 
Summary: Reply to Freedman
by Peter Spirtes and Richard Scheines
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
