A Time-Scaled ETAS Model for Earthquake Forecasting

Agniva Das; Muralidharan K

REVIEW 5 major objections 6 minor 26 references

A Time-Scaled ETAS Model for Earthquake Forecasting

T0 review · 5 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper claims that rescaling time before fitting an ETAS model yields accurate earthquake forecasts for Nepal and could support early warning systems.

desk verdict A workmanlike in-sample ETAS fit for Nepal with time-scale transformations, but the abstract's forecasting claim is not backed by any out-of-sample or prospective validation. read the letter →

arxiv 2505.24412 v2 pith:IRBK2R7H submitted 2025-05-30 stat.AP stat.ME

Agniva Das , Muralidharan K This is my paper

classification stat.APstat.ME

keywords earthquakepredictiontime-scaledETASspatio-temporalpointprocesstriggeredvsbackgroundseismicitystochasticde-clusteringmaximumlikelihoodestimationNepalprobabilisticforecasting

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper contends that an Epidemic Type Aftershock Sequence (ETAS) model—a point process that splits seismicity into a stationary background rate and a triggering kernel for aftershocks—can accurately forecast Nepal earthquakes once the time axis is rescaled before fitting. The authors fit several time-scaled variants to the 1990–2022 ANSS catalogue of magnitude-5 and larger events, and report that a calibration time scale with $\omega$ near 1000 markedly improves log-likelihood over unscaled alternatives while keeping parameters interpretable. Diagnostic checks on the fitted catalogue, including a Kolmogorov–Smirnov test on transformed event times with $p = 0.4386$, are taken as evidence that the model captures the catalogue's temporal structure. If the claim holds, the model's separation of background and triggered events could guide aftershock hazard assessment and early warning in Nepal.

What carries the argument

The load-bearing object is the conditional intensity function $\lambda(t,x,y,m|\mathcal{H}_t)$ of the marked spatio-temporal ETAS point process, written as a stationary background rate $\mu u(x,y)$ plus a sum over past events of a productivity term $\kappa(m_i)$, an Omori-type time kernel $g_{c,p}(t-t_i)$, and a radially symmetric spatial kernel $f_{D,\gamma,q}$; the time-scaled variant first replaces clock time $t$ with a transformed time $t_Z = \phi(t,\ldots)$ (examples tried include $t/\omega$, $t/Z(t)$, $\log t$, and $t^\omega$) before fitting. The transformation is what the paper uses to make background versus triggered events easier to distinguish, and the fitted model then assigns each event a de-clustering probability via the stochastic reconstruction formula, which drives the spatial interpretation.

What would settle it

Refit the time-scaled ETAS model using only catalogue events before April 25, 2015, then compute one-step-ahead predicted intensities for the 2015–2022 period and score them against a homogeneous Poisson baseline; if the ETAS model does not outperform the baseline on held-out events under a proper scoring rule, the paper's forecasting claim is not supported.

Watch

Extended reading notes

Core claim

The discovery the paper asserts is that rescaling time before applying ETAS—most successfully with the calibration scale $t_Z = t/\omega$ at $\omega$ around 1000—yields a model for the Nepal catalogue whose parameters are both more interpretable and closer to those of the iteratively de-clustered ETAS, and whose log-likelihood is far better than the unscaled ground-intensity fits. The fitted model locates high background seismicity in northwestern Nepal (Karnali) and a high clustering coefficient, hence high aftershock potential, in central Nepal (Kathmandu–Narayani), with most near-Kathmandu events classified as triggered and most northwestern events as spontaneous. These conclusions rest on in-sample diagnostics: residual maps and a Kolmogorov–Smirnov test on the transformed times. The paper reads the good KS p-value as confirmation that the model's intensity truly describes the catalogue's triggering structure, and from there infers forecasting ability.

Load-bearing premise

The forecasting claim stands or falls on whether the in-sample fit—residuals and the Kolmogorov–Smirnov test on the fitted 1990–2022 catalogue—carries over to earthquakes the model has not already seen.

