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109EnviroGenomarkers: The Interplay Between Mechanisms and Difference Making in Establishing Causal ClaimsMedicine Studies 3 (4): 249-262. 2012.According to Russo and Williamson (Int Stud Philos Sci 21(2):157–170, 2007, Hist Philos Life Sci 33:389–396, 2011a, Philos Sci 1(1):47–69, 2011b ), in order to establish a causal claim of the form, ‘_C_ is a cause of _E_’, one typically needs evidence that there is an underlying mechanism between _C_ and _E_ as well as evidence that _C_ makes a difference to _E_. This thesis has been used to argue that hierarchies of evidence, as championed by evidence-based movements, tend to give primacy to ev…Read more
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42This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general.
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23This paper addresses the problem of finding a Bayesian net representation of the probability function that agrees with the distributions of multiple consistent datasets and otherwise has maximum entropy. We give a general algorithm which is significantly more efficient than the standard brute-force approach. Furthermore, we show that in a wide range of cases such a Bayesian net can be obtained without solving any optimisation problem.
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56Evidence can be complex in various ways: e.g., it may exhibit structural complexity, containing information about causal, hierarchical or logical structure as well as empirical data, or it may exhibit combinatorial complexity, containing a complex combination of kinds of information. This paper examines evidential complexity from the point of view of Bayesian epistemology, asking: how should complex evidence impact on an agent’s degrees of belief? The paper presents a high-level overview of an o…Read more
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78Mechanistic Theories of Causality Part IPhilosophy Compass 6 (6): 421-432. 2011.Part I of this paper introduces a range of mechanistic theories of causality, including process theories and the complex-systems theories, and some of the problems they face. Part II argues that while there is a decisive case against a purely mechanistic analysis, a viable theory of causality must incorporate mechanisms as an ingredient, and describes one way of providing an analysis of causality which reaps the rewards of the mechanistic approach without succumbing to its pitfalls
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103Causality in the sciences (edited book)Oxford University Press. 2011.The book tackles these questions as well as others concerning the use of causality in the sciences.
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86Calibration and Convexity: Response to Gregory WheelerBritish Journal for the Philosophy of Science 63 (4): 851-857. 2012.This note responds to some criticisms of my recent book In Defence of Objective Bayesianism that were provided by Gregory Wheeler in his ‘Objective Bayesian Calibration and the Problem of Non-convex Evidence’
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29Logical relations in a statistical problemIn Benedikt Lowe, Jan-Willem Romeijn & Eric Pacuit (eds.), Foundations of the Formal Sciences Vi: Probabilistic Reasoning and Reasoning With Probabilities. Studies in Logic, College Publications. 2008.This paper presents the progicnet programme. It proposes a general framework for probabilistic logic that can guide inference based on both logical and probabilistic input. After an introduction to the framework as such, it is illustrated by means of a toy example from psychometrics. It is shown that the framework can accommodate a number of approaches to probabilistic reasoning: Bayesian statistical inference, evidential probability, probabilistic argumentation, and objective Bayesianism. The f…Read more
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217Modelling mechanisms with causal cyclesSynthese 191 (8): 1-31. 2014.Mechanistic philosophy of science views a large part of scientific activity as engaged in modelling mechanisms. While science textbooks tend to offer qualitative models of mechanisms, there is increasing demand for models from which one can draw quantitative predictions and explanations. Casini et al. (Theoria 26(1):5–33, 2011) put forward the Recursive Bayesian Networks (RBN) formalism as well suited to this end. The RBN formalism is an extension of the standard Bayesian net formalism, an exten…Read more
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32How should we reason with causal relationships? Much recent work on this question has been devoted to the theses (i) that Bayesian nets provide a calculus for causal reasoning and (ii) that we can learn causal relationships by the automated learning of Bayesian nets from observational data. The aim of this book is to..
