Suppose X and Y are binary exposure and outcome variables, and we have full knowledge of the distribution of Y, given application of X. We are interested in assessing whether an outcome in some case is due to the exposure. This “probability of causation” is of interest in comparative...

Abstract 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...

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

Abstract 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...

This letter comments on the report “Forensic Science in Criminal Courts: Ensuring Scientific Validity of Feature-comparison Methods” released in September 2016, by the President's Council of Advisors on Science and Technology (PCAST). The report advocates a two-stage procedure for evaluation...

We present an overview of the decision-theoretic framework of statistical causality, which is well suited for formulating and solving problems of determining the effects of applied causes. The approach is described in detail, and it is related to and contrasted with other current formulations,...

A scoring rule <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$S(x; q)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>S</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>;</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> provides a way of judging the quality of a quoted probability density <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$q$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>q</mi> </math> </EquationSource> </InlineEquation> for a random variable <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$X$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>X</mi> </math> </EquationSource> </InlineEquation> in the light of its outcome <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$x$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>x</mi> </math> </EquationSource> </InlineEquation>. It is called proper if honesty is your best policy, i.e., when you believe <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$X$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>X</mi>...</math></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

The skew-normal model is a class of distributions that extends the Gaussian family by including a skewness parameter. This model presents some inferential problems linked to the estimation of the skewness parameter. In particular its maximum likelihood estimator can be infinite especially for...