Many legal cases require decisions about causality, responsibility or blame, and these may be bas... more Many legal cases require decisions about causality, responsibility or blame, and these may be based on statistical data. However, causal inferences from such data are beset by subtle conceptual and practical difficulties, and in general it is, at best, possible to identify the ‘probability of causation’ as lying between certain empirically informed limits. These limits can be refined and improved if we can obtain additional information, from statistical or scientific data, relating to the internal workings of the causal processes. In this article we review and extend recent work in this area, where additional information may be available on covariate and/or mediating variables.
We welcome Professor Pearl’s comment on our original article, Dawid et al. Our focus there on the... more We welcome Professor Pearl’s comment on our original article, Dawid et al. Our focus there on the distinction between the “Effects of Causes” (EoC) and the “Causes of Effects” (CoE) concerned two fundamental problems, one a theoretical challenge in statistics and the other a practical challenge for trial courts. In this response, we seek to accomplish several things. First, using Pearl’s own notation, we attempt to clarify the similarities and differences between his technical approach and that in Dawid et al. Second, we consider the more practical challenges for CoE in the trial court setting, and explain why we believe Pearl’s analyses, as described via his example, fail to address these. Finally, we offer some concluding remarks.
We display pseudo-likelihood as a special case of a general estimation technique based on proper ... more We display pseudo-likelihood as a special case of a general estimation technique based on proper scoring rules. Such a rule supplies an unbiased estimating equation for any statistical model, and this can be extended to allow for missing data. When the scoring rule has a simple local structure, as in many spatial models, the need to compute problematic normalising constants is avoided. We illustrate the approach through an analysis of data on disease in bell pepper plants.
Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, 1991
Probabilistic expert systems are intended to provide reasoned guidance in complex environments ch... more Probabilistic expert systems are intended to provide reasoned guidance in complex environments characterized by extensive uncertainty . An explicit 'causal' model is constructed for the process being observed, in which an acyclic directed graph is used to express conditional independence assumptions about variables, and probability assessments specify a full joint probability distribution. The resulting graphical structure can cope with a range of issues that arise in realistic modelling. Here we consider a particular example of assessing the chance that a suspected adverse reaction is due to a particular drug under suspicion. The background biological knowledge provides an appropriate model and probability assessments are obtained from expert microbiologists. The model allows a variety of interpretations for ‘causality’. Details of the graphical and computational algorithms used to perform efficient calculations of conditional probabilities on complex graphical structures a...
Communicated by D. A. S. Fraser We investigate the structure of distributions for matrices which ... more Communicated by D. A. S. Fraser We investigate the structure of distributions for matrices which can be embedded in arbitrarily large matrices whose distributions have properties of invariance under orthogonal rotations.
Many legal cases require decisions about causality, responsibility or blame, and these may be bas... more Many legal cases require decisions about causality, responsibility or blame, and these may be based on statistical data. However, causal inferences from such data are beset by subtle conceptual and practical difficulties, and in general it is, at best, possible to identify the ‘probability of causation’ as lying between certain empirically informed limits. These limits can be refined and improved if we can obtain additional information, from statistical or scientific data, relating to the internal workings of the causal processes. In this article we review and extend recent work in this area, where additional information may be available on covariate and/or mediating variables.
We welcome Professor Pearl’s comment on our original article, Dawid et al. Our focus there on the... more We welcome Professor Pearl’s comment on our original article, Dawid et al. Our focus there on the distinction between the “Effects of Causes” (EoC) and the “Causes of Effects” (CoE) concerned two fundamental problems, one a theoretical challenge in statistics and the other a practical challenge for trial courts. In this response, we seek to accomplish several things. First, using Pearl’s own notation, we attempt to clarify the similarities and differences between his technical approach and that in Dawid et al. Second, we consider the more practical challenges for CoE in the trial court setting, and explain why we believe Pearl’s analyses, as described via his example, fail to address these. Finally, we offer some concluding remarks.
We display pseudo-likelihood as a special case of a general estimation technique based on proper ... more We display pseudo-likelihood as a special case of a general estimation technique based on proper scoring rules. Such a rule supplies an unbiased estimating equation for any statistical model, and this can be extended to allow for missing data. When the scoring rule has a simple local structure, as in many spatial models, the need to compute problematic normalising constants is avoided. We illustrate the approach through an analysis of data on disease in bell pepper plants.
Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, 1991
Probabilistic expert systems are intended to provide reasoned guidance in complex environments ch... more Probabilistic expert systems are intended to provide reasoned guidance in complex environments characterized by extensive uncertainty . An explicit 'causal' model is constructed for the process being observed, in which an acyclic directed graph is used to express conditional independence assumptions about variables, and probability assessments specify a full joint probability distribution. The resulting graphical structure can cope with a range of issues that arise in realistic modelling. Here we consider a particular example of assessing the chance that a suspected adverse reaction is due to a particular drug under suspicion. The background biological knowledge provides an appropriate model and probability assessments are obtained from expert microbiologists. The model allows a variety of interpretations for ‘causality’. Details of the graphical and computational algorithms used to perform efficient calculations of conditional probabilities on complex graphical structures a...
Communicated by D. A. S. Fraser We investigate the structure of distributions for matrices which ... more Communicated by D. A. S. Fraser We investigate the structure of distributions for matrices which can be embedded in arbitrarily large matrices whose distributions have properties of invariance under orthogonal rotations.
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Papers by Philip Dawid