  Causal discovery procedures aim to deduce causal relationships among
variables in a multivariate dataset. While various methods have been proposed
for estimating a single causal model or a single equivalence class of models,
less attention has been given to quantifying uncertainty in causal discovery in
terms of confidence statements. The primary challenge in causal discovery is
determining a causal ordering among the variables. Our research offers a
framework for constructing confidence sets of causal orderings that the data do
not rule out. Our methodology applies to structural equation models and is
based on a residual bootstrap procedure to test the goodness-of-fit of causal
orderings. We demonstrate the asymptotic validity of the confidence set
constructed using this goodness-of-fit test and explain how the confidence set
may be used to form sub/supersets of ancestral relationships as well as
confidence intervals for causal effects that incorporate model uncertainty.
