HIDDEN MARKOV MODEL ON EARTHQUAKES IN INDONESIA (CASE STUDY: ANNUAL MAXIMUM MAGNITUDE DATA) - Amrullah Taufiq, Afif
Stress levels on faults are important in the analysis of earthquakes in an area. However, these data are difficult to obtain because they require direct measurements and limited accessibility to the site. The magnitude of an earthquake can be considered as the result of stress release on a fault. For this reason, this pair of sequences can be analyzed by a model that is widely applied in the field of bioinformatics, namely the Hidden Markov Model (HMM). The hidden state is the stress level on the fault and it follows a Markov chain, denoted by H, and the observable is the earthquake magnitude sequence, denoted by O. Furthermore, H is divided into 3 states namely low, medium, and high. O is divided into 3 states namely magnitude < 6.5, 6.5 ? magnitude < 7, and magnitude ? 7. This thesis used graph theory, specifically junction tree propagation and Dawid algorithm, to solve two main problems on HMM as follows. 1) Evaluation problem, determine the conditional probability ????(????|????,????,????) where ???? is the matrix of transition probabilities between hidden events, ???? is the matrix of emission probabilities resulting in observed events, and ???? is the initial probability vector indicating the probability of the hidden state at the initial time. 2) Decode problem, determine the optimal hidden state sequence ????????????????1,…,????????????(????,????|????,????,????). In this study, ????(????|????,????,????) of forward-backward (algorithm of Rabiner, 1989) is worse than junction tree propagation. ????????????????1,…,????????????(????,????|????,????,????) of Viterbi (algorithm of Rabiner, 1989) is worse than Dawid. Furthermore, it is found that the longer the H sequence analyzed, the higher the entropy value and of course the computation time required.