MODELING THE MANY EARTHQUAKES IN SUMATRA USING POISSON HIDDEN MARKOV MODELS AND EXPECTATION MAXIMIZATION ALGORITHM

Abstract

Sumatra Island is one of the islands that are prone to earthquakes because Sumatra Island is located at the confluence of three plates, namely the large Indo-Australian plate, the Eurasian plate and the Philippine plate. In general, the number of earthquake events follows the Poisson distribution, but there are cases where there is overdispersion in the Poisson distribution. The Poisson Hidden Markov Models (PHMMs) method is used to overcome overdispersion, then applying the Expectation-Maximization Algorithm (EM algorithm) to each model to obtain the estimated parameters. From the models obtained, the best model will be selected based on the smallest Akaike Information Criterion (AIC) value. The data used is secondary data on earthquake events on the island of Sumatra from January 2000 to December 2022 with a depth of ≤ 70 Km and a magnitude of ≥ 4.4 Mw. From the research, the model with m = 3 is the best estimation model with an AIC value of 1503,286. From the best model, estimates are obtained for Poisson Hidden Markov Models with an average occurrence of earthquakes of 5.7633 ≈ 6 events within one month.