Results for 'causal Bayes nets'

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  1. A causal Bayes net analysis of dispositions.Alexander Gebharter & Florian Fischer - 2021 - Synthese 198 (5):4873-4895.
    In this paper we develop an analysis of dispositions by means of causal Bayes nets. In particular, we analyze dispositions as cause-effect structures that increase the probability of the manifestation when the stimulus is brought about by intervention in certain circumstances. We then highlight several advantages of our analysis and how it can handle problems arising for classical analyses of dispositions such as masks, mimickers, and finks.
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  2.  73
    Causal Bayes nets as psychological theories of causal reasoning: evidence from psychological research.York Hagmayer - 2016 - Synthese 193 (4):1107-1126.
    Causal Bayes nets have been developed in philosophy, statistics, and computer sciences to provide a formalism to represent causal structures, to induce causal structure from data and to derive predictions. Causal Bayes nets have been used as psychological theories in at least two ways. They were used as rational, computational models of causal reasoning and they were used as formal models of mental causal models. A crucial assumption made by them (...)
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  3. A Causal Bayes Net Analysis of Glennan’s Mechanistic Account of Higher-Level Causation.Alexander Gebharter - 2022 - British Journal for the Philosophy of Science 73 (1):185-210.
    One of Stuart Glennan's most prominent contributions to the new mechanist debate consists in his reductive analysis of higher-level causation in terms of mechanisms (Glennan, 1996). In this paper I employ the causal Bayes net framework to reconstruct his analysis. This allows for specifying general assumptions which have to be satis ed to get Glennan's approach working. I show that once these assumptions are in place, they imply (against the background of the causal Bayes net machinery) (...)
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  4.  56
    Causal Bayes nets and token-causation: Closing the gap between token-level and type-level.Alexander Gebharter & Andreas Hüttemann - forthcoming - Erkenntnis:1-23.
    Causal Bayes nets (CBNs) provide one of the most powerful tools for modelling coarse-grained type-level causal structure. As in other fields (e.g., thermodynamics) the question arises how such coarse-grained characterisations are related to the characterisation of their underlying structure (in this case: token-level causal relations). Answering this question meets what is called a “coherence-requirement” in the reduction debate: How are different accounts of one and the same system (or kind of system) related to each other. (...)
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  5.  75
    Combining causal Bayes nets and cellular automata: A hybrid modelling approach to mechanisms.Alexander Gebharter & Daniel Koch - 2021 - British Journal for the Philosophy of Science 72 (3):839-864.
    Causal Bayes nets (CBNs) can be used to model causal relationships up to whole mechanisms. Though modelling mechanisms with CBNs comes with many advantages, CBNs might fail to adequately represent some biological mechanisms because—as Kaiser (2016) pointed out—they have problems with capturing relevant spatial and structural information. In this paper we propose a hybrid approach for modelling mechanisms that combines CBNs and cellular automata. Our approach can incorporate spatial and structural information while, at the same time, (...)
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  6. Causal Exclusion and Causal Bayes Nets.Alexander Gebharter - 2017 - Philosophy and Phenomenological Research 95 (2):353-375.
    In this paper I reconstruct and evaluate the validity of two versions of causal exclusion arguments within the theory of causal Bayes nets. I argue that supervenience relations formally behave like causal relations. If this is correct, then it turns out that both versions of the exclusion argument are valid when assuming the causal Markov condition and the causal minimality condition. I also investigate some consequences for the recent discussion of causal exclusion (...)
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  7. Learning, prediction and causal Bayes nets.Clark Glymour - 2003 - Trends in Cognitive Sciences 7 (1):43-48.
  8.  74
    From colliding billiard balls to colluding desperate housewives: causal Bayes nets as rational models of everyday causal reasoning.York Hagmayer & Magda Osman - 2012 - Synthese 189 (S1):17-28.
    Many of our decisions pertain to causal systems. Nevertheless, only recently has it been claimed that people use causal models when making judgments, decisions and predictions, and that causal Bayes nets allow us to formally describe these inferences. Experimental research has been limited to simple, artificial problems, which are unrepresentative of the complex dynamic systems we successfully deal with in everyday life. For instance, in social interactions, we can explain the actions of other's on the (...)
