  The Epidemic Type Aftershock Sequence (ETAS) model is widely used to model
seismic sequences and underpins Operational Earthquake Forecasting (OEF).
However, it remains challenging to assess the reliability of inverted ETAS
parameters for a range of reasons. The most common algorithms just return point
estimates with little quantification of uncertainty, and Bayesian Markov Chain
Monte Carlo implementations remain slow to run, do not scale well and few have
been extended to include spatial structure. Here we present a new approach to
ETAS modelling using an alternative Bayesian method, the Integrated Nested
Laplace Approximation (INLA). We have implemented this model in a new R-Package
called ETAS.inlabru, which builds on the R packages R-INLA and inlabru . Whilst
we just present the temporal component here, the model scales to a
spatio-temporal model and may include a variety of spatial covariates. Using a
series of synthetic case studies, we explore the robustness of our ETAS
inversion method. We demonstrate that reliable estimates of the model
parameters require that the catalogue data contains periods of relative
quiescence as well as triggered sequences. We explore the robustness under
stochastic uncertainty in the training data and show that the method is robust
to a wide range of starting conditions. We show how the inclusion of historic
earthquakes prior to the modelled domain affects the quality of the inversion.
Finally, we show that rate dependent incompleteness after large earthquakes has
a significant and detrimental effect on the ETAS posteriors. We believe that
the speed of the inlabru inversion, which include a rigorous estimation of
uncertainty, will enable a deeper exploration of how to use ETAS robustly for
seismicity modelling and operational earthquake forecasting.