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47Inductive Influence (review)British Journal for the Philosophy of Science 58 (4): 689-708. 2007.Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief 12 to the next raven being black, however many other black ravens have been observed. I argue that this objection can be overcome by appealing to objective Bayesian nets, a formalism for representing objective Bayesian degrees of belief. Under this account, previous observations exert an inductive influence on the next observation. I show how this approach c…Read more
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4Metabolism is a set of chemical reactions, used by living organisms to process chemical compounds in order to take energy and eliminate toxic compounds, for example. Its processes are referred as metabolic pathways. Understanding metabolism is imperative to biology, toxicology and medicine, but the number and complexity of metabolic pathways makes this a difficult task. In our paper, we investigate the use of causal Bayesian networks to model the pathways of yeast saccharomyces cerevisiae metabo…Read more
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132A dynamic interaction between machine learning and the philosophy of scienceMinds and Machines 14 (4): 539-549. 2004.The relationship between machine learning and the philosophy of science can be classed as a dynamic interaction: a mutually beneficial connection between two autonomous fields that changes direction over time. I discuss the nature of this interaction and give a case study highlighting interactions between research on Bayesian networks in machine learning and research on causality and probability in the philosophy of science
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41Foundations for Bayesian networksIn David Corfield & Jon Williamson (eds.), Foundations of Bayesianism, Kluwer Academic Publishers. pp. 75--115. 2001.Bayesian networks may either be treated purely formally or be given an interpretation. I argue that current foundations are problematic, and put forward new foundations which involve aspects of both the interpreted and the formal approaches
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10this paper we argue that the formalism can also be applied to modelling the hierarchical structure of physical 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 are vital for prediction, explanation and control respectively, a recursive Bayesian net can be applied to all these tasks. We show how a Recurs…Read more
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94Investigation of the use of intervention data in estimating parameters in a Bayesian network
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78This paper develops connections between objective Bayesian epistemology—which holds that the strengths of an agent’s beliefs should be representable by probabilities, should be calibrated with evidence of empirical probability, and should otherwise be equivocal—and probabilistic logic. After introducing objective Bayesian epistemology over propositional languages, the formalism is extended to handle predicate languages. A rather general probabilistic logic is formulated and then given a natural …Read more
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Why look at Causality in the Sciences?In Phyllis McKay Illari, Federica Russo & Jon Williamson (eds.), Causality in the Sciences, Oxford University Press. 2011.
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151Dispositional versus epistemic causalityMinds and Machines 16 (3): 259-276. 2006.I put forward several desiderata that a philosophical theory of causality should satisfy: it should account for the objectivity of causality, it should underpin formalisms for causal reasoning, it should admit a viable epistemology, it should be able to cope with the great variety of causal claims that are made, and it should be ontologically parsimonious. I argue that Nancy Cartwright’s dispositional account of causality goes part way towards meeting these criteria but is lacking in important r…Read more
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103Kyburg goes half-way towards objective Bayesianism. He accepts that frequencies constrain rational belief to an interval but stops short of isolating an optimal degree of belief within this interval. I examine the case for going the whole hog.
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40While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches to probabilistic logic into a simple unifying framework: logically complex evidence can be used to associate probability intervals or probabilities with sentences.
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106This chapter addresses two questions: what are causal relationships? how can one discover causal relationships? I provide a survey of the principal answers given to these questions, followed by an introduction to my own view, epistemic causality, and then a comparison of epistemic causality with accounts provided by Judea Pearl and Huw Price.
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49Introduction: Bayesianism into the 21st CenturyIn David Corfield & Jon Williamson (eds.), Foundations of Bayesianism, Kluwer Academic Publishers. pp. 1--16. 2001.Bayesian theory now incorporates a vast body of mathematical, statistical and computational techniques that are widely applied in a panoply of disciplines, from artificial intelligence to zoology. Yet Bayesians rarely agree on the basics, even on the question of what Bayesianism actually is. This book is about the basics e about the opportunities, questions and problems that face Bayesianism today
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51This introduction to the volume begins with a manifesto that puts forward two theses: first, that the sciences are the best place to turn in order to understand causality; second, that scientifically-informed philosophical investigation can bring something to the sciences too. Next, the chapter goes through the various parts of the volume, drawing out relevant background and themes of the chapters in those parts. Finally, the chapter discusses the progeny of the papers and identifies some next step…Read more
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89Abduction, reason, and science: Processes of discovery and explanationBritish Journal for the Philosophy of Science 54 (2): 353-358. 2003.