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  9.  16
    Bayes nets and graphical causal models in psychology.Clark Glymour - unknown
    These are chapters from a book forthcoming from MIT Press. Comments to the author at [email protected] would be most welcome. Still time for changes.
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  10.  20
    The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology.C. Hitchcock - 2003 - Erkenntnis 59 (1):136-140.
  11. A Theory of Causal Learning in Children: Causal Maps and Bayes Nets.Alison Gopnik, Clark Glymour, Laura Schulz, Tamar Kushnir & David Danks - 2004 - Psychological Review 111 (1):3-32.
    We propose that children employ specialized cognitive systems that allow them to recover an accurate “causal map” of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or “Bayes nets”. Children’s causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with (...)
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  12.  33
    Causal maps and Bayes nets: A cognitive and computational account of theory-formation.Alison Gopnik & Clark Glymour - 2002 - In Peter Carruthers, Stephen P. Stich & Michael Siegal (eds.), The Cognitive Basis of Science. Cambridge University Press. pp. 117--132.
  13. Causal inference. How can Bayes nets contribute?Isabelle Drouet - 2007 - In Federica Russo & Jon Williamson (eds.), Causality and Probability in the Sciences. pp. 487--501.
  14.  16
    The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology. [REVIEW]C. Hitchcock - 2003 - Mind 112 (446):340-343.
  15. Causal learning in children: Causal maps and Bayes nets.Alison Gopnik, Clark Glymour, David M. Sobel & Laura E. Schultz - unknown
    We outline a cognitive and computational account of causal learning in children. We propose that children employ specialized cognitive systems that allow them to recover an accurate “causal map” of the world: an abstract, coherent representation of the causal relations among events. This kind of knowledge can be perspicuously represented by the formalism of directed graphical causal models, or “Bayes nets”. Human causal learning and inference may involve computations similar to those for learnig (...)
     
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  16. What Is Wrong With Bayes Nets?Nancy Cartwright - 2001 - The Monist 84 (2):242-264.
    Probability is a guide to life partly because it is a guide to causality. Work over the last two decades using Bayes nets supposes that probability is a very sure guide to causality. I think not, and I shall argue that here. Almost all the objections I list are well-known. But I have come to see them in a different light by reflecting again on the original work in this area by Wolfgang Spohn and his recent defense of (...)
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  17.  15
    The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology. [REVIEW]Christopher Hitchcock - 2003 - Mind 112 (446):340-343.
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  18. What is right with 'bayes net methods' and what is wrong with 'hunting causes and using them'?Clark Glymour - 2010 - British Journal for the Philosophy of Science 61 (1):161-211.
    Nancy Cartwright's recent criticisms of efforts and methods to obtain causal information from sample data using automated search are considered. In addition to reviewing that effort, I argue that almost all of her criticisms are false and rest on misreading, overgeneralization, or neglect of the relevant literature.
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  19.  26
    Clark Glymour, The Mind’s Arrows: Bayes Nets and Graphical Causal Models in Psychology. Cambridge, MA: MIT Press , 240 pp., $30.00. [REVIEW]Charles Twardy - 2005 - Philosophy of Science 72 (3):494-498.
  20.  85
    Review: The mind's arrows: Bayes nets and graphical causal models in psychology. [REVIEW]Christopher Hitchcock - 2003 - Mind 112 (446):340-343.
  21.  10
    Causal Models and Screening‐Off.Juhwa Park & Steven A. Sloman - 2016 - In Justin Sytsma & Wesley Buckwalter (eds.), A Companion to Experimental Philosophy. Malden, MA: Wiley. pp. 450–462.
    This chapter explains the screening‐off rule in the psychological laboratory. The Markov assumption states that any variable in a set is independent in probability of all its ancestors in the set conditional on its own parents. The screening‐off rule is also critical to allow Bayes nets to make an inference of the state of an unknown variable in a causal structure from the states of other variables in that structure. The chapter examines which causal representations people (...)
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  22. The causal problem of entanglement.Paul M. Näger - 2016 - Synthese 193 (4):1127-1155.
    This paper expounds that besides the well-known spatio-temporal problem there is a causal problem of entanglement: even when one neglects spatio-temporal constraints, the peculiar statistics of EPR/B experiment is inconsistent with usual principles of causal explanation as stated by the theory of causal Bayes nets. The conflict amounts to a dilemma that either there are uncaused correlations or there are caused independences . I argue that the central ideas of causal explanations can be saved (...)
