Clark Glymour

A general principle for good pedagogic strategy is this: other things equal, make the essential principles of the subject explicit rather than tacit. We think that this principle is routinely violated in conventional instruction in statistics. Even though most of the early history of probability theory has been driven by causal considerations, the terms “cause” and “causation” have practically disappeared from statistics textbooks. Statistics curricula guide students away from the concept of causality, into remembering perhaps the cliche disclaimer “correlation does not mean causation,” but rarely thinking about what correlation does mean. The treatment of causality is a serious handicap to later studies of such topics as experimental design, where often the main goal is to establish (or disprove) causation. Much of the technical vocabulary of the language used in research design textbooks consists in euphemisms for specific causal relations, e.g, “latent variable,” “intervening variable,” “confounding factor,” etc. The multiplicity of terms used to refer to causation results in confusion and, in effect, may hinder understanding of the basic principles of research design.

Recent literature in philosophy of science has addressed purported notions of explanatory virtues—‘explanatory power’, ‘unification’, and ‘coherence’. In each case, a probabilistic relation between a theory and data is said to measure the power of an explanation, or degree of unification, or degree of coherence. This essay argues that the measures do not capture cases that are paradigms of scientific explanation, that the available psychological evidence indicates that the measures do not capture judgements of explanatory power, and, finally, that the measures do not provide useful methods for selecting hypotheses. 1. Introduction2. Some Proposed Measures of Explanatory Virtues3. Descriptive Inadequacy3.1 Excellent but false explanations3.2 Causal explanation4. Psychological Inadequacy5. Finding the Truth6. Conclusion

Rather than attempting to characterize a relation of confirmation between evidence and theory, epistemology might better consider which methods of forming conjectures from evidence, or of altering beliefs in the light of evidence, are most reliable for getting to the truth. A logical framework for such a study was constructed in the early 1960s by E. Mark Gold and Hilary Putnam. This essay describes some of the results that have been obtained in that framework and their significance for philosophy of science, artificial intelligence, and for normative epistemology when truth is relative.

Through their transcript products genes regulate the rates at which an immense variety of transcripts and subsequent proteins occur. Understanding the mechanisms that determine which genes are expressed, and when they are expressed, is one of the keys to genetic manipulation for many purposes, including the development of new treatments for disease. Viewing each gene in a genome as a distinct variable that is either on or off, or more realistically as a continuous variable, the values of some of these variables influence the values of others through the regulatory proteins they express, including, of course, the possibility that the rate of expression of a gene at one time may, in various circumstances, influence the rate of expression of that same gene at a later time. If we imagine an arrow drawn from each gene expression variable at a given time to a gene variable whose expression it influences a short while after, the result is a network, technically a directed acyclic graph. For example, the DAG in Figure 1 is a representation of a system in which the expression level of gene G1 at time 1 ) causes the expression level of G2, which in turn causes the expression level of G3. The arrows in Figure 1 which do not have a variable at their tails are “error terms” which represent all of the causes of a variable other than the ones explicitly represented in the DAG. The DAG describes more than associations—it describes causal connections among gene expression rates. A shock to a cell—by mutation, heating, chemical treatment, etc. may alter the DAG describing the relations among gene expressions, for example by activating a gene that was otherwise not expressed, producing a cascade of new expression effects. Although “knockout” experiments can reveal some of the underlying causal network of gene expression levels, unless guided by information from other sources, such experiments are limited in how much of the network structure they can reveal, due to the sheer number of possible combinations of experimental manipulations of genes necessary to reveal the complete causal network. Recent developments have made it possible to compare quantitatively the expression of tens of thousands of genes in cells from different sources in a single experiment, and to trace gene expression over time in thousands of genes simultaneously. cDNA microarrays are already producing extensive data, much of it available on the web. Thus there are calls for analytic software that can be applied to microarray and other data to help infer regulatory networks. In this paper we will review current techniques that are available for searching for the causal relations between variables, describe algorithmic and data gathering obstacles to applying these techniques to gene expression levels, and describe the prospects for overcoming these obstacles

The use of ceteris paribus clauses in philosophy and in the sciences has a long and fascinating history. Persky (1990) traces the use by economists of ceteris paribus clauses in qualifying generalizations as far back as William Petty’s Treatise of Taxes and Contributions (1662). John Cairnes’ The Character and Logical Method of Political Economy (1857) is credited with enunciating the idea that the conclusions of economic investigations hold “only in the absence of disturbing causes”.1 His Leading Principles (1874) contains the classic example of a ceteris paribus law: “The rate of wage, other things being equal, varies inversely with the supply of labour”. Carines’ ideas were popularized by Alfred Marshall in his Principles of Economics (1890) where he argued for a methodology that involved holding disturbing causes “in a pound called Caeteris Paribus”. It is unclear when the notion of ceteris paribus laws made its appearance in the philosophical literature; but in the nineteenth century it is to be found in Mill’s System of Logic (1843), and in the twentieth century it gained prominence in the Hempel-inspired debates of the 1950’s over the role of general laws in historical explanations, albeit under other labels such as quasi-laws (Rescher) or grounded generalizations (Scriven).

Data mining is on the interface of Computer Science and Statistics, utilizing advances in both disciplines to make progress in extracting information from large databases. It is an emerging field that has attracted much attention in a very short period of time. This article highlights some statistical themes and lessons that are directly relevant to data mining and attempts to identify opportunities where close cooperation between the statistical and computational communities might reasonably provide synergy for further progress in data analysis.

The Bell Curve aims to establish a set of causal claims. I argue that the methodology of The Bell Curve is typical of much of contemporary social science and is intrinsically defective. I claim better methods are available for causal inference from observational data, but that those methods would yield no causal conclusions from the data used in the formal analyses in The Bell Curve. Against the laissez-faire social policies advocated in the book, I claim that when combined with common sense and other information, the informal data mustered in The Bell Curve support a range of "liberal" social policies

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

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.

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).

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.