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Improving understanding of current seismic risk is often dependent ondeveloping a more complete characterization of earthquakes that have occurredin the past, and in particular before the development of modern sensingequipment in the middle of the twentieth century. However, accounts of suchevents are typically anecdotal in nature, limiting efforts to model them tomore heuristic approaches. To address this shortfall, we develop a frameworkbased in Bayesian inference to provide a more rigorous methodology forestimating pre-instrumental earthquakes. By directly modeling accounts ofresultant tsunamis via probability distributions, the framework allowspractitioners to make principled estimates of key characteristics (e.g.,magnitude and location) of historical earthquakes. To illustrate this idea, weapply the methodology to the estimation of an earthquake in Eastern Indonesiain the mid 19th century, the source of which is currently the subject ofconsiderable debate in the geological community. The approach taken here givesevidence that even "small data" that is limited in scope and extremelyuncertain can still be used to yield information on past seismic events.Moreover, sensitivity bounds indicate that the results obtained here are robustdespite the inherent uncertainty in the observations.

Embracing Uncertainty in "Small Data" Problems: Estimating Earthquakes from Historical Anecdotes