Non-stationary GP-ETAS model

The Epidemic Type Aftershock Sequence (ETAS) model, an example of a self-exciting, spatiotemporal, marked Hawkes process, is widely used in statistical seismology to describe the self-exciting mechanism of earthquake occurrences. Fitting an ETAS model to data requires estimating the conditional intensity function, which represents the rate at which earthquake events occur, conditioned on the history of previous events. Many existing methods, both parametric and non-parametric, have limitations in quantifying uncertainty, as most estimation techniques provide only a point estimate. The GP-ETAS model defines the background intensity in a Bayesian non-parametric way through a Gaussian Process prior, enabling us to incorporate prior knowledge and effectively encode the uncertainty arising from both data and prior information. Building on the spatiotemporal GP-ETAS model, we have developed the non-stationary GP-ETAS model, which allows the background intensity and aftershock productivity parameter to be time-dependent. We aim to use the non-stationary GP-ETAS model to study seismicity in areas with slow-slip earthquakes.