Understanding the relation between the recurrence of large and small earthquakes is a formidable challenge, because multiple data sets with poorly known uncertainties are combined to explore phenomena that may vary from place to place and whose underlying physics are unknown. This problem often arises in attempts to assess the recurrence intervals of large earthquakes, which are important for earthquake physics, tectonics, and seismic hazard analysis. For example, we often seek to infer the sizes and rates of future large earthquakes from an earthquake record containing seismological, geological, and cultural records. This process, however, is far from straightforward and is...

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