  This paper develops a novel method, based on hidden Markov models, to
forecast earthquakes and applies the method to mainshock seismic activity in
southern California and western Nevada. The forecasts are of the probability of
a mainshock within one, five, and ten days in the entire study region or in
specific subregions and are based on the observations available at the forecast
time, namely the inter event times and locations of the previous mainshocks and
the elapsed time since the most recent one. Hidden Markov models have been
applied to many problems, including earthquake classification; this is the
first application to earthquake forecasting.
