Selection Bias in Extreme Event Attribution Studies

22 Pages Posted: 12 Mar 2023 Last revised: 29 Aug 2023

See all articles by Ophelia Miralles

Ophelia Miralles


Anthony C. Davison

École Polytechnique Fédérale de Lausanne

Date Written: February 1, 2023


Selection bias may arise when data have been chosen in a way that is not accounted for in subsequent analysis.  Such bias can arise in climate event attribution studies, which are often performed rapidly after a devastating "trigger event", whose occurrence can be regarded as a form of stopping rule.  Intuition suggests that including the trigger event in a fit in which it is the final observation will bias its importance downwards, and that excluding it will have the opposite effect, but in either case the effect of the stopping rule should be taken into account.  The resulting timing bias has recently been discussed in the statistical literature (Barlow et al., 2020), and here we investigate the implications for climate event attribution. Simulations in the univariate setting show substantially lower relative bias and root mean squared error for estimation of the 200-year return level when the timing bias is accounted for. In the bivariate setting, simulations show that not accounting for the stopping rule can lead to both over- and under-estimation of return levels, but bias can be reduced by more appropriate analysis. We also discuss biases arising when an extreme event occurs in one of several related time series but this is not accounted for in data analysis, and show that the estimated  return period for the "trigger event" based on a dataset that contains this event can be biased and very uncertain  and thus should be avoided. The ideas are illustrated by analysis of rainfall data from Venezuela and temperature data from India.

Keywords: Climate event attribution, Climate extreme event, Likelihood-based inference, Spatial selection, Timing bias

Suggested Citation

Miralles, Ophelia and Davison, Anthony C., Selection Bias in Extreme Event Attribution Studies (February 1, 2023). Available at SSRN: or

Anthony C. Davison

École Polytechnique Fédérale de Lausanne ( email )

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