Multiple Outlier Detection in Samples with Exponential &amp; Pareto Tails: Redeeming the Inward Approach &amp; Detecting Dragon Kings

Wheatley, Spencer; Sornette, Didier

doi:10.2139/ssrn.2645709

Cited by 12 publications

(10 citation statements)

References 53 publications

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“…The Aki or Hill log likelihood estimator is the same (by changing x to ln(x)). We refer the reader to Wheatley and Sornette [2015], where the authors make this point crystal clear for the application to extreme statistics. BothM 2 c andM 1 c seem to be systematically larger in offshore regions and Mexico.…”

Section: 1002/2016jb013266mentioning

confidence: 99%

Objective estimation of spatially variable parameters of epidemic type aftershock sequence model: Application to California

Nandan

Ouillon²,

Wiemer

et al. 2017

JGR Solid Earth

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The Epidemic Type Aftershock Sequence (ETAS) model is widely employed to model the spatiotemporal distribution of earthquakes, generally using spatially invariant parameters. We propose an efficient method for the estimation of spatially varying parameters, using the expectation maximization (EM) algorithm and spatial Voronoi tessellation ensembles. We use the Bayesian information criterion (BIC) to rank inverted models given their likelihood and complexity and select the best models to finally compute an ensemble model at any location. Using a synthetic catalog, we also check that the proposed method correctly inverts the known parameters. We apply the proposed method to earthquakes included in the Advanced National Seismic System catalog that occurred within the time period 1981–2015 in a spatial polygon around California. The results indicate significant spatial variation of the ETAS parameters. We find that the efficiency of earthquakes to trigger future ones (quantified by the branching ratio) positively correlates with surface heat flow. In contrast, the rate of earthquakes triggered by far‐field tectonic loading or background seismicity rate shows no such correlation, suggesting the relevance of triggering possibly through fluid‐induced activation. Furthermore, the branching ratio and background seismicity rate are found to be uncorrelated with hypocentral depths, indicating that the seismic coupling remains invariant of hypocentral depths in the study region. Additionally, triggering seems to be mostly dominated by small earthquakes. Consequently, the static stress change studies should not only focus on the Coulomb stress changes caused by specific moderate to large earthquakes but also account for the secondary static stress changes caused by smaller earthquakes.

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Section: 1002/2016jb013266mentioning

confidence: 99%

Objective estimation of spatially variable parameters of epidemic type aftershock sequence model: Application to California

Nandan

Ouillon²,

Wiemer

et al. 2017

JGR Solid Earth

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“…Let us now make the above observations more rigorous by testing the apparent DK points as statistical outliers. There are many tests available to determine if large observations are significantly outlying relative to the exponential (or Pareto) distribution . A suitable approach to assess the NAMS outliers is by estimating a mixture of an Exponential and a Gaussian density,

\begin{matrix} true \\ left f_{NAMS} (x | x > 3.5) = π α exp {- α x} \\ left + false(1 - π false) φ false(x; μ, σ false), α, σ > 0, \end{matrix}

where the Gaussian density

φ (x; μ, σ)

provides the outlier regime, and

0 \leq π \leq 1

is a weight.…”

Section: Runaway Disasters As “Dragon‐king” Outliersmentioning

confidence: 99%

“…as many as the three largest points could be outlying. For this we consider the sum‐robust‐sum (SRS) test statistic,

T_{r}^{S R S} = \frac{\sum_{i = 1}^{r} x_{(i)}}{\sum_{i = r + 1}^{n} x_{(i)}}, m \geq 1,

for the ordered sample

x_{(1)} > x_{(2)} > \dots > x_{(n)}

, which compares the sum of the outliers to the sum of the nonoutliers . This test was performed for

r = 2

and

r = 3

outliers for a range of upper samples—i.e., the sample in excess of a growing lower threshold.…”

Section: Runaway Disasters As “Dragon‐king” Outliersmentioning

confidence: 99%

“…There are many tests available to determine if large observations are significantly outlying relative to the exponential (or Pareto) distribution. (56)(57)(58)(59) A suitable approach to assess the NAMS outliers is by estimating a mixture of an Exponential and a Gaussian density,…”

Section: Runaway Disasters As "Dragon-king" Outliersmentioning

confidence: 99%

“…for the ordered sample x (1) > x (2) > · · · > x (n) , which compares the sum of the outliers to the sum of the nonoutliers. (59) This test was performed for r = 2 and r = 3 outliers for a range of upper samples-i.e., the sample in excess of a growing lower threshold. For r = 2, the p-value fluctuates between 0.05 and 0.1, for samples ranging from the 10 to the 40 largest points.…”

Section: Runaway Disasters As "Dragon-king" Outliersmentioning

confidence: 99%

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Of Disasters and Dragon Kings: A Statistical Analysis of Nuclear Power Incidents and Accidents

2016

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We perform a statistical study of risk in nuclear energy systems. This study provides and analyzes a data set that is twice the size of the previous best data set on nuclear incidents and accidents, comparing three measures of severity: the industry standard International Nuclear Event Scale, the Nuclear Accident Magnitude Scale of radiation release, and cost in U.S. dollars. The rate of nuclear accidents with cost above 20 MM 2013 USD, per reactor per year, has decreased from the 1970s until the present time. Along the way, the rate dropped significantly after Chernobyl (April 1986) and is expected to be roughly stable around a level of 0.003, suggesting an average of just over one event per year across the current global fleet. The distribution of costs appears to have changed following the Three Mile Island major accident (March 1979). The median cost became approximately 3.5 times smaller, but an extremely heavy tail emerged, being well described by a Pareto distribution with parameter α = 0.5-0.6. For instance, the cost of the two largest events, Chernobyl and Fukushima (March 2011), is equal to nearly five times the sum of the 173 other events. We also document a significant runaway disaster regime in both radiation release and cost data, which we associate with the "dragon-king" phenomenon. Since the major accident at Fukushima (March 2011) occurred recently, we are unable to quantify an impact of the industry response to this disaster. Excluding such improvements, in terms of costs, our range of models suggests that there is presently a 50% chance that (i) a Fukushima event (or larger) occurs every 60-150 years, and (ii) that a Three Mile Island event (or larger) occurs every 10-20 years. Further-even assuming that it is no longer possible to suffer an event more costly than Chernobyl or Fukushima-the expected annual cost and its standard error bracket the cost of a new plant. This highlights the importance of improvements not only immediately following Fukushima, but also deeper improvements to effectively exclude the possibility of "dragon-king" disasters. Finally, we find that the International Nuclear Event Scale (INES) is inconsistent in terms of both cost and radiation released. To be consistent with cost data, the Chernobyl and Fukushima disasters would need to have between an INES level of 10 and 11, rather than the maximum of 7.

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Extreme events in dynamical systems and random walkers: A review

et al. 2022

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Multiple Outlier Detection in Samples with Exponential & Pareto Tails: Redeeming the Inward Approach & Detecting Dragon Kings

Cited by 12 publications

References 53 publications

Objective estimation of spatially variable parameters of epidemic type aftershock sequence model: Application to California

Objective estimation of spatially variable parameters of epidemic type aftershock sequence model: Application to California

Of Disasters and Dragon Kings: A Statistical Analysis of Nuclear Power Incidents and Accidents

Extreme events in dynamical systems and random walkers: A review

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