We survey a variety of possible explications of the term “Individual Risk.” These in turn are based on a variety of interpretations of “Probability,” including classical, enumerative, frequency, formal, metaphysical, personal, propensity, chance and logical conceptions of probability, which we review and compare. We distinguish between “groupist” and “individualist” understandings of probability, and explore both “group to individual” and “individual to group” approaches to characterising individual risk. Although in the end that concept remains subtle and elusive, some pragmatic suggestions for (...) progress are made. (shrink)

We develop a mathematical and interpretative foundation for the enterprise of decision-theoretic (DT) statistical causality, which is a straightforward way of representing and addressing causal questions. DT reframes causal inference as “assisted decision-making” and aims to understand when, and how, I can make use of external data, typically observational, to help me solve a decision problem by taking advantage of assumed relationships between the data and my problem. The relationships embodied in any representation of a causal problem require deeper justification, (...) which is necessarily context-dependent. Here we clarify the considerations needed to support applications of the DT methodology. Exchangeability considerations are used to structure the required relationships, and a distinction drawn between intention to treat and intervention to treat forms the basis for the enabling condition of “ignorability.” We also show how the DT perspective unifies and sheds light on other popular formalisations of statistical causality, including potential responses and directed acyclic graphs. (shrink)

Beauty challenges conventional approaches to the subject through an interdisciplinary approach that forges connections between the arts, sciences and mathematics. Classical, conventional aspects of beauty are addressed in subtle, unexpected ways: symmetry in mathematics, attraction in the animal world and beauty in the cosmos. This collection arises from the Darwin College Lecture Series of 2011 and includes essays from eight distinguished scholars, all of whom are held in esteem not only for their research but also for their ability to communicate (...) their subject to popular audiences. Each essay is entertaining, accessible and thought-provoking and is accompanied by images illustrating beauty in practice. Contributors include the artist José Hernández, Nobel Prize Laureate Frank Wilczek, Lord May of Oxford and Jeanne Altmann. (shrink)

I thank Ilya Shpitser for his comments on my article, and discuss the use of models with restricted interventions.

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.

Scholars in diverse academic disciplines discuss the ways in which evidence is conceived, used, and manipulated in their own fields. They explore the possibilities for cross-disciplinary fertilisation and ask if it is possible or desirable to develop general multidisciplinary criteria and methods for studying and handling evidence.

Methods for performing complex probabilistic reasoning tasks, often based on masses of different forms of evidence obtained from a variety of different sources, are being sought by, and developed for, persons in many important contexts including law, medical diagnosis, and intelligence analysis. The complexity of these tasks can often be captured and represented by graphical structures now called inference networks. These networks are directed acyclic graphs, consisting of nodes, representing relevant hypotheses, items of evidence, and unobserved variables, and arcs joining (...) some of the nodes, representing dependency relations among them. This chapter describes and comments on two different approaches to inference network construction. In the first approach, a DAG network structure is explicitly constructed as a vehicle for probabilistic analyses. Since the associated computations can be regarded as generalising the use of Bayes' rule, such networks are commonly called Bayesian networks. The second approach stems from the work of the American jurist John H. Wigmore who was the very first person to attempt a systematic study of inference networks. (shrink)