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  23. Causal exclusion without physical completeness and no overdetermination.Alexander Gebharter - 2017 - Abstracta 10:3-14.
    Hitchcock demonstrated that the validity of causal exclusion arguments as well as the plausibility of several of their premises hinges on the specific theory of causation endorsed. In this paper I show that the validity of causal exclusion arguments—if represented within the theory of causal Bayes nets the way Gebharter suggests—actually requires much weaker premises than the ones which are typically assumed. In particular, neither completeness of the physical domain nor the no overdetermination assumption are (...)
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  24.  35
    Agents and Causes: Dispositional Intuitions As a Guide to Causal Structure.Ralf Mayrhofer & Michael R. Waldmann - 2015 - Cognitive Science 39 (1):65-95.
    Currently, two frameworks of causal reasoning compete: Whereas dependency theories focus on dependencies between causes and effects, dispositional theories model causation as an interaction between agents and patients endowed with intrinsic dispositions. One important finding providing a bridge between these two frameworks is that failures of causes to generate their effects tend to be differentially attributed to agents and patients regardless of their location on either the cause or the effect side. To model different types of error attribution, we (...)
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  25.  80
    Green and grue causal variables.Frederick Eberhardt - 2016 - Synthese 193 (4).
    The causal Bayes net framework specifies a set of axioms for causal discovery. This article explores the set of causal variables that function as relata in these axioms. Spirtes showed how a causal system can be equivalently described by two different sets of variables that stand in a non-trivial translation-relation to each other, suggesting that there is no “correct” set of causal variables. I extend Spirtes’ result to the general framework of linear structural equation (...)
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  26.  56
    Two causal theories of counterfactual conditionals.Lance J. Rips - 2010 - Cognitive Science 34 (2):175-221.
    Bayes nets are formal representations of causal systems that many psychologists have claimed as plausible mental representations. One purported advantage of Bayes nets is that they may provide a theory of counterfactual conditionals, such as If Calvin had been at the party, Miriam would have left early. This article compares two proposed Bayes net theories as models of people's understanding of counterfactuals. Experiments 1-3 show that neither theory makes correct predictions about backtracking counterfactuals (in (...)
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  27. Why adoption of causal modeling methods requires some metaphysics.Holly Andersen - 2023 - In Federica Russo (ed.), Routledge Handbook of Causality and Causal Methods,. Routledge.
    I highlight a metaphysical concern that stands in the way of more widespread adoption of causal modeling techniques such as causal Bayes nets. Researchers in some fields may resist adoption due to concerns that they don't 'really' understand what they are saying about a system when they apply such techniques. Students in these fields are repeated exhorted to be cautious about application of statistical techniques to their data without a clear understanding of the conditions required for (...)
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  28.  48
    Inferring Hidden Causal Structure.Tamar Kushnir, Alison Gopnik, Chris Lucas & Laura Schulz - 2010 - Cognitive Science 34 (1):148-160.
    We used a new method to assess how people can infer unobserved causal structure from patterns of observed events. Participants were taught to draw causal graphs, and then shown a pattern of associations and interventions on a novel causal system. Given minimal training and no feedback, participants in Experiment 1 used causal graph notation to spontaneously draw structures containing one observed cause, one unobserved common cause, and two unobserved independent causes, depending on the pattern of associations (...)
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  29.  84
    Counterfactuals and Causal Models: Introduction to the Special Issue.Steven A. Sloman - 2013 - Cognitive Science 37 (6):969-976.
    Judea Pearl won the 2010 Rumelhart Prize in computational cognitive science due to his seminal contributions to the development of Bayes nets and causal Bayes nets, frameworks that are central to multiple domains of the computational study of mind. At the heart of the causal Bayes nets formalism is the notion of a counterfactual, a representation of something false or nonexistent. Pearl refers to Bayes nets as oracles for intervention, and (...)
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  30.  73
    Causal concepts and temporal ordering.Reuben Stern - 2019 - Synthese 198 (Suppl 27):6505-6527.