Editorial extensions

If this is right

If the time-scaled ETAS forecasts are trustworthy, central Nepal's elevated clustering coefficient implies that large mainshocks there should be followed by proportionally more aftershocks than in the northwest, guiding where aftershock monitoring is prioritized.
The de-clustering probabilities give a map of spontaneous versus triggered seismicity, which could be used to set region-specific alert thresholds in an early warning system.
The calibration time scale with $\omega \approx 1000$ produces the best log-likelihood among the ground-intensity variants, indicating that time rescaling can substantially improve ETAS fit without changing the kernel structure.
The gamma magnitude distribution fits marginally better than the exponential in every time scale tested, but the paper notes that the extra parameter may not pay for itself in larger samples.
The paper's comparison positions the iteratively de-clustered ETAS (ISDM) as the overall best fit, so any operational forecasting system in Nepal would likely build on that variant.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper, a true out-of-sample test—refitting on data before the April 2015 Gorkha mainshock and forecasting 2015–2022—would settle whether the in-sample KS diagnostic confers genuine predictive skill.
The large $\omega$ calibration scale stretches time and shrinks the fitted $c$ parameter, so part of the log-likelihood gain may be a reparameterization effect rather than a better physical description; comparing AIC across scales would clarify this.
The paper's own suggestion to use Himalayan uplift or glacial melt rates as usage measures for the proportional-hazards scale is untested; connecting ETAS time scaling to geodetic loading data is a plausible next step.
Given the sparse catalogue at the $m_0=5$ threshold, the fitted parameters are likely sensitive to the 2015 Gorkha cluster; a sensitivity analysis that down-weights that cluster would reveal how much the conclusions depend on it.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The short version: this is a straightforward ETAS fitting exercise with time-scale transformations borrowed from survival analysis, applied to a Nepal catalogue. The only genuinely new element is the application; the model itself is Ogata's ETAS and the time scales are quoted from Kordonsky–Gertsbakh and Duchesne–Lawless. The paper's central claim—accurate forecasting for Nepal—is not supported by the evidence, which is entirely in-sample.

To its credit, the paper uses a real catalogue, reports parameter estimates and log-likelihoods across several time scales, and includes residual diagnostics and a KS test. That is a legitimate descriptive modeling exercise, and the comparison between estimation approaches is more than hand-waving. The references are standard and properly credited.

The load-bearing problem is validation. The transformed-time residuals, the Q-Q plot, the KS p-value, and the selection of omega all come from the same data used to fit the model. That is necessary but not sufficient. There is no holdout period, no pseudo-prospective forecast, and no comparison against a baseline on unseen data. The abstract overstates what the paper shows. I agree with the reader's stress-test note here: the forecasting claim falls on this.

There are also internal consistency issues. Tables 6 and 7 are labelled as phi1(t)=t in their headers even though the text describes log-linear and power scales. More importantly, several reported fits have p < 1 (e.g., p=0.916 in Table 6 and p=0.982 in Table 7), which violates the p > 1 requirement for integrability in Eq. 5, yet these are presented as valid fits. That is not a minor typo; it means those fitted intensities do not integrate to finite expected counts. Table 2's gamma column also looks misaligned, with a p estimate of 0.0139 that cannot be a sensible Omori exponent.

Who is this for? Someone working on ETAS applications in the Himalaya, or a methods course wanting a clean example of why in-sample diagnostics do not equal forecast skill. It deserves a serious referee because the empirical application is non-trivial and the main flaws are identifiable and fixable in revision. My own verdict after review would be reject or major revision unless a genuine out-of-sample evaluation is added.

Send it to peer review, but the reviewers should insist on a holdout or prospective forecast comparison, correction of the table labels, and removal or re-estimation of the p < 1 fits. I would not cite it in its current form.

