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Tad Blalock and the Statistical Characterization of Causal Structures

In a series of papers and books starting in the 1960's Tad Blalock, building on earlier work by Herbert Simon and Herman Wold, undertook a systematic investigation of the statistical implications of linear causal models involving several variables. In particular, for linear models containing four variables he investigated which correlations and partial correlations would vanish. This was absolutely seminal work, which led directly to many questions:

* Are there general methods for determining when a given partial correlation will vanish for all values of the parameters of a linear causal model?

* When will two linear structural models give rise to the same pattern of vanishing partial correlations?

* Which causal models may be defined statistically purely via vanishing partial correlations?

* Given a pattern of vanishing partial correlations arising from an unknown model can we infer anything about the structure itself?

* Do these ideas extend beyond linear models to non-parametric settings?

The search for answers to these and related questions stimulated the development of Directed Acyclic Graph (DAG) models in Statistics also known as 'Bayesian networks' in Computer Science, and ultimately precipitated what has been called "a renaissance in thinking and using causal concepts".