    Though common sense says that causes must temporally precede their effects, the hugely influential interventionist account of causation makes no reference to temporal precedence. Does common sense lead us astray? In this paper, I evaluate the power of the commonsense assumption from within the interventionist approach to causal modeling. I first argue that if causes temporally precede their effects, then one need not consider the outcomes of interventions in order to infer causal relevance, and that one can instead (...)
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  31.  38
    Imprecise Bayesian Networks as Causal Models.David Kinney - 2018 - Information 9 (9):211.
    This article considers the extent to which Bayesian networks with imprecise probabilities, which are used in statistics and computer science for predictive purposes, can be used to represent causal structure. It is argued that the adequacy conditions for causal representation in the precise context—the Causal Markov Condition and Minimality—do not readily translate into the imprecise context. Crucial to this argument is the fact that the independence relation between random variables can be understood in several different ways when (...)
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  32.  35
    Dynamical Causal Learning.David Danks, Thomas L. Griffiths & Joshua B. Tenenbaum - unknown
    Current psychological theories of human causal learning and judgment focus primarily on long-run predictions: two by estimating parameters of a causal Bayes nets, and a third through structural learning. This paper focuses on people’s short-run behavior by examining dynamical versions of these three theories, and comparing their predictions to a real-world dataset.
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  33. A comparison of three Occam’s razors for Markovian causal models.Jiji Zhang - 2013 - British Journal for the Philosophy of Science 64 (2):423-448.
    The framework of causal Bayes nets, currently influential in several scientific disciplines, provides a rich formalism to study the connection between causality and probability from an epistemological perspective. This article compares three assumptions in the literature that seem to constrain the connection between causality and probability in the style of Occam's razor. The trio includes two minimality assumptions—one formulated by Spirtes, Glymour, and Scheines (SGS) and the other due to Pearl—and the more well-known faithfulness or stability assumption. (...)
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  34.  41
    Causal Discovery and the Problem of Ignorance. An Adaptive Logic Approach.Bert Leuridan - 2009 - Journal of Applied Logic 7 (2):188-205.
    In this paper, I want to substantiate three related claims regarding causal discovery from non-experimental data. Firstly, in scientific practice, the problem of ignorance is ubiquitous, persistent, and far-reaching. Intuitively, the problem of ignorance bears upon the following situation. A set of random variables V is studied but only partly tested for (conditional) independencies; i.e. for some variables A and B it is not known whether they are (conditionally) independent. Secondly, Judea Pearl’s most meritorious and influential algorithm for (...) discovery (the IC algorithm) cannot be applied in cases of ignorance. It presupposes that a full list of (conditional) independence relations is on hand and it would lead to unsatisfactory results when applied to partial lists. Finally, the problem of ignorance is successfully treated by means of ALIC, the adaptive logic for causal discovery presented in this paper. (shrink)
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  35.  31
    Another Counterexample to Markov Causation from Quantum Mechanics: Single Photon Experiments and the Mach-Zehnder Interferometer.Nina Retzlaff - 2017 - Kriterion - Journal of Philosophy 31 (2):17-42.
    The theory of causal Bayes nets [15, 19] is, from an empirical point of view, currently one of the most promising approaches to causation on the market. There are, however, counterexamples to its core axiom, the causal Markov condition. Probably the most serious of these counterexamples are EPR/B experiments in quantum mechanics (cf. [13, 23]). However, these are also the only counterexamples yet known from the quantum realm. One might therefore wonder whether they are the only (...)
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  36.  57
    Unification and explanation from a causal perspective.Alexander Gebharter & Christian J. Feldbacher-Escamilla - 2023 - Studies in History and Philosophy of Science Part A 99 (C):28-36.
    We discuss two influential views of unification: mutual information unification (MIU) and common origin unification (COU). We propose a simple probabilistic measure for COU and compare it with Myrvold’s (2003, 2017) probabilistic measure for MIU. We then explore how well these two measures perform in simple causal settings. After highlighting several deficiencies, we propose causal constraints for both measures. A comparison with explanatory power shows that the causal version of COU is one step ahead in simple (...) settings. However, slightly increasing the complexity of the underlying causal structure shows that both measures can easily disagree with explanatory power. The upshot of this is that even sophisticated causally constrained measures for unification ultimately fail to track explanatory relevance. This shows that unification and explanation are not as closely related as many philosophers thought. (shrink)
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  37.  58
    The supposed competition between theories of human causal inference.David Danks - 2005 - Philosophical Psychology 18 (2):259 – 272.
