Reconciling risk-based and storyline attribution with Bayes theorem

The question to what extent climate change is responsible for extreme weather events has been at the forefront of public and scholarly discussion for years. Proponents of the "risk-based" approach to attribution attempt to give an unconditional answer based on the probability of some class of events in a world with and without human influences. As an alternative, so-called "storyline" studies investigate the impact of a warmer world on a single, specific weather event. This can be seen as a conditional attribution statement. In this study, we connect conditional to unconditional attribution using Bayes theorem: in essence, the conditional statement is composed of two unconditional statements, one based on all available data (event and conditions) and one based on the conditions alone. We explore the effects of the conditioning in a simple statistical toy model and a real-world attribution of European summer temperatures conditional on blocking. The resulting attribution statement is generally strengthened if the conditions are not affected by climate change. Conversely, if part of the trend is contained in the conditions, a weaker attribution statement may result.