[S-TT38] 最先端ベイズ統計学が拓く地震ビッグデータ解析

[STT38-05] Bayesian non-parametric inference for the ETAS model

*牛 源源¹、庄 建倉^1,2 (1.総合研究大学院大学、2.統計数理研究所)

The epidemic type aftershock sequence (ETAS) model, which is an example of a self-exciting, spatio-temporal, marked Hawkes process, is widely used in statistical seismology to describe the self-exciting mechanism of earthquake occurrences. The ETAS model is characterized by its rate of arriving earthquake events conditioned on the history of previous events, which is also called the conditional intensity function. Fitting an ETAS model to data requires us to estimate the conditional intensity function. Many previous methods, including parametric and non-parametric methods, have certain limitations in quantifying uncertainty since most estimation techniques deliver a point estimate for the conditional intensity function. The GP-ETAS model models the background intensity in a Bayesian non-parametric way through a Gaussian Process prior, allowing us to incorporate prior knowledge and effectively encode the uncertainty of the quantities arising from data and prior information. Three data augmentations (a latent branching structure, a latent Poisson process, and latent Pólya–Gamma random variables) are used to let us obtain a likelihood representation which is conditionally conjugate to the GP prior. These three data augmentations help us to estimate the posterior using an efficient Gibbs sampling algorithm. Based on this model, we have carried out some new research topics, and some work is still ongoing. This presentation mainly introduces the GP-ETAS model and some developments.