Sufficient Condition for Pooling Data from different Distributions

We consider the problems arising from using sequences of experiments to discover the causal structure among a set of variables, none of whom are known ahead of time to be an “outcome”. In particular, we present various approaches to resolve conflicts in the experimental results arising from sampling variability in the experiments. We provide a sufficient condition that allows for pooling of data from experiments with different joint distributions over the variables. Satisfaction of the condition allows for more powerful independence tests that may resolve some of the conflicts in the experimental results. The pooling condition has its own problems, but should – due to its generality – be informative to techniques for meta-analysis.