On the Estimation of the Aftershock Intensity Function by Means of an Adaptive Bayesian Estimator

Reference No.	2026a041
Type/Category	Grant for Project Research- Short-term Visiting Researcher
Title of Research Project	On the Estimation of the Aftershock Intensity Function by Means of an Adaptive Bayesian Estimator
Principal Investigator	Shuntaro Suzuki（Graduate School of Engineering Science, The University of Osaka・Doctoral Program (Second Year)）
Research Period
Keyword(s) of Research Fields	bayes estimation, adaptive estimation
Abstract for Research Report	The probability of aftershock occurrence following a mainshock has been empirically studied, and it is well known that large aftershocks tend to occur within one day after the mainshock. However, observations during this period often suffer from substantial missing data, making accurate evaluation difficult. A notable study addressing this issue is Forecasting large aftershocks within one day after the main shock. Specifically, in Omi et al. (2013), the observed aftershock intensity function is modeled parametrically using both the probability of detecting earthquakes above a certain magnitude threshold (detection probability) and the true underlying aftershock intensity function. Parameter estimation in their approach is conducted in two stages: first, the parameters of the detection probability are estimated, and subsequently, the parameters of the true aftershock intensity function are inferred. However, depending on the modeling of the detection probability, the optimization of the loss function in the first stage may involve numerous local optima, leading to numerical instability in estimation. To address this issue, the present study proposes a sequential estimation method in which the detection probability is estimated via Bayesian inference, thereby avoiding the need for loss function optimization. The estimated detection probability is then plugged into the likelihood function of the intensity model, and the remaining parameters are obtained via maximum likelihood estimation. Through this approach, we aim to achieve numerically stable estimation of the aftershock intensity function. This enables the use of expressive mathematical models capable of capturing realistic aftershock behavior, while maintaining numerical stability in the estimation process. Reference Omi, T., Ogata, Y., Hirata, Y., & Aihara, K. (2013). Forecasting large aftershocks within one day after the main shock. Scientific reports, 3(1), 2218.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Shuntaro Suzuki（Graduate School of Engineering Science, Osaka University・Doctoral Program (Second Year)）