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The $b$-value in earthquake magnitude-frequency distribution quantifies the relative frequency of large versus small earthquakes. Monitoring its evolution could provide fundamental insights into temporal variations of stress on different…

Geophysics · Physics 2023-06-19 Eugenio Lippiello , Giuseppe Petrillo

The Stochastic Approximation EM (SAEM) algorithm, a variant stochastic approximation of EM, is a versatile tool for inference in incomplete data models. In this paper, we review the fundamental EM algorithm and then focus especially on the…

Methodology · Statistics 2018-11-30 Vahid Tadayon

Machine learning (ML) catalogs contain many more earthquakes than routine catalogs, but their performance in phase picking and earthquake detection has not been fully evaluated. We develop station-level detection probabilities using…

We report an empirical determination of the probability density functions P(r) of the number r of earthquakes in finite space-time windows for the California catalog, over fixed spatial boxes 5 x 5 km^2 and time intervals dt =1, 10, 100 and…

Geophysics · Physics 2007-05-23 A. Saichev , D. Sornette

Aftershocks of aftershocks - and their aftershock cascades - substantially contribute to the increased seismicity rate and the associated elevated seismic hazard after the occurrence of a large earthquake. Current state-of-the-art…

Geophysics · Physics 2024-11-07 Leila Mizrahi , Dario Jozinović

Numerical models are starting to be used for determining the future behaviour of seismic faults and fault networks. Their final goal would be to forecast future large earthquakes. In order to use them for this task, it is necessary to…

Electroencephalography (EEG) is an objective tool for emotion recognition and shows promising performance. However, the label scarcity problem is a main challenge in this field, which limits the wide application of EEG-based emotion…

Signal Processing · Electrical Eng. & Systems 2024-09-02 Rushuang Zhou , Weishan Ye , Zhiguo Zhang , Yanyang Luo , Li Zhang , Linling Li , Gan Huang , Yining Dong , Yuan-Ting Zhang , Zhen Liang

Reliable probabilities are critical in high-risk applications, yet common calibration criteria (confidence, class-wise) are only necessary for full distributional calibration, and post-hoc methods often lack distribution-free guarantees. We…

Machine Learning · Statistics 2025-10-17 Daniil Kazantsev , Mohsen Guizani , Eric Moulines , Maxim Panov , Nikita Kotelevskii

We present an analytical solution and numerical tests of the epidemic-type aftershock (ETAS) model for aftershocks, which describes foreshocks, aftershocks and mainshocks on the same footing. The occurrence rate of aftershocks triggered by…

Statistical Mechanics · Physics 2015-06-24 A. Helmstetter , D. Sornette

Probabilistic forecasts in the form of ensemble of scenarios are required for complex decision making processes. Ensemble forecasting systems provide such products but the spatio-temporal structures of the forecast uncertainty is lost when…

Applications · Statistics 2016-12-21 Zied Ben Bouallegue , Tobias Heppelmann , Susanne E. Theis , Pierre Pinson

Meta analysis is commonly-used to synthesize multiple results from individual studies. However, its validation is usually threatened by publication bias and between-study heterogeneity, which can be captured by the Copas selection model.…

Methodology · Statistics 2025-07-21 Mengke Li , Yukun Liu , Pengfei Li , Jing Qin

Despite extensive research on neural network calibration, existing methods typically apply global transformations that treat all predictions uniformly, overlooking the heterogeneous reliability of individual predictions. Furthermore, the…

Machine Learning · Computer Science 2025-10-22 Hassan Gharoun , Mohammad Sadegh Khorshidi , Kasra Ranjbarigderi , Fang Chen , Amir H. Gandomi

Long-range ensemble forecasts are typically verified as anomalies with respect to a lead-time dependent climatological mean to remove the influence of systematic biases. However, common methods for calculating anomalies result in…

Atmospheric and Oceanic Physics · Physics 2025-06-11 Christopher D. Roberts , Martin Leutbecher

We develop an efficient numerical scheme to solve accurately the set of nonlinear integral equations derived previously in (Saichev and Sornette, 2007), which describes the distribution of inter-event times in the framework of a general…

Data Analysis, Statistics and Probability · Physics 2009-11-13 D. Sornette , S. Utkin , A. Saichev

This paper introduces EQShapelets (EarthQuake Shapelets) a time-series shape-based approach embedded in machine learning to autonomously detect earthquakes. It promises to overcome the challenges in the field of seismology related to…

Machine Learning · Computer Science 2019-11-21 Monica Arul , Ahsan Kareem

Recent studies in the literature have introduced a new approach to earthquake forecasting based on representing the space-time patterns of localized seismicity by a time-dependent system state vector in a real-valued Hilbert space and…

The stochastic approximation EM algorithm (SAEM) is described for the estimation of item and person parameters given test data coded as dichotomous or ordinal variables. The method hinges upon the eigenanalysis of missing variables sampled…

Methodology · Statistics 2020-01-01 Eugene Geis

Nowadays, weather prediction is based on numerical weather prediction (NWP) models to produce an ensemble of forecasts. Despite of large improvements over the last few decades, they still tend to exhibit systematic bias and dispersion…

Applications · Statistics 2024-02-02 David Jobst , Annette Möller , Jürgen Groß

This paper considers an approximate dynamic matrix factor model that accounts for the time series nature of the data by explicitly modelling the time evolution of the factors. We study estimation of the model parameters based on the…

Methodology · Statistics 2026-01-08 Matteo Barigozzi , Luca Trapin

Yes. Interval statistics have been used to conclude that major earthquakes are random events in time and cannot be anticipated or predicted. Machine learning is a powerful new technique that enhances our ability to understand the…