    Newsome ((2003). The debate between current versions of covariation and mechanism approaches to causal inference. Philosophical Psychology, 16, 87-107.) recently published a critical review of psychological theories of human causal inference. In that review, he characterized covariation and mechanism theories, the two dominant theory types, as competing, and offered possible ways to integrate them. I argue that Newsome has misunderstood the theoretical landscape, and that covariation and mechanism theories do not directly conflict. Rather, they rely on distinct sets (...)
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  38. The Structure of Scientific Theories, Explanation, and Unification. A Causal–Structural Account.Bert Leuridan - 2014 - British Journal for the Philosophy of Science 65 (4):717-771.
    What are scientific theories and how should they be represented? In this article, I propose a causal–structural account, according to which scientific theories are to be represented as sets of interrelated causal and credal nets. In contrast with other accounts of scientific theories (such as Sneedian structuralism, Kitcher’s unificationist view, and Darden’s theory of theoretical components), this leaves room for causality to play a substantial role. As a result, an interesting account of explanation is provided, which sheds (...)
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  39. Measuring causal interaction in bayesian networks.Charles Twardy - manuscript
    Artificial Intelligence (AI) and Philosophy of Science share a fundamental problem—understanding causality. Bayesian networks have recently been used by Judea Pearl in a new approach to understanding causality (Pearl, 2000). Part of understanding causality is understanding causal interaction. Bayes nets can represent any degree of causal interaction, and researchers normally try to limit interactions, usually by replacing the full CPT with a noisy-OR function. But we show that noisy-OR and another common model are merely special cases (...)
     
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  40.  95
    How Occam's razor provides a neat definition of direct causation.Alexander Gebharter & Gerhard Schurz - 2014 - In J. M. Mooij, D. Janzing, J. Peters, T. Claassen & A. Hyttinen (eds.), Proceedings of the UAI Workshop Causal Inference: Learning and Prediction. CEUR-WS. pp. 1-10.
    In this paper we show that the application of Occam’s razor to the theory of causal Bayes nets gives us a neat definition of direct causation. In particular we show that Occam’s razor implies Woodward’s (2003) definition of direct causation, provided suitable intervention variables exist and the causal Markov condition (CMC) is satisfied. We also show how Occam’s razor can account for direct causal relationships Woodward style when only stochastic intervention variables are available.
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  41.  58
    Teaching the normative theory of causal reasoning.Richard Scheines, Matt Easterday & David Danks - 2007 - In Alison Gopnik & Laura Schulz (eds.), Causal Learning: Psychology, Philosophy, and Computation. Oxford University Press. pp. 119--38.
    There is now substantial agreement about the representational component of a normative theory of causal reasoning: Causal Bayes Nets. There is less agreement about a normative theory of causal discovery from data, either computationally or cognitively, and almost no work investigating how teaching the Causal Bayes Nets representational apparatus might help individuals faced with a causal learning task. Psychologists working to describe how naïve participants represent and learn causal structure from (...)
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  42.  29
    Suppes’ probabilistic theory of causality and causal inference in economics.Julian Reiss - 2016 - Journal of Economic Methodology 23 (3):289-304.
    This paper examines Patrick Suppes’ probabilistic theory of causality understood as a theory of causal inference, and draws some lessons for empirical economics and contemporary debates in the foundations of econometrics. It argues that a standard method of empirical economics, multiple regression, is inadequate for most but the simplest applications, that the Bayesnets approach, which can be understood as a generalisation of Suppes’ theory, constitutes a considerable improvement but is still subject to important limitations, and that (...)
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  43. Conditionals and the Hierarchy of Causal Queries.Niels Skovgaard-Olsen, Simon Stephan & Michael R. Waldmann - 2021 - Journal of Experimental Psychology: General 1 (12):2472-2505.
    Recent studies indicate that indicative conditionals like "If people wear masks, the spread of Covid-19 will be diminished" require a probabilistic dependency between their antecedents and consequents to be acceptable (Skovgaard-Olsen et al., 2016). But it is easy to make the slip from this claim to the thesis that indicative conditionals are acceptable only if this probabilistic dependency results from a causal relation between antecedent and consequent. According to Pearl (2009), understanding a causal relation involves multiple, hierarchically organized (...)
