Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1412.1922

Nonstationary ETAS models for nonstandard earthquakes

Takao Kumazawa·Yosihiko Ogata
View original source ↗Read source document ↗Export metadata ↓

Abstract

The conditional intensity function of a point process is a useful tool for generating probability forecasts of earthquakes. The epidemic-type aftershock sequence (ETAS) model is defined by a conditional intensity function, and the corresponding point process is equivalent to a branching process, assuming that an earthquake generates a cluster of offspring earthquakes (triggered earthquakes or so-called aftershocks). Further, the size of the first-generation cluster depends on the magnitude of the triggering (parent) earthquake. The ETAS model provides a good fit to standard earthquake occurrences. However, there are nonstandard earthquake series that appear under transient stress changes caused by aseismic forces such as volcanic magma or fluid intrusions. These events trigger transient nonstandard earthquake swarms, and they are poorly fitted by the stationary ETAS model. In this study, we examine nonstationary extensions of the ETAS model that cover nonstandard cases. These models allow the parameters to be time-dependent and can be estimated by the empirical Bayes method. The best model is selected among the competing models to provide the inversion solutions of nonstationary changes. To address issues of the uniqueness and robustness of the inversion procedure, this method is demonstrated on an inland swarm activity induced by the 2011 Tohoku-Oki, Japan earthquake of magnitude 9.0.

Explore related subjects

stat.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Takao Kumazawa, Yosihiko Ogata. 2014-12-05. Nonstationary ETAS models for nonstandard earthquakes. https://doi.org/10.1214/14-aoas759

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Relegation, promotion and the components of scoring in water polo

Relegation, not the championship, decides the outcome of many European water polo leagues: one club has won every recent national title in Italy, Spain and Hungary. We make the relegation decision our object of inference. Serie A1 relegates one club for finishing last and a second through a three-match play-out, and we ask at each stage how much can be known and when. Promoted clubs arrive with no top-flight record, so we also compare four ways of setting their prior. These analyses rest on the first Bayesian hierarchical model of water polo, which splits scoring into even-strength, man-up and penalty components, models opportunities and conversions separately, and lets abilities evolve between seasons. Treating the components as independent proves untenable, since they compete for a common budget of possessions. Fitted to a new dataset of 940 matches, the model identifies the directly relegated club from the ninth round, before the league table does, predicts the play-out field better than the table, and shows the play-out itself to be close to a coin toss. Promoted clubs start below the league on every component except drawing exclusions: knowing a club was promoted improves forecasts; knowing how does not.

stat.AP↗
arXiv2026

Geospatial Foundation Models Capture Health-Relevant Dimensions of Place Beyond Conventional Social Risk Indices

Area-based social risk indices summarize residents' socioeconomic conditions but incompletely capture physical features of place that may affect health. We evaluated whether numerical representations of physical place produced by four geospatial foundation model families from 2022 satellite data explained residual variance in tract-level associations between the Area Deprivation Index, Social Deprivation Index, and Social Vulnerability Index with health outcomes. We used LightGBM to predict variables from the American Community Survey and 40 chronic disease and health-behavior outcomes from CDC PLACES across 82,646 census tracts in the contiguous United States, evaluating performance across 10 held-out states. Among survey variables, models were moderately predictive of some variables including housing type (R-squared up to 0.54) but weak for disability, unemployment, and income disparity. For health outcomes, models explained up to 54% of variance left unexplained by social risk indices, with the largest gains for annual checkups, arthritis, and high blood pressure. Mean total variance explained by geospatial foundation models across the 40 health-related outcomes increased from 0.31 in the smallest tract-size decile to 0.39 in the largest. Geospatial foundation models capture health-relevant features of place not represented by conventional social risk indices and may usefully augment them in epidemiological analyses.

stat.AP↗
arXiv2026

Transporting summary measures of relative effects from randomised trials to the treated patient population: an application to breast cancer endocrine therapy

Randomised trials often report relative treatment effects, such as risk ratios and hazard ratios, for trial populations. Clinical decision-making, however, often benefits from estimates of absolute treatment effects in the population eligible for treatment. Trial participants may not represent this target population well, and restrictions on access to individual participant trial data can further complicate absolute effect estimation. Routine care data are often representative of the target population but may be subject to uncontrolled confounding. We consider estimation of the average treatment effect on the treated (ATT), an absolute measure, by combining a representative sample of treated routine care patients with summary measures (i.e., estimated risk or hazard ratios) from either a randomised trial or a meta-analysis of trials. Under marginal or conditional transportability assumptions, the ATT is shown to be identifiable. The implications of collapsibility of the effect measure on transportability are discussed, and plug-in estimators of the ATT are presented. Simulation studies are used to assess finite sample performance of the estimators in a range of settings. The proposed methods are applied to estimate the ATT of endocrine therapy on 15-year breast cancer mortality using results from a meta-analysis of randomised trials and England's National Disease Registration Service.

stat.AP↗