Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

The causal Markov condition (CMC) plays an important role in much recent work on the problem of causal inference from statistical data. It is commonly thought that the CMC is a more problematic assumption for genuinely indeterministic systems than for deterministic ones. In this essay, I critically examine this proposition. I show how the usual motivation for the CMC—that it is true of any acyclic, deterministic causal system in which the exogenous variables are independent—can be extended to the indeterministic case. (...) In light of this result, I consider several arguments for supposing indeterminism a particularly hostile environment for the CMC, but conclude that none are persuasive. Introduction Functional models and directed graphs The causal Markov theorem The causal Markov theorem and genuine indeterminism Are the exogenous variables independent? EPR Conclusion. (shrink)

Twenty years ago, Nancy Cartwright wrote a perceptive essay in which she clearly distinguished causal relations from associations, introduced philosophers to Simpson’s paradox, articulated the difficulties for reductive probabilistic analyses of causation that flow from these observations, and connected causal relations with strategies of action (Cartwright 1979). Five years later, without appreciating her essay, I and my (then) students began to develop formal representations of causal and probabilistic relations, which, subsequently informed by the work of computer scientists and statisticians, led (...) eventually to a practical theory of causal inference and prediction, a theory incorporating some of the sensibilities Cartwright had voiced (Glymour et al. 1987; Spirtes et al. 1993). That theory, and ideas related to it, have become a subfield of computer science with contributions far deeper than mine from many sources, and its inferential and predictive techniques have been successfully applied in biology, economics, educational research, geology and space physics. (shrink)

The Dappled World: A Study of the Boundaries of Science. nancy cartwright. Plato's Reception of Parmenides. john a. palmer.

Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

Causality in Macroeconomics examines causality while taking macroeconomics seriously. A pragmatic and realistic philosophy is joined to a macroeconomic foundation that refines Herbert Simon's well-known work on causal order to make a case for a structural approach to causality. The structural approach is used to understand modern rational expectations models, regime switching models, Granger causality, vector autoregressions, the Lucas critique, and concept exogeneity. Techniques of causal inference based on patterns of stability and instability in the face of identified regime changes (...) are developed and illustrated in two empirical case studies. (shrink)

It is often supposed that the spectacular successes of our modern mathematical sciences support a lofty vision of a world completely ordered by one single elegant theory. In this book Nancy Cartwright argues to the contrary. When we draw our image of the world from the way modern science works - as empiricism teaches us we should - we end up with a world where some features are precisely ordered, others are given to rough regularity and still others behave in (...) their own diverse ways. This patchwork makes sense when we realise that laws are very special productions of nature, requiring very special arrangements for their generation. Combining classic and newly written essays on physics and economics, The Dappled World carries important philosophical consequences and offers serious lessons for both the natural and the social sciences. (shrink)

Of the many proposals for inferring genetic regulatory structure from microarray measurements of mRNA transcript hybridization, several aim to estimate regulatory structure from the associations of gene expression levels measured in repeated samples. The repeated samples may be from a single experimental condition, or from several distinct experimental conditions; they may be “equilibrium” measurements or time series; the associations may be estimated by correlation coefficients or by conditional frequencies (for discretized measurements) or by some other statistic. This paper describes two (...) elementary statistical difficulties for all such procedures, no matter whether based on Bayesian updating, conditional independence testing, or other machine learning procedures such as simulated annealing or neural net pruning. One difficulty obtains if large numbers of cells are aggregated in a measurement of expression levels from a common population of cells; the other obtains if small numbers of cells are aggregated or if samples are separately aggregated over different populations of cells. (shrink)

Of the many proposals for inferring genetic regulatory structure from microarray measurements of mRNA transcript hybridization, several aim to estimate regulatory structure from the associations of gene expression levels measured in repeated samples. The repeated samples may be from a single experimental condition, or from several distinct experimental conditions; they may be “equilibrium” measurements or time series; the associations may be estimated by correlation coefficients or by conditional frequencies (for discretized measurements) or by some other statistic. This paper describes two (...) elementary statistical difficulties for all such procedures, no matter whether based on Bayesian updating, conditional independence testing, or other machine learning procedures such as simulated annealing or neural net pruning. One difficulty obtains if large numbers of cells are aggregated in a measurement of expression levels from a common population of cells; the other obtains if small numbers of cells are aggregated or if samples are separately aggregated over different populations of cells. (shrink)

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