In many applications, such as medical disputes at Law, interest lies in whether an observed outcome in an individual case was caused by a specific exposure. An important approach aims to evaluate the probability that the outcome in this case was in fact caused by the exposure, using statistical data on similar individuals. Even the best possible experimental data on exposure and outcome typically can not identify this "probability of causation" (PC) exactly, but can only supply bounds for it. These bounds can be significantly improved by accounting for information about internal processes, using additional variables such as covariates and mediators. This work extends such bounds to the case where we have an instrumental variable.

I thank Thomas Richardson and James Robins for their discussion of my article, and discuss the similarities and differences between their approach to causal modelling, based on single world intervention graphs, and my own decision-theoretic approach.

We compare three graphical methods for displaying evidence in a legal case: Wigmore Charts, Bayesian Networks and Chain Event Graphs. We find that these methods are aimed at three distinct audiences, respectively lawyers, forensic scientists and the police. The methods are illustrated using part of the evidence in the case of the murder of Meredith Kercher. More specifically, we focus on representing the list of propositions, evidence, testimony and facts given in the first trial against Raffaele Sollecito and Amanda Knox with these graphical methodologies.

We conduct a review of the fiducial approach to statistical inference, following its journey from its initiation by R. A. Fisher, through various problems and criticisms, on to its general neglect, and then to its more recent resurgence. Emphasis is laid on the functional model formulation, which helps clarify the very limited conditions under which fiducial inference can be conducted in an unambiguous and self-consistent way.

This article surveys the variety of ways in which a directed acyclic graph (DAG) can be used to represent a problem of probabilistic causality. For each of these ways, we describe the relevant formal or informal semantics governing that representation. It is suggested that the cleanest such representation is that embodied in an augmented DAG, which contains nodes for non-stochastic intervention indicators in addition to the usual nodes for domain variables.

Suppose X and Y are binary exposure and outcome variables, and we have full knowledge of the distribution of Y, given application of X. From this we know the average causal effect of X on Y. We are now interested in assessing, for a case that was exposed and exhibited a positive outcome, whether it was the exposure that caused the outcome. The relevant probability of causation, PC, typically is not identified by the distribution of Y given X, but bounds can be placed on it, and these bounds can be improved if we have further information about the causal process. Here we consider cases where we know the probabilistic structure for a sequence of complete mediators between X and Y. We derive a general formula for calculating bounds on PC for any pattern of data on the mediators (including the case with no data). We show that the largest and smallest upper and lower bounds that can result from any complete mediation process can be obtained in processes with at most two steps. We also consider homogeneous processes with many mediators. PC can sometimes be identified as 0 with negative data, but it cannot be identified at 1 even with positive data on an infinite set of mediators. The results have implications for learning about causation from knowledge of general processes and of data on cases.

We consider the problem of assessing whether, in an individual case, there is a causal relationship between an observed exposure and a response variable. When data are available on similar individuals we may be able to estimate prospective probabilities, but even under ideal conditions these are typically inadequate to identify the "probability of causation": instead we can only derive bounds for this. These bounds can be improved or amended when we have information on additional variables, such as mediators or covariates. When a covariate is unobserved or ignored, this will typically lead to biased inferences. We show by examples how serious such biases can be.

We consider the problem of assessing whether, in an individual case, there is a causal relationship between an observed exposure and a response variable. When data are available on similar individuals we may be able to estimate prospective probabilities, but even under ideal conditions these are typically inadequate to identify the "probability of causation": instead we can only derive bounds for this. These bounds can be improved or amended when we have information on additional variables, such as mediators or covariates. When a covariate is unobserved or ignored, this will typically lead to biased inferences. We show by examples how serious such biases can be.

This article is a response to recent proposals by Pearl and others for a new approach to personalised treatment decisions, in contrast to the traditional one based on statistical decision theory. We argue that this approach is dangerously misguided and should not be used in practice.

