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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.

It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlations in the sense of Reichenbach's definition of common cause. It is shown, further, that, given any quantum probability space and any set of commuting events in it which are correlated with respect to a fixed quantum state, the quantum probability space can be extended in such a way that the extension contains common causes of all the selected correlations, where common cause is again taken in the sense of Reichenbach's definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle.

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.

Research suggests that causal judgment is influenced primarily by counterfactual or covariational reasoning. In contrast, the author of this article develops judgment dissociation theory (JDT), which predicts that these types of reasoning differ in function and can lead to divergent judgments. The actuality principle proposes that causal selections focus on antecedents that are sufficient to generate the actual outcome. The substitution principle proposes that ad hoc categorization plays a key role in counterfactual and covariational reasoning such that counterfactual selections focus on antecedents that would have been sufficient to prevent the outcome or something like it and covariational selections focus on antecedents that yield the largest increase in the probability of the outcome or something like it. The findings of 4 experiments support JDT but not the competing counterfactual and covariational accounts. If causation is the cement of the universe, as the philosopher David Hume (1740/1938) put it, then it is fair to say that causal knowledge is the cement that binds together each person’s representational universe. Causal reasoning—the process that generates this glue—confers many functional advantages. In virtually every sphere of human interest, our abilities to learn and categorize

INTRODUCTION KDD is better known by the oversimplified name of Data Mining (DM). Actually, most academics are rather interested by DM which develops methods for extracting knowledge from a given set of data. Industrialists and experts should be more interested in KDD which comprises the whole process of data selection, data cleaning, transfer to a DM technique, applying the DM technique, validating the results of the DM technique, and finally interpreting them for the user. In general, this process is a cycle that improves under the criticism of the expert. Machine Learning (ML) and KDD have in common a very strong link : they both acknowledge the importance of induction as a normal way of thinking, while other scientific fields are reluctant to accept it, to say the least. We shall first explore this common point. We believe that this reluctance relies on a misuse of apparent contradictions inside the theory of confirmation, that is we shall revisit Hempel paradox in order t

According to common judicial standard, judgment in favor of plaintiff should be made if and only if it is "more probable than not" that the defendant's action was the cause for the plaintiff's damage (or death). This paper provides formal semantics, based on structural models of counterfactuals, for the probability that event x was a necessary or sufficient cause (or both) of another event y. The paper then explicates conditions under which the probability of necessary (or sufficient) causation can be learned from statistical data, and shows how data from both experimental and nonexperimental studies can be combined to yield information that neither study alone can provide. Finally,weshow that necessity and sufficiency are two independent aspects of causation, and that both should be invoked in the construction of causal explanations for specific scenarios.

An important element of learning from examples is the extraction of patterns and regularities from data. This paper investigates the structure of patterns in data defined over discrete features, i.e. features with two or more qualitatively distinct values. Any such pattern can be algebraically decomposed into a spectrum of component patterns, each of which is a simpler or more atomic ‘‘regularity.’ ’ Each component regularity involves a certain number of features, referred to as its degree. Regularities of lower degree represent simpler or more coarse patterns in the original pattern, while regularities of higher degree represent finer or more idiosyncratic patterns. The full spectral breakdown of a pattern into component regularities of minimal degree, referred to as its power series, expresses the original pattern in terms of the regular rules or patterns it obeys, amounting to a kind of ‘‘theory’ ’ of the pattern. The number of regularities at various degrees necessary to represent the pattern is tabulated in its power spectrum, which expresses how much of a pattern’s structure can be explained by regularities of various levels of complexity. A weighted mean of the pattern’s spectral power gives a useful numeric summary of its overall complexity, called its algebraic complexity. The basic theory of algebraic decomposition is extended in several ways, including algebraic accounts of the typicality of individual objects within concepts, and estimation of the power series from noisy data. Finally some relations between these algebraic quantities and empirical data are discussed.

Philosophical theories summarized here include regularity and necessity theories from Hume to the present; manipulability theory; the theory of powerful particulars; causation as connected changes within a defined state of affairs; departures from "normal " events or from some standard for compar-ison; causation as a transfer of something between objects; and causal propagation and production. Issues found in this literature and of relevance for psychology include whether actual causal relations can be perceived or known; what sorts of things people believe can be causes; different levels of causal analysis; the distinction between the causal relation itself and cues to causal relations; causal frames or fields; internal and external causes; and understanding of causation in different realms of the world, such as the natural and artificial realms. A full theory of causal inference by laypeople should address all of these issues. The main purpose of this article is to survey philosophical theories of causation in a manner intended to be suitable for psychologists interested in causation. The article has two sec-tions: The first presents brief summaries of philosophical theo-ries of causation from Aristotle to the present. In the second, issues found in the philosophical literature are used to suggest new approaches to the study of causation in psychology. Philosophical Theories of Causation Several psychologists have written about selected philosophi-cal theories of causation (Cook & Campbell, 1979; Einhorn &

In this essay I present a general characterization of qualitative probability, including a partial taxonomy of possible approaches. I discuss some of these in further depth, identify central issues, and suggest some general comparisons. 1. Introduction In the standard theory of probability, degrees of belief for events or propositions take values in the real interval [0,1]. From degrees of belief on the primitive propositions, the theory dictates degrees of belief for various compound and conditional propositions, and vice versa. Computational schemes for probabilistic reasoning apply this theory to the automated derivation of degrees of belief for designated propositions of interest given prespecified degrees of belief over some other propositions and some particular conditioning propositions observed or hypothesized. This approach has, among other advantages, those accruing to a well understood and powerful underlying theory. Despite these virtues, many have objected to the straig...