Clark Glymour

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 causal relations among 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.

Reverse inference in cognitive neuropsychology has been characterized as inference to ‘psychological processes’ from ‘patterns of activation’ revealed by functional magnetic resonance or other scanning techniques. Several arguments have been provided against the possibility. Focusing on Machery’s presentation, we attempt to clarify the issues, rebut the impossibility arguments, and propose and illustrate a strategy for reverse inference. 1 The Problem of Reverse Inference in Cognitive Neuropsychology2 The Arguments2.1 The anti-Bayesian argument3 Patterns of Activation4 Reverse Inference Practiced5 Seek and Ye Shall Find, Maybe6 Conclusion

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.

Magnani, Lorenzo (2001), Abduction, Reason, and Science: Processes of Discovery and Explanation. New York: Kluwer Academic/ Plenum Publishers. Magnani. Lorenzo, and Nancy Nersessian (eds.) (2002), Model-Based Reasoning: Technology, Science, Values. New York: Kluwer Academic/ Plenum Publishers. Joseph E. Earley, Sr. (ed.), Chemical Explanation: Characteristics, Development, Autonomy, Annals of the New York Academy of Sciences, vol. 988. New York Academy of Sciences (2003), 370 pp., $130.00 (cloth).

For most of the contributions to this volume, the project is this: Fill out “Event X is a cause of event Y if and only if……” where the dots on the right are to be filled in by a claims formulated in terms using any of (1) descriptions of possible worlds and their relations; (2) a special predicate, “is a law;” (3) “chances;” and (4) anything else one thinks one needs. The form of analysis is roughly the same as that sought in the Meno, and the methodology is likewise Socratic—proposals, examples, counterexamples, more proposals. The norms of the enterprise seem to be as follows (i) a proposal is defeated if someone can imagine a circumstance in which it would be false, or perhaps if one can imagine such a circumstance that is not obviously inconsistent with physical laws; (ii) approximately correct solutions, those which cover most but not all cases, are of no value unless they can be modified to cover all cases; (iii) no account is required of how the relations in the right hand side of a proposed analysis could be known or reliably..

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.

Various proposals have suggested that an adequate explanatory theory should reduce the number or the cardinality of the set of logically independent claims that need be accepted in order to entail a body of data. A (and perhaps the only) well-formed proposal of this kind is William Kneale’s: an explanatory theory should be finitely axiomatizable but it’s set of logical consequences in the data language should not be finitely axiomatizable. Craig and Vaught showed that Kneale theories (almost) always exist for any recursively enumerable but not finitely axiomatizable set of data sentences in a first order language with identity. Kneale’s criterion underdetermines explanation even given all possible data in the data language; gratuitous axioms may be “tacked on.” Define a Kneale theory, T, to be logically minimal if it is deducible from every Kneale theory (in the vocabulary of T) that entails the same statements in the data language as does T. If they exist, minimal Kneale theories are candidates for best explanations: they are “bold” in a sense close to Popper’s; some minimal Kneale theory is true if any Kneale theory is true; the minimal Kneale theory that is data equivalent to any given Kneale theory is unique; and no Kneale theory is more probable than some minimal Kneale theory. I show that under the Craig-Vaught conditions, no minimal Kneale theories exist

Jaegwon Kim's Mind in a Physical World is an argument about mental causation that provides both a metaphysical theory and a lucid commentary on contemporary philosophical views. While I strongly recommend Kim's book to anyone interested in the subject, my endorsement is not unconditional, because I cannot make the same recomendation of the subject itself. Considering arguments of Davidson, Putnam, Burge, Block, and Kim himself, I conclude that the subject turns on a variety of implausible but received arguments, and that a useful study of mental causation cannot be divorced from scientific details of cognitive psychology, physics, and neuroscience.

By combining experimental interventions with search procedures for graphical causal models we show that under familiar assumptions, with perfect data, N - 1 experiments suffice to determine the causal relations among N > 2 variables when each experiment randomizes at most one variable. We show the same bound holds for adaptive learners, but does not hold for N > 4 when each experiment can simultaneously randomize more than one variable. This bound provides a type of ideal for the measure of success of heuristic approached in active learning methods of casual discovery, which currently use less informative measures

& Carnegie Mellon University Abstract The rationality of human causal judgments has been the focus of a great deal of recent research. We argue against two major trends in this research, and for a quite different way of thinking about causal mechanisms and probabilistic data. Our position rejects a false dichotomy between "mechanistic" and "probabilistic" analyses of causal inference -- a dichotomy that both overlooks the nature of the evidence that supports the induction of mechanisms and misses some important probabilistic implications of mechanisms. This dichotomy has obscured an alternative conception of causal learning: for discrete events, a central adaptive task is to induce causal mechanisms in the environment from probabilistic data and prior knowledge. Viewed from this perspective, it is apparent that the probabilistic norms assumed in the human causal judgment literature often do not map onto the mechanisms generating the probabilities. Our alternative conception of causal judgment is more congruent with both scientific uses of the notion of causation and observed causal judgments of untutored reasoners. We illustrate some of the relevant variables under this conception, using a framework for causal representation now widely adopted in computer science and, increasingly, in statistics. We also review the formulation and evidence for a theory of human causal induction (Cheng, 1997) that adopts this alternative conception.