Referee Report

5 major / 6 minor

Summary. The paper proposes time-scaled variants of the space-time ETAS model—using identity, calibration, proportional-hazards, log-linear, and power time scales—and fits them to a catalogue of Nepalese earthquakes (magnitude ≥ 5) spanning roughly 1990–2022. It compares in-sample log-likelihoods across these models, reports background/triggered classifications and residual diagnostics, and concludes that the time-scaled ETAS model can accurately forecast Nepalese earthquakes and could support early warning systems. No out-of-sample, holdout, or prospective evaluation is performed; all model assessments are computed on the same catalogue used for parameter estimation.

Significance. If substantiated, the paper would offer a useful exploratory comparison of time-scaled ETAS formulations in the Nepal Himalaya, a region where such models have not been widely applied. The exploration of multiple time scales and the use of a real catalogue are strengths. However, the central forecasting claim currently rests entirely on in-sample fit; no predictive experiment is presented, and several fitted models violate the model's own integrability condition. The paper therefore does not yet establish forecast skill, although the approach is worth testing with a proper validation design.

major comments (5)

[Section 2, Fig. 3; Tables 1–7] The abstract claims the model 'is able to accurately forecast earthquake occurrences in Nepal,' but no out-of-sample or holdout evaluation is reported. Every model comparison uses the in-sample log-likelihood on the same catalogue used for fitting, and the reported diagnostics (transformed times τ_j, Q-Q plot, KS p-value) are computed from the fitted parameters on that same catalogue. In-sample fit is not evidence of forecast skill; for a forecasting claim, the authors must provide a prospective or pseudo-prospective experiment, such as fitting on events before a cutoff and evaluating predictive log-likelihood or event counts after it, ideally against a baseline model.
[Eq. (5); Tables 2, 6, 7] The temporal kernel g_{c,p} is defined only for p > 1, yet Table 2 (Gamma column, p = 0.0139), Table 6 (Exponential column, p = 0.91649), and Table 7 (both columns, p = 0.98172 and 0.97418) report fits with p < 1. These fits are therefore not valid ETAS intensity functions, and the log-likelihood values reported for them (-4461.1, -3637.2, -974.85, -928.10) cannot be interpreted as evidence for or against any time scale.
[Tables 6 and 7 captions] Table 6 is headed tZ = φ1(t) = t but the surrounding text describes a log-linear time scale (φ4(t) = log t), and Table 7 is also headed tZ = φ1(t) = t while the text describes a power time scale (φ5(t, ω) = t^ω with ω = 1/2). The headers contradict the text, so the reader cannot tell which transformation generated the reported parameter estimates; this must be corrected before the comparisons can be interpreted.
[Tables 3–4; Section 2] The calibration time-scale parameter ω is selected by inspecting in-sample log-likelihood at two hand-picked values (ω = 5 and ω = 1000), and the text notes that a search algorithm could be used but is not. Selecting ω on the same data that are then used to evaluate model performance inflates the apparent improvement; without a validation split or a selection criterion that accounts for the search, the reported log-likelihood comparisons among time scales are not a fair assessment.
[Section 2, Fig. 3] The Kolmogorov-Smirnov test with p-value 0.4386 is performed on the transformed times U_j computed with parameters estimated from the same catalogue. Under estimated parameters, the U_j are neither independent nor exactly U(0,1) under the null, so the standard KS null distribution does not apply; a parametric bootstrap or holdout-based residual test is needed before this can be cited as evidence of fit.

minor comments (6)

