Earthquakes are a natural phenomenon that is random, irregular in space and time. Until now the forecast of earthquake occurrence at a location is still difficult to be estimated so that the development of earthquake forecast methodology is still carried out both from seismology aspect and stochastic aspect. To explain the random nature phenomena, both in space and time, a point process approach can be used. There are two types of point processes: temporal point process and spatial point process. The temporal point process relates to events observed over time as a sequence of time, whereas the spatial point process describes the location of objects in two or three dimensional spaces.

The points on the point process can be labeled with additional information called marks. A marked point process can be considered as a pair (x, m) where x is the point of location and m is the mark attached to the point of that location. This study aims to model marked point process indexed by time on earthquake data in Sumatra Island and Java Island. This model can be used to analyze seismic activity through its intensity function by considering the history process up to time before t. Based on data obtained from U.S. Geological Survey from 1973 to 2016 with magnitude threshold 5, we obtained maximum likelihood estimate of model parameters for the gamma distribution which dependent on the history (full model) and for exponential distribution which independent on the history (null model). For earthquake data in Sumatra, log-likelihood function for full model is greater than log-likelihood function for null model. In addition, the AIC value for the full model is smaller than the AIC value of the null model. This shows that the full model is better for describing the seismic intensity than the null model. The same results are also shown for earthquake data in Java Island. The estimation of model parameters shows that the seismic activity in Sumatra Island is greater than Java Island.