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102Bayesianism and language changeJournal of Logic, Language and Information 12 (1): 53-97. 2003.Bayesian probability is normally defined over a fixed language or eventspace. But in practice language is susceptible to change, and thequestion naturally arises as to how Bayesian degrees of belief shouldchange as language changes. I argue here that this question poses aserious challenge to Bayesianism. The Bayesian may be able to meet thischallenge however, and I outline a practical method for changing degreesof belief over changes in finite propositional languages
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35Lectures on Inductive LogicOxford University Press. 2017.Logic is a field studied mainly by researchers and students of philosophy, mathematics and computing. Inductive logic seeks to determine the extent to which the premises of an argument entail its conclusion, aiming to provide a theory of how one should reason in the face of uncertainty. It has applications to decision making and artificial intelligence, as well as how scientists should reason when not in possession of the full facts. In this work, Jon Williamson embarks on a quest to find a gene…Read more
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281Mechanisms and the Evidence HierarchyTopoi 33 (2): 339-360. 2014.Evidence-based medicine (EBM) makes use of explicit procedures for grading evidence for causal claims. Normally, these procedures categorise evidence of correlation produced by statistical trials as better evidence for a causal claim than evidence of mechanisms produced by other methods. We argue, in contrast, that evidence of mechanisms needs to be viewed as complementary to, rather than inferior to, evidence of correlation. In this paper we first set out the case for treating evidence of mecha…Read more
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21Special issue on Combining Probability and LogicJournal of Applied Logic 1 (3-4): 135-138. 2003.
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107Possible Semantics for a Common Framework of Probabilistic LogicsIn V. N. Huynh (ed.), International Workshop on Interval Probabilistic Uncertainty and Non-Classical Logics, Springer. 2008.Summary. This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular semantics, no general solution is possible. The paper discusses several possible semantics by looking at it from the perspective of probabilistic argumentation.
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132Inductive influenceBritish Journal for the Philosophy of Science 58 (4). 2007.Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief ½ 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 ca…Read more
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90Scientific Evidence and the Law: An Objective Bayesian Formalisation of the Precautionary Principle in Pharmaceutical RegulationJournal of Philosophy, Science and Law 11 1-24. 2011.The paper considers the legal tools that have been developed in German pharmaceutical regulation as a result of the precautionary attitude inaugurated by the Contergan decision. These tools are the notion of “well-founded suspicion”, which attenuates the requirements for safety intervention by relaxing the requirement of a proved causal connection between danger and source, and the introduction of the reversal of proof burden in liability norms. The paper focuses on the first and proposes seeing…Read more
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286From Bayesianism to the Epistemic View of Mathematics: Review of R. Jeffrey, Subjective Probability: The Real Thing (review)Philosophia Mathematica 14 (3): 365-369. 2006.Subjective Probability: The Real Thing is the last book written by the late Richard Jeffrey, a key proponent of the Bayesian interpretation of probability.Bayesians hold that probability is a mental notion: saying that the probability of rain is 0.7 is just saying that you believe it will rain to degree 0.7. Degrees of belief are themselves cashed out in terms of bets—in this case you consider 7:3 to be fair odds for a bet on rain. There are two extreme Bayesian positions. Strict subjectivists t…Read more
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195Probabilistic theories of causalityIn Helen Beebee, Peter Menzies & Christopher Hitchcock (eds.), The Oxford Handbook of Causation, Oxford University Press. pp. 185--212. 2009.This chapter provides an overview of a range of probabilistic theories of causality, including those of Reichenbach, Good and Suppes, and the contemporary causal net approach. It discusses two key problems for probabilistic accounts: counterexamples to these theories and their failure to account for the relationship between causality and mechanisms. It is argued that to overcome the problems, an epistemic theory of causality is required
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435What is a mechanism? Thinking about mechanisms across the sciencesEuropean Journal for Philosophy of Science 2 (1): 119-135. 2012.After a decade of intense debate about mechanisms, there is still no consensus characterization. In this paper we argue for a characterization that applies widely to mechanisms across the sciences. We examine and defend our disagreements with the major current contenders for characterizations of mechanisms. Ultimately, we indicate that the major contenders can all sign up to our characterization
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97Deliberation, judgement and the nature of evidenceEconomics and Philosophy 31 (1): 27-65. 2015.:A normative Bayesian theory of deliberation and judgement requires a procedure for merging the evidence of a collection of agents. In order to provide such a procedure, one needs to ask what the evidence is that grounds Bayesian probabilities. After finding fault with several views on the nature of evidence, it is argued that evidence is whatever is rationally taken for granted. This view is shown to have consequences for an account of merging evidence, and it is argued that standard axioms for…Read more
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43Cancer treatment decisions should be based on all available evidence. But this evidence is complex and varied: it includes not only the patient’s symptoms and expert knowledge of the relevant causal processes, but also clinical databases relating to past patients, databases of observations made at the molecular level, and evidence encapsulated in scientific papers and medical informatics systems. Objective Bayesian nets offer a principled path to knowledge integration, and we show in this chapte…Read more
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32B. de Finetti, Philosophical lectures on probability (review)Philosophia Mathematica 18 (1): 130-135. 2010.(No abstract is available for this citation)
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376Models for prediction, explanation and control: recursive bayesian networksTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 26 (1): 5-33. 2011.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 an…Read more
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206Why Frequentists and Bayesians Need Each OtherErkenntnis 78 (2): 293-318. 2013.The orthodox view in statistics has it that frequentism and Bayesianism are diametrically opposed—two totally incompatible takes on the problem of statistical inference. This paper argues to the contrary that the two approaches are complementary and need to mesh if probabilistic reasoning is to be carried out correctly
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65An objective Bayesian account of confirmationIn Dennis Dieks, Wenceslao Gonzalo, Thomas Uebel, Stephan Hartmann & Marcel Weber (eds.), Explanation, Prediction, and Confirmation, Springer. pp. 53--81. 2011.
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7Key Terms in Logic (edited book)Continuum Press. 2010.An accessible guide for those facing the study of Logic For The first time, this book covers key thinkers, terms and texts.
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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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103How Uncertain Do We Need to Be?Erkenntnis 79 (6): 1249-1271. 2014.Expert probability forecasts can be useful for decision making . But levels of uncertainty escalate: however the forecaster expresses the uncertainty that attaches to a forecast, there are good reasons for her to express a further level of uncertainty, in the shape of either imprecision or higher order uncertainty . Bayesian epistemology provides the means to halt this escalator, by tying expressions of uncertainty to the propositions expressible in an agent’s language . But Bayesian epistemolog…Read more
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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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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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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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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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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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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