[Abstract; Section 1] The abstract states the dataset covers 2000–2020, while Section 1 states Jan 1, 1990 to May 31, 2022; these dates should be aligned.
[Eq. (8)] The expected number of triggered events is given as Aβ/(β−α), but this requires β > α for the integral to converge; this condition should be stated explicitly.
[Figure 1 caption] The caption says 'January 11, 1990' while the text and other figures say 'Jan 1, 1990'; the correct starting date should be used consistently.
[Section 3; Acknowledgments] There are several typographical issues: 'outtakes' should be 'takeaways' in the conclusions, and the acknowledgments contain 'This was was supported'; these should be corrected.
[Table 5 and Section 2] The usage measure Z(t) for the proportional-hazards time scale is described informally as 'average depth of all minor earthquakes, between two major quakes'; a formal definition with a formula is needed for reproducibility.
[Tables 1–7] Table 2 reports AIC, but Tables 3–7 do not; for comparing time scales, an information criterion such as AIC or BIC should be given consistently across all models, accounting for any additional tuning parameters like ω.

Circularity Check

1 steps flagged · score 6.0 of 10

The forecasting claim is supported only by in-sample fit: the same Nepal catalogue is used to fit and to 'validate' the time-scaled ETAS model, so the reported forecast accuracy reduces to training-data residuals.

fitted input called prediction [Abstract; Introduction paragraph 5; Section 2 (Fig. 3 diagnostics)]
"The dataset of earthquake occurrences in Nepal from 2000 to 2020 was collected and used to fit the time-scaled ETAS model. The model was then validated using the earthquake data from Nepal."

The abstract's conclusion ('able to accurately forecast earthquake occurrences in Nepal') is supported only by validation on the same data used for fitting. The evidence in Section 2 is the transformed-time residual plot, the Q-Q plot of Uj, and a Kolmogorov-Smirnov p-value computed from the fitted model on the fitting catalogue; no holdout period, pseudo-prospective experiment, or comparison on unseen events is reported. Because the parameters were estimated by maximum likelihood from these very events, the residuals measure how well the model was made to fit the training data, not whether it predicts future occurrences. The forecast claim therefore reduces by construction to an in-sample goodness-of-fit check.

full rationale

The mathematical core of the paper is standard ETAS with time-scale transformations borrowed from survival analysis, and I found no definitional identity or self-citation chain that forces the parameter estimates themselves. The circularity is partial and located in the forecasting claim: the model is fitted and 'validated' on the same Nepal catalogue, and the time-scale value ω is chosen by inspecting in-sample log-likelihoods across a small grid. Consequently the abstract's 'accurate forecast' statement is an in-sample fit renamed as prediction, which is statistically forced but not a demonstration of out-of-sample skill. This supports a score of 6 rather than 0, while stopping short of 8-10 because the ETAS derivation itself is not circular.

Assumptions & free parameters 11 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard ETAS assumptions plus a hand-chosen time-scale transformation; no new entities are postulated. The free parameters are all fitted by maximum likelihood to the same catalogue, and the time-scale parameter is chosen ad hoc.

free parameters (11)

background rate mu = 1.1153 (ISDM, exponential); 1.3978 (calibration omega=1000, gamma)
Estimated by MLE; sets the stationary background Poisson intensity.
productivity constant A = 0.2102 (ISDM, exponential)
Estimated by MLE; controls expected number of triggered events per mainshock.
triggering exponent alpha = 1.5979 (ISDM, exponential)
Estimated by MLE; controls magnitude dependence of triggering.
Omori c = 0.0071 (ISDM, exponential)
Time scale of aftershock decay; estimated by MLE.
Omori p = 1.1395 (ISDM, exponential); invalid values below 1 appear in Tables 6 and 7
Decay exponent; must exceed 1 for integrability; some reported fits violate this.
magnitude distribution parameter beta = 3.5912 (ISDM, exponential)
Exponential magnitude parameter; separate from ETAS triggering.
spatial scale D = 0.0033 (ISDM, exponential)
Spatial kernel scale; estimated by MLE.
spatial shape q = 1.8398 (ISDM, exponential)
Spatial kernel tail exponent; estimated by MLE.
spatial triggering coefficient gamma = 1.2236 (ISDM, exponential)
Magnitude-dependent spatial spread; estimated by MLE.
time-scale parameter omega = 5, 1000 (calibration), 0.5 (power), chosen by hand
Not estimated; a few values are tried and the best in-sample fit is reported, without penalty or uncertainty.
magnitude threshold m0 = 5.0
Completeness threshold for the catalogue; chosen without sensitivity analysis.

