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Inferring the effect of interventions within complex systems is a fundamentalproblem of statistics. A widely studied approach employs structural causalmodels that postulate noisy functional relations among a set of interactingvariables. The underlying causal structure is then naturally represented by adirected graph whose edges indicate direct causal dependencies. In a recentline of work, additional assumptions on the causal models have been shown torender this causal graph identifiable from observational data alone. Oneexample is the assumption of linear causal relations with equal error variancesthat we will take up in this work. When the graph structure is known, classicalmethods may be used for calculating estimates and confidence intervals forcausal effects. However, in many applications, expert knowledge that providesan a priori valid causal structure is not available. Lacking alternatives, acommonly used two-step approach first learns a graph and then treats the graphas known in inference. This, however, yields confidence intervals that areoverly optimistic and fail to account for the data-driven model choice. Weargue that to draw reliable conclusions, it is necessary to incorporate theremaining uncertainty about the underlying causal structure in confidencestatements about causal effects. To address this issue, we present a frameworkbased on test inversion that allows us to give confidence regions for totalcausal effects that capture both sources of uncertainty: causal structure andnumerical size of nonzero effects.

Confidence in Causal Inference under Structure Uncertainty in Linear Causal Models with Equal Variances