Embracing Uncertainty in “Small Data” Problems: Estimating Earthquakes From Historical Anecdotes

Abstract Seismic risk estimates are greatly improved with an increased understanding of historical (and pre‐historical) seismic events. Although Bayesian inference has been shown to provide reasonable estimates of the location and magnitude of historical earthquakes from anecdotal tsunamigenic evidence, the validity and robustness of such an approach has yet to be definitively demonstrated. Thus, in this article we present a careful analysis of the uncertainty inherent to this statistical recreation of historical seismic events. Using a priori estimates on the posterior and numerical approximations of the Hessian, we demonstrate that the 1852 Banda Sea earthquake and tsunami is well‐understood given certain explicit hypotheses. Using the same techniques we also find that the 1820 south Sulawesi event may best be explained by a dual fault rupture, best attributed to the Kalatoa fault potentially conjoining the Flores thrust and Walanae/Selayar fault.