assumptions (6)

domain assumption Background events form a stationary Poisson process with intensity mu u(x,y) (Eq. 9)
Standard ETAS assumption, invoked in Section 1.
domain assumption Triggered events are produced by a non-stationary Poisson process with kernels in Eqs. 4-6
The specific parametric forms of productivity, Omori decay, and spatial density are assumed without empirical check.
domain assumption Magnitudes follow the exponential density v_beta(m) (Eq. 2) or the gamma/exponential distributions used in the ground-intensity fits
Distributional assumption that the paper switches between without justification.
standard math Time transformations (t/omega, log t, t^omega, t/Z(t)) yield a valid point process intensity under change of time
Standard change-of-time result, but the depth-based usage measure Z(t) is constructed from the same data and treated as known.
standard math Stationarity/integrability condition A*beta/(beta-alpha) < 1 (Eq. 8) holds for the fitted models
Needed for a well-defined stationary ETAS; several reported p-values below 1 violate the integrability of the Omori kernel.
domain assumption The de-clustering probabilities (Eqs. 11-12) correctly separate background and triggered events
Used for the classification map in Fig. 4, but depends on the fitted model being correct.

how reviews work

0 comments

Cite this review

Pith. "Pith review of A Time-Scaled ETAS Model for Earthquake Forecasting." pith.science (2026). https://pith.science/paper/IRBK2R7H

@misc{pith2026250524412,
  author       = {Pith},
  title        = {Pith review of: A Time-Scaled ETAS Model for Earthquake Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IRBK2R7H}},
  note         = {Machine review of arXiv:2505.24412}
}

read the original abstract

The Himalayan region, including Nepal, is prone to frequent and large earthquakes. Accurate forecasting of these earthquakes is crucial for minimizing loss of life and damage to infrastructure. In this study, we propose various time-scaled Epidemic Type Aftershock Sequence (ETAS) models to forecast earthquakes in Nepal. The ETAS model is a statistical model that describes the temporal and spatial patterns of aftershocks following a main shock. A dataset of earthquake occurrences in Nepal from 2000 to 2020 was collected, and this data was used to fit the models showcased in this article. Our results show that the time-scaled ETAS model is able to accurately forecast earthquake occurrences in Nepal, and could be a useful tool for earthquake early warning systems in the region.

Figures

Figures reproduced from arXiv: 2505.24412 by the authors.

**Figure 2.** Plots of estimates of the background seismicity rate, total spatial intensity, clustering (triggering) coefficient [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Diagnostic plots for the fitted ETAS model to the Nepal catalogue: the temporal residuals (top-left), smoothed [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Most likely (Probability > 0.95) background and triggered events detected by estimated de-clustering probabilities pj [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

26 extracted references · 26 canonical work pages

[1]

The influence of tectonic regimes on the earthquake size distribution: A case study for italy

Laura Gulia and Stefan Wiemer. The influence of tectonic regimes on the earthquake size distribution: A case study for italy. Geophysical Research Letters, 37(10), 2010

work page 2010
[2]

Spatial variability of seismicity parameters in aftershock zones

Stefan Wiemer and Kei Katsumata. Spatial variability of seismicity parameters in aftershock zones. Journal of Geophysical Research: Solid Earth, 104(B6):13135–13151, 1999

work page 1999
[3]

Statistical models for earthquake occurrences and residual analysis for point processes

Yosihiko Ogata. Statistical models for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical association, 83(401):9–27, 1988

work page 1988
[4]

Space–time etas models and an improved extension

Yosihiko Ogata and Jiancang Zhuang. Space–time etas models and an improved extension. Tectonophysics, 413(1-2):13–23, 2006

work page 2006
[5]

