The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject-matter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data. If so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions; otherwise, the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained. Key words: Causal inference, graph models, interventions treatment effect 1 Introduction The tools introduced in this paper are aimed at helping researchers communicate qualitative assumptions about cause-effect relationships, elucidate the ramifications of such assumptions, and derive causal inferences from a combination...

propose a preliminary set of research guidelines aimed at stimulating discussion among software researchers. They are based on a review of research guidelines developed for medical researchers and on our own experience in doing and reviewing software engineering research. The guidelines are intended to assist researchers, reviewers, and meta-analysts in designing, conducting, and evaluating empirical studies. Editorial boards of software engineering journals may wish to use our recommendations as a basis for developing guidelines for reviewers and for framing policies for dealing with the design, data collection, and analysis and reporting of empirical studies. Index TermsÐEmpirical software research, research guidelines, statistical mistakes. 1

Although published works rarely include causal estimates from more than a few model specifications, authors usually choose the presented estimates from numerous trial runs readers never see. Given the often large variation in estimates across choices of control variables, functional forms, and other modeling assumptions, how can researchers ensure that the few estimates presented are accurate or representative? How do readers know that publications are not merely demonstrations that it is possible to find a specification that fits the author’s favorite hypothesis? And how do we evaluate or even define statistical properties like unbiasedness or mean squared error when no unique model or estimator even exists? Matching methods, which offer the promise of causal inference with fewer assumptions, constitute one possible way forward, but crucial results in this fast-growing methodological

... this paper is to use experimental or observational data to estimate decision regimes that result in a maximal mean response. To explicate our objective and state assumptions, we use the potential outcomes model. The proposed method makes smooth, parametric assumptions only on quantities directly relevant to the goal of estimating the optimal rules. We illustrate the proposed methodology via a small simulation.

this paper we consider two fundamental issues concerning Robins' theory. Firstly, do his assumed relations (between observed and unobserved---factual and counterfactual---random variables) place restrictions on the distribution of the observed variables. If the answer is yes, adopting his approach means making restrictive implicit assumptions---not very desirable. If however the answer is no, his approach is neutral. One can freely use it in modelling and estimation, exploring the consequences (for the unobserved variables) of the model. This follows the highly succesful tradition in all sciences of making thought experiments. In what philosophical sense counterfactuals actually exist seems to us less relevant. But it is important to know if a certain thought experiment is a priori ruled out by existing data

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Causality is a very intuitive notion that is difficult to make precise without lapsing into tautology. Two ingredients are central to any definition: (1) a set of possible outcomes (counterfactuals) generated by a function of a set of ‘‘factors’ ’ or ‘‘determinants’ ’ and (2) a manipulation where one (or more) of the ‘‘factors’ ’ or ‘‘determinants’’ is changed. An effect is realized as a change in the argument of a stable function that produces the same change in the outcome for a class of interventions that change the ‘‘factors’ ’ by the same amount. The outcomes are compared at different levels of the factors or generating variables. Holding all factors save one at a constant level, the change in the outcome associated with manipulation of the varied factor is called a causal effect of the manipulated factor. This definition, or some version of it, goes back to Mill (1848) and Marshall (1890). Haavelmo’s (1943) made it more precise within the context of linear equations models. The phrase ‘ceteris paribus’ (everything else held constant) is a mainstay of economic analysis

Abstract: This review presents empirical researchers with recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called “causal effects ” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret, ” “attribution” or “causes of effects”) and (3) queries about direct and indirect effects (also known as “mediation”). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiosis analysis that uses the strong features of both.

This paper aims at assisting empirical researchers benefit from recent advances in causal inference. The paper stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, and the conditional nature of causal claims inferred from nonexperimental studies. These emphases are illustrated through a brief survey of recent results, including the control of confounding, the assessment of causal effects, the interpretation of counterfactuals, and a symbiosis between counterfactual and graphical methods of analysis.