We consider the dispute between causal decision theorists and evidential decision theorists over Newcomb-like problems. We introduce a framework relating causation and directed graphs developed by Spirtes et al. (1993) and evaluate several arguments in this context. We argue that much of the debate between the two camps is misplaced; the disputes turn on the distinction between conditioning on an event E as against conditioning on an event I which is an action to bring about E. We give the essential (...) machinery for calculating the effect of an intervention and consider recent work which extends the basic account given here to the case where causal Knowledge is incomplete. (shrink)

Chris Meek. Strong-Completeness and Faithfulness in Belief Networks.

Whenever the use of non-experimental data for discovering causal relations or predicting the outcomes of experiments or interventions is contemplated, two difficulties are routinely faced. One is the problem of latent variables, or confounders: factors influencing two or more measured variables may not themselves have been measured or recorded. The other is the problem of sample selection bias: values of the variables or features under study may themselves influence whether a unit is included in the data sample.

Linear structural equation models (SEMs) are widely used in sociology, econometrics, biology, and other sciences. A SEM (without free parameters) has two parts: a probability distribution (in the Normal case specified by a set of linear structural equations and a covariance matrix among the “error” or “disturbance” terms), and an associated path diagram corresponding to the functional composition of variables specified by the structural equations and the correlations among the error terms. It is often thought that the path diagram is (...) nothing more than a heuristic device for illustrating the assumptions of the model. However, in this paper, we will show how path diagrams can be used to solve a number of important problems in structural equation modelling. (shrink)

This paper describes the application of eight statistical and machine-learning methods to derive computer models for predicting mortality of hospital patients with pneumonia from their findings at initial presentation. The eight models were each constructed based on 9847 patient cases and they were each evaluated on 4352 additional cases. The primary evaluation metric was the error in predicted survival as a function of the fraction of patients predicted to survive. This metric is useful in assessing a model’s potential to assist (...) a clinician in deciding whether to treat a given patient in the hospital or at home. We examined the error rates of the models when predicting that a given fraction of patients will survive. We examined survival fractions between 0.1 and 0.6. Over this range, each model’s predictive error rate was within 1% of the error rate of every other model. When predicting that approximately 30°K of the patients will survive, all the models have an error rate of less than 1.5%. The models are distinguished more by the number of variables and parameters that they contain than by their error rates; these differences suggest which models may be the most amenable to future implementation as paper-based guidelines. (shrink)

Peter Spirtes, Clark Glymour, Richard Scheines, Christopher Meek, S. Fineberg, E. Slate. Prediction and Experimental Design with Graphical Causal Models.

Clark Glymour, Richard Scheines, Peter Spirtes, and Christopher Meek. Regression and Causation.

Christopher Meek. Complete Orientation Rules for Patterns.

Christopher Meek. Related Graphical Frameworks: Undircted, Directed Acyclic and Chain Graph Models.

independence facts implied by a particular directed acyclic graph; an alternative equivalent rule has been proposed by Lauritzen et al. (1990). Geiger et al. (1990) have shown that d-separation is atomic-complete for independence statements..

It has been shown in Spirtes(1995) that X and Y are d-separated given Z in a directed graph associated with a recursive or non-recursive linear model without correlated errors if and only if the model entails that ρXY.Z = 0. This result cannot be directly applied to a linear model with correlated errors, however, because the standard graphical representation of a linear model with correlated errors is not a directed graph. The main result of this paper is to show how (...) to associate a directed graph with a linear model L with correlated errors, and then use d-separation in the associated directed graph to determine whether L entails that a particular partial correlation is zero. (shrink)