Etas: an r package for fitting the space-time etas model to earthquake data

Abdollah Jalilian. Etas: an r package for fitting the space-time etas model to earthquake data. Journal of Statistical Software, 88:1–39, 2019

work page 2019
[6]

Analyzing earthquake clustering features by using stochastic reconstruction

Jiancang Zhuang, Yosihiko Ogata, and David Vere-Jones. Analyzing earthquake clustering features by using stochastic reconstruction. Journal of Geophysical Research: Solid Earth, 109(B5), 2004

work page 2004
[7]

Temporal point process models for nepal earthquake aftershocks

Rupal Shah, K Muralidharan, and Ayush Parajuli. Temporal point process models for nepal earthquake aftershocks. International Journal of Statistics and Reliability Engineering, 7(2):275–285, 2020

work page 2020
[8]

Alternative time scales and failure time models

Thierry Duchesne and Jerry Lawless. Alternative time scales and failure time models. Lifetime data analysis, 6:157–179, 2000. 10 A Time-Scaled ETAS Model for Earthquake Forecasting

work page 2000

Show all 26 references

[9]

Semiparametric inference methods for general time scale models

Thierry Duchesne and Jerry Lawless. Semiparametric inference methods for general time scale models. Lifetime Data Analysis, 8:263–276, 2002

2002
[10]

Statistical models and methods for lifetime data

Jerald F Lawless. Statistical models and methods for lifetime data. John Wiley & Sons, 2011

2011
[11]

Multiple Time Scales in Survival Analysis

Thierry Duchesne. Multiple Time Scales in Survival Analysis. PhD thesis, University of Waterloo, 1999

1999
[12]

Multiple time scales and the lifetime coefficient of variation: engineering applications

Kh B Kordonsky and I Gertsbakh. Multiple time scales and the lifetime coefficient of variation: engineering applications. Lifetime data analysis, 3:139–156, 1997

1997
[13]

Choice of the best time scale for system reliability analysis.European Journal of Operational Research, 65(2):235–246, 1993

Kh B Kordonsky and IB Gertsbakh. Choice of the best time scale for system reliability analysis.European Journal of Operational Research, 65(2):235–246, 1993

1993
[14]

System state monitoring and lifetime scales—i

Kh B Kordonsky and IB Gertsbakh. System state monitoring and lifetime scales—i. Reliability Engineering & System Safety, 47(1):1–14, 1995

1995
[15]

Multiple time scales in survival analysis

David Oakes. Multiple time scales in survival analysis. Lifetime data analysis, 1:7–18, 1995

1995
[16]

Estimation of residual lifetime-theory and practical problems

Christof Sumereder and Hans Michael Muhr. Estimation of residual lifetime-theory and practical problems. In 8th Höfler’s Days. Elektroinstitut Milan Vidmar, 2005

2005
[17]

A simplex method for function minimization

John A Nelder and Roger Mead. A simplex method for function minimization. The computer journal, 7(4):308– 313, 1965

1965
[18]

A new approach to model the counts of earthquakes: Inarpqx (1) process

Emrah Altun, Deepesh Bhati, and Naushad Mamode Khan. A new approach to model the counts of earthquakes: Inarpqx (1) process. SN Applied Sciences, 3:1–17, 2021

2021
[19]

Aftershock probabilistic seismic hazard analysis for bushehr province in iran using etas model

Nader Davoudi, Hamid Reza Tavakoli, Mehdi Zare, and Abdollah Jalilian. Aftershock probabilistic seismic hazard analysis for bushehr province in iran using etas model. Natural Hazards, 100(3):1159–1170, 2020

2020
[20]

Characteristics of foreshocks revealed by an earthquake fore- casting method based on precursory swarm activity

F Hirose, K Tamaribuchi, and K Maeda. Characteristics of foreshocks revealed by an earthquake fore- casting method based on precursory swarm activity. Journal of Geophysical Research: Solid Earth , 126(9):e2021JB021673, 2021

