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Additionally, this growth demands that existing forecasting models efficiently scale to handle the increased data volume. Approximate inference methods such as , which is based on the Integrated nested Laplace approximation, offer improved computational efficiencies and the ability to perform inference on more complex point-process models compared to traditional MCMC approaches. We present SB-ETAS: a simulation based inference procedure for the epidemic-type aftershock sequence (ETAS) model. This approximate Bayesian method uses sequential neural posterior estimation (SNPE) to learn posterior distributions from simulations, rather than typical MCMC sampling using the likelihood. On synthetic earthquake catalogs, SB-ETAS provides better coverage of ETAS posterior distributions compared with . Furthermore, we demonstrate that using a simulation based procedure for inference improves the scalability from <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal {O}(n^2)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:msup>\n                      <mml:mi>n<\/mml:mi>\n                      <mml:mn>2<\/mml:mn>\n                    <\/mml:msup>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> to <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal {O}(n\\log n)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>log<\/mml:mo>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. This makes it feasible to fit to very large earthquake catalogs, such as one for Southern California dating back to 1981. SB-ETAS can find Bayesian estimates of ETAS parameters for this catalog in less than 10\u00a0h on a standard laptop, a task that would have taken over 2 weeks using MCMC. Beyond the standard ETAS model, this simulation based framework allows earthquake modellers to define and infer parameters for much more complex models by removing the need to define a likelihood function.<\/jats:p>","DOI":"10.1007\/s11222-024-10486-6","type":"journal-article","created":{"date-parts":[[2024,8,29]],"date-time":"2024-08-29T07:02:44Z","timestamp":1724914964000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["SB-ETAS: using simulation based inference for scalable, likelihood-free inference for the ETAS model of earthquake occurrences"],"prefix":"10.1007","volume":"34","author":[{"given":"Samuel","family":"Stockman","sequence":"first","affiliation":[]},{"given":"Daniel J.","family":"Lawson","sequence":"additional","affiliation":[]},{"given":"Maximilian J.","family":"Werner","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,8,29]]},"reference":[{"issue":"8","key":"10486_CR1","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1080\/14697688.2015.1123287","volume":"16","author":"E Bacry","year":"2016","unstructured":"Bacry, E., Jaisson, T., Muzy, J.-F.: Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics. 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