Reply to Freedman

In Causation, Prediction, and Search (Spirtes, Glymour, and Scheines 1993), we undertook a three part project. (Henceforth we will refer to Causation, Prediction, and Search as CPS.) First, we characterized when causal models are indistinguishable by population conditional independence relations under several different assumptions relating causality to probability. Second, we proposed a number of algorithms that take sample data and optional background knowledge as input, and output a class of causal models compatible with the data and the background knowledge; the algorithms (with the exception of the heuristic algorithm described in Chapter 11) were accompanied by proofs of their correctness given assumptions that were clearly stated in CPS, and that we will restate below. Finally, we offered a theory of how to predict the effects of interventions in causal structures, given only partial knowledge of causal structure. Freedman's objections are all directed against the causal inference algorithms we proposed. We do not have room here to discuss all of his criticisms, but we have answered his major points. With regard to the points we do not have room to discuss, the reader should be warned that Freedman is an unreliable interpreter of what we have written. For convenience, we have divided Freedman's objections into the following categories. 1.) Freedman questions some of the assumptions on which our correctness theorems are based. Some of his criticisms are based on covariance matrices that he constructed. None of the examples he constructed in sections 11.2, 11.3, or 12.3 are counterexamples to any theorem that we stated, nor are they even germane to the question of how probable are the assumptions we make. His examples only illustrate points discussed in detail in our book (particularly in the chapter on indistinguishability), in which we give similar examples. 2.) The most serious charge that Freedman makes is that the algorithms do not compute what we say they do..
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