2021
[21]

Multi-stream based marked point process

Sujun Hong and Hirotaka Hachiya. Multi-stream based marked point process. In Asian Conference on Machine Learning, pages 1269–1284. PMLR, 2021

2021
[22]

Point-process modeling of secondary crashes

Samarth Motagi, Sirish Namilae, Audrey Gbaguidi, Scott Parr, and Dahai Liu. Point-process modeling of secondary crashes. Plos one, 18(12):e0295343, 2023

2023
[23]

Aftershock forcasting experiment for bushehr province of iran using the epidemic-type aftershock sequence (etas) model

H Tavakoli, Nader Davoodi, Abdollah Jalilian, and Mehdi Zare. Aftershock forcasting experiment for bushehr province of iran using the epidemic-type aftershock sequence (etas) model. In 16th European Conf. Earthquake Engineering, pages 18–21, 2018

2018
[24]

Models and estimation for systems with recurrent events and usage processes

Jerald F Lawless and Martin J Crowder. Models and estimation for systems with recurrent events and usage processes. Lifetime data analysis, 16:547–570, 2010

2010
[25]

Seismic risk assessment for the infrastructure in the regions adjacent to the russian federation baikal–amur mainline based on the unified scaling law for earthquakes

Anastasiya Nekrasova and Vladimir Kossobokov. Seismic risk assessment for the infrastructure in the regions adjacent to the russian federation baikal–amur mainline based on the unified scaling law for earthquakes. Natural Hazards, 116(2):1995–2010, 2023

1995
[26]

Alternative scales in reliability models for a repairable system

Annamraju Syamsundar, Vallayil N Achutha Naikan, and Shaomin Wu. Alternative scales in reliability models for a repairable system. Reliability Engineering & System Safety, 193:106599, 2020. 11

2020

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

The influence of tectonic regimes on the earthquake size distribution: A case study for italy

Laura Gulia and Stefan Wiemer. The influence of tectonic regimes on the earthquake size distribution: A case study for italy. Geophysical Research Letters, 37(10), 2010

work page 2010

[2] [2]

Spatial variability of seismicity parameters in aftershock zones

Stefan Wiemer and Kei Katsumata. Spatial variability of seismicity parameters in aftershock zones. Journal of Geophysical Research: Solid Earth, 104(B6):13135–13151, 1999

work page 1999

[3] [3]

Statistical models for earthquake occurrences and residual analysis for point processes

Yosihiko Ogata. Statistical models for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical association, 83(401):9–27, 1988

work page 1988

[4] [4]

Space–time etas models and an improved extension

Yosihiko Ogata and Jiancang Zhuang. Space–time etas models and an improved extension. Tectonophysics, 413(1-2):13–23, 2006

work page 2006

[5] [5]

Etas: an r package for fitting the space-time etas model to earthquake data

Abdollah Jalilian. Etas: an r package for fitting the space-time etas model to earthquake data. Journal of Statistical Software, 88:1–39, 2019

work page 2019

[6] [6]

Analyzing earthquake clustering features by using stochastic reconstruction

Jiancang Zhuang, Yosihiko Ogata, and David Vere-Jones. Analyzing earthquake clustering features by using stochastic reconstruction. Journal of Geophysical Research: Solid Earth, 109(B5), 2004

work page 2004

[7] [7]

Temporal point process models for nepal earthquake aftershocks

Rupal Shah, K Muralidharan, and Ayush Parajuli. Temporal point process models for nepal earthquake aftershocks. International Journal of Statistics and Reliability Engineering, 7(2):275–285, 2020

work page 2020

[8] [8]

Alternative time scales and failure time models

Thierry Duchesne and Jerry Lawless. Alternative time scales and failure time models. Lifetime data analysis, 6:157–179, 2000. 10 A Time-Scaled ETAS Model for Earthquake Forecasting

work page 2000