  Event attribution in the context of climate change seeks to understand the
role of anthropogenic greenhouse gas emissions on extreme weather events,
either specific events or classes of events. A common approach to event
attribution uses climate model output under factual (real-world) and
counterfactual (world that might have been without anthropogenic greenhouse gas
emissions) scenarios to estimate the probabilities of the event of interest
under the two scenarios. Event attribution is then quantified by the ratio of
the two probabilities. While this approach has been applied many times in the
last 15 years, the statistical techniques used to estimate the risk ratio based
on climate model ensembles have not drawn on the full set of methods available
in the statistical literature and have in some cases used and interpreted the
bootstrap method in non-standard ways. We present a precise frequentist
statistical framework for quantifying the effect of sampling uncertainty on
estimation of the risk ratio, propose the use of statistical methods that are
new to event attribution, and evaluate a variety of methods using statistical
simulations. We conclude that existing statistical methods not yet in use for
event attribution have several advantages over the widely-used bootstrap,
including better statistical performance in repeated samples and robustness to
small estimated probabilities. Software for using the methods is available
through the climextRemes package available for R or Python. While we focus on
frequentist statistical methods, Bayesian methods are likely to be particularly
useful when considering sources of uncertainty beyond sampling uncertainty.