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  44.  99
    Structural Decision Theory.Tung-Ying Wu - 2021 - Philosophy of Science 88 (5):951-960.
    Judging an act’s causal efficacy plays a crucial role in causal decision theory. A recent development appeals to the causal modeling framework with an emphasis on the analysis of intervention based on the causal Bayes net for clarifying what causally depends on our acts. However, few writers have focused on exploring the usefulness of extending structural causal models to decision problems that are not ideal for intervention analysis. The thesis concludes that structural models provide (...)
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  45.  52
    Concrete Causation: About the Structures of Causal Knowledge.Roland Poellinger - 2012 - Dissertation, Lmu Munich
    Concrete Causation centers about theories of causation, their interpretation, and their embedding in metaphysical-ontological questions, as well as the application of such theories in the context of science and decision theory. The dissertation is divided into four chapters, that firstly undertake the historical-systematic localization of central problems (chapter 1) to then give a rendition of the concepts and the formalisms underlying David Lewis' and Judea Pearl's theories (chapter 2). After philosophically motivated conceptual deliberations Pearl's mathematical-technical framework is drawn on for (...)
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  46.  53
    Bayesian Networks and Causal Ecumenism.David Kinney - 2020 - Erkenntnis 88 (1):147-172.
    Proponents of various causal exclusion arguments claim that for any given event, there is often a unique level of granularity at which that event is caused. Against these causal exclusion arguments, causal ecumenists argue that the same event or phenomenon can be caused at multiple levels of granularity. This paper argues that the Bayesian network approach to representing the causal structure of target systems is consistent with causal ecumenism. Given the ubiquity of Bayesian networks as (...)
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  47.  26
    Sufficiency and Necessity Assumptions in Causal Structure Induction.Ralf Mayrhofer & Michael R. Waldmann - 2016 - Cognitive Science 40 (8):2137-2150.
    Research on human causal induction has shown that people have general prior assumptions about causal strength and about how causes interact with the background. We propose that these prior assumptions about the parameters of causal systems do not only manifest themselves in estimations of causal strength or the selection of causes but also when deciding between alternative causal structures. In three experiments, we requested subjects to choose which of two observable variables was the cause and (...)
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  48.  65
    Bayes Nets and Rationality.Stephan Hartmann - 2021 - In The Handbook of Rationality. Boston, Massachusetts, USA:
    Bayes nets are a powerful tool for researchers in statistics and artificial intelligence. This chapter demonstrates that they are also of much use for philosophers and psychologists interested in (Bayesian) rationality. To do so, we outline the general methodology of Bayes nets modeling in rationality research and illustrate it with several examples from the philosophy and psychology of reasoning and argumentation. Along the way, we discuss the normative foundations of Bayes nets modeling and address (...)
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  49.  68
    Combining argumentation and bayesian nets for breast cancer prognosis.Matt Williams & Jon Williamson - 2006 - Journal of Logic, Language and Information 15 (1-2):155-178.
    We present a new framework for combining logic with probability, and demonstrate the application of this framework to breast cancer prognosis. Background knowledge concerning breast cancer prognosis is represented using logical arguments. This background knowledge and a database are used to build a Bayesian net that captures the probabilistic relationships amongst the variables. Causal hypotheses gleaned from the Bayesian net in turn generate new arguments. The Bayesian net can be queried to help decide when one argument attacks another. The (...)
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  50. From metaphysics to method: Comments on manipulability and the causal Markov condition.Nancy Cartwright - 2006 - British Journal for the Philosophy of Science 57 (1):197-218.
    Daniel Hausman and James Woodward claim to prove that the causal Markov condition, so important to Bayes-nets methods for causal inference, is the ‘flip side’ of an important metaphysical fact about causation—that causes can be used to manipulate their effects. This paper disagrees. First, the premise of their proof does not demand that causes can be used to manipulate their effects but rather that if a relation passes a certain specific kind of test, it is (...). Second, the proof is invalid. Third, the kind of testability they require can easily be had without the causal Markov condition. Introduction Earlier views: manipulability v testability Increasingly weaker theses The proof is invalid MOD* is implausible Two alternative claims and their defects A true claim and a valid argument Indeterminism Overall conclusion. (shrink)
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