rule and define conditional probabilities differently, this contributes nothing to solving the philosophical problems which surround quantum mechanics.
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  42. James Berger (1995). Discussion of David Freedman's “Some Issues in the Foundations of Statistics”. Foundations of Science 1 (1):41-67.
    While results from statistical modelling too often receive blind acceptance, we question whether there is any real alternative to use of modelling. This does not diminish the main point of Professor Freedman, which is that healthy scepticism towards models is needed. While agreeing with many of Professor Freedman's points concerning the objectivist debate, we argue that there is a Bayesian school of objectivists that possesses considerable advantages over the classical objectivist school. At the least, the debate needs to be enlarged (...)
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  43. Zackary Berger (2010). Bayesian and Frequentist Models: Legitimate Choices for Different Purposes of Clinical Research. Journal of Evaluation in Clinical Practice 16 (6):1045-1047.
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  44. José Luis Bermúdez (2011). Decision Theory and Rationality. OUP Oxford.
    The concept of rationality is a common thread through the human and social sciences -- from political science to philosophy, from economics to sociology, and from management science to decision analysis. But what counts as rational action and rational behavior? José Luis Bermúdez explores decision theory as a theory of rationality. Decision theory is the mathematical theory of choice and for many social scientists it makes the concept of rationality mathematically tractable and scientifically legitimate. Yet rationality is a concept with (...)
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  45. Bénédicte Bes, Steven Sloman, Christopher G. Lucas & Éric Raufaste (2012). Non-Bayesian Inference: Causal Structure Trumps Correlation. Cognitive Science 36 (7):1178-1203.
    The study tests the hypothesis that conditional probability judgments can be influenced by causal links between the target event and the evidence even when the statistical relations among variables are held constant. Three experiments varied the causal structure relating three variables and found that (a) the target event was perceived as more probable when it was linked to evidence by a causal chain than when both variables shared a common cause; (b) predictive chains in which evidence is a cause of (...)
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  46. Pierre Bessière (forthcoming). Common Bayesian Models for Common Cognitive Issues. Acta Biotheoretica.
    How can an incomplete and uncertain model of the environment be used to perceive, infer, decide and act efficiently? This is the challenge that both living and artificial cognitive systems have to face. Symbolic logic is, by its nature, unable to deal with this question. The subjectivist approach to probability is an extension to logic that is designed specifically to face this challenge. In this paper, we review a number of frequently encountered cognitive issues and cast them into a common (...)
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  47. Gregor Betz (2013). Degrees of Justification, Bayes’ Rule, and Rationality. In Frank Zenker (ed.), Bayesian Argumentation – The Practical Side of Probability. Springer.
    Based on the theory of dialectical structures, I review the concept of degree of justification of a partial position a proponent may hold in a controversial debate. The formal concept of degree of justification dovetails with our pre-theoretic intuitions about a thesis' strength of justification. The central claim I'm going to defend in this paper maintains that degrees of justification, as defined within the theory of dialectical structures, correlate with a proponent position's verisimilitude. I vindicate this thesis with the results (...)
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  48. Gregor Betz (2013). Revamping Hypothetico-Deductivism: A Dialectic Account of Confirmation. [REVIEW] Erkenntnis 78 (5):991-1009.
    We use recently developed approaches in argumentation theory in order to revamp the hypothetico-deductive model of confirmation, thus alleviating the well-known paradoxes the H-D account faces. More specifically, we introduce the concept of dialectic confirmation on the background of the so-called theory of dialectical structures (Betz 2010, 2012b). Dialectic confirmation generalises hypothetico-deductive confirmation and mitigates the raven paradox, the grue paradox, the tacking paradox, the paradox from conceptual difference, and the problem of surprising evidence.
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