Discussing causes in science, if we are to do so in away that is sensible, begins at the root. All too often, we jump to discussing specific postulated causes but do not first consider what we mean by, for example, causes of obesity or how we discernwhether something is a cause. In this paper, we address whatwe mean by a cause, discuss what might and might not constitute a reasonable causal model in the abstract, speculate about what the causal structure of obesity might be like overall and the types of things we should be looking for, and finally, delve into methods for evaluating postulated causes and estimating causal effects. We offer the view that different meanings of the concept of causal factors in obesity research are regularly being conflated, leading to confusion, unclear thinking and sometimes nonsense. We emphasize the idea of different kinds of studies for evaluating various aspects of causal effects and discuss experimental methods, assumptions and evaluations. We use analogies from other areas of research to express the plausibility that only inelegant solutions will be truly informative. Finally, we offer comments on some specific postulated causal factors. This article is part of a discussion meeting issue 'Causes of obesity: theories, conjectures and evidence (Part II)'.

The estimation of parameters and model structure for informing infectious disease response has become a focal point of the recent pandemic. However, it has also highlighted a plethora of challenges remaining in the fast and robust extraction of information using data and models to help inform policy. In this paper, we identify and discuss four broad challenges in the estimation paradigm relating to infectious disease modelling, namely the Uncertainty Quantification framework, data challenges in estimation, model-based inference and prediction, and expert judgement. We also postulate priorities in estimation methodology to facilitate preparation for future pandemics.

This editorial article is a biography of Glenn Shafer, briefly covering his early years, his education, and his contributions as an academic to research, teaching, and administration.

chapter Share on The Tale Wags the DAG Author: Philip Dawid University of Cambridge University of CambridgeSearch about this author Authors Info & Claims Probabilistic and Causal Inference: The Works of Judea PearlFebruary 2022 Pages 557–574https://doi.org/10.1145/3501714.3501744Online:04 March 2022Publication History 0citation8DownloadsMetricsTotal Citations0Total Downloads8Last 12 Months8Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

We describe and contrast two distinct problem areas for statistical causality: studying the likely effects of an intervention (effects of causes) and studying whether there is a causal link between the observed exposure and outcome in an individual case (causes of effects). For each of these, we introduce and compare various formal frameworks that have been proposed for that purpose, including the decision-theoretic approach, structural equations, structural and stochastic causal models, and potential outcomes. We argue that counterfactual concepts are unnecessary for studying effects of causes but are needed for analyzing causes of effects. They are, however, subject to a degree of arbitrariness, which can be reduced, though not in general eliminated, by taking account of additional structure in the problem.

I thank Judea Pearl for his discussion of my paper and respond to the points he raises. In particular, his attachment to unaugmented directed acyclic graphs has led to a misapprehension of my own proposals. I also discuss the possibilities for developing a non-manipulative understanding of causality.

We give an overview of various topics tied to the expression of uncertainty about a variable or event by means of a probability distribution. We first consider methods used to evaluate a single probability forecaster, including scoring rules, calibration, resolution and refinement. We next revisit methods for combining several experts’ distributions, including the linear and logarithmic opinion pools. We discuss the model-based approach and the axiomatic approach to opinion pooling and describe the implications of imposing coherence constraints, based on a specific understanding of “expertise”. In the final part, we revisit from a statistical standpoint some results in the economics literature on prediction markets, where individuals sequentially place bets on the outcome of a future event. This leaves a trail of personal probabilities for the event, each conditional on the current individual’s private background knowledge and on the previously announced probabilities of other individuals. In particular, we consider the case of two individuals who start with the same probability distribution but have different private information and take turns in updating their probabilities. We note convergence of the announced probabilities to a limiting value, which may or may not be the same as that based on pooling their private information.

This chapter is dedicated to the memories of Stephen and Joyce Fienberg. In this chapter, we address the problem of inference about individual causation on the basis of statistical data collected on groups. While such information typically cannot identify precisely the probability of causation, it can supply bounds on it. We show how these bounds can be improved by taking account of information on additional variables, specifically covariates and mediators.