  Improving understanding of current seismic risk is often dependent on
developing a more complete characterization of earthquakes that have occurred
in the past, and in particular before the development of modern sensing
equipment in the middle of the twentieth century. However, accounts of such
events are typically anecdotal in nature, limiting efforts to model them to
more heuristic approaches. To address this shortfall, we develop a framework
based in Bayesian inference to provide a more rigorous methodology for
estimating pre-instrumental earthquakes. By directly modeling accounts of
resultant tsunamis via probability distributions, the framework allows
practitioners to make principled estimates of key characteristics (e.g.,
magnitude and location) of historical earthquakes. To illustrate this idea, we
apply the methodology to the estimation of an earthquake in Eastern Indonesia
in the mid 19th century, the source of which is currently the subject of
considerable debate in the geological community. The approach taken here gives
evidence that even "small data" that is limited in scope and extremely
uncertain can still be used to yield information on past seismic events.
Moreover, sensitivity bounds indicate that the results obtained here are robust
despite the inherent uncertainty in the observations.
