Neumann et al. (2010) aim to find directed graphical representations of the independence and dependence relations among activities in brain regions by applying a search procedure to merged fMRI activity records from a large number of contrasts obtained under a variety of conditions. To that end, Neumann et al., obtain three graphical models, justifying their search procedure with simulations that find that merging the data sampled from probability distributions characterized by two distinct Bayes net graphs results in a graphical object that combines the edges in the individual graphs. We argue that the graphical objects they obtain cannot be interpreted as representations of conditional independence and dependence relations among localized neural activities; specifically, directed edges and directed pathways in their graphical results may be artifacts of the manner in which separate studies are combined in the meta-analytic procedure. With a larger simulation study, we argue that their simulation results with combined data sets are an artifact of their choice of examples. We provide sufficient conditions and necessary conditions for the merger of two or more probability distributions, each characterized by the Markov equivalence class of a directed acyclic graph, to be describable by a Markov equivalence class whose edges are a union of those for the individual distributions. Contrary to Neumann et al., we argue that the scientific value of searches for network representations from imaging data lies in attempting to characterize large scaled neural mechanisms, and we suggest several alternative strategies for combining data from multiple experiments.
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