Related papers: Earthquake Number Forecasts Testing
We discuss various statistical distributions of earthquake numbers. Previously we derived several discrete distributions to describe earthquake numbers for the branching model of earthquake occurrence: these distributions are the Poisson,…
Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete…
We propose a new method to test the effectiveness of a spatial point process forecast based on a log-likelihood score for predicted point density and the information gain for events that actually occurred in the test period. The method…
Rank-ordering statistics provides a perspective on the rare, largest elements of a population, whereas the statistics of cumulative distributions are dominated by the more numerous small events. The exponent of a power law distribution can…
Statistical tests of earthquake predictions require a null hypothesis to model occasional chance successes. To define and quantify `chance success' is knotty. Some null hypotheses ascribe chance to the Earth: Seismicity is modeled as…
Standard approaches to forecasting the weekly number of earthquakes on a spatial grid rely on the Poisson distribution with a single global dispersion assumption. We show that this assumption is systematically violated in seismic data from…
In this paper, we used the Global Catalog of the National Earthquake Information Center US Geological Survey (NEIC USGS) for analysis of the magnitude-frequency distribution of earthquakes. We selected the unimodal part of the distribution…
We present the "condensation" method that exploits the heterogeneity of the probability distribution functions (PDF) of event locations to improve the spatial information content of seismic catalogs. The method reduces the size of seismic…
Forecasting the full distribution of the number of earthquakes is revealed to be inherently superior to forecasting their mean. Forecasting the full distribution of earthquake numbers is also shown to yield robust projections in the…
The Collaboratory for the Study of Earthquake Predictability (CSEP) aims to prospectively test time-dependent earthquake probability forecasts on their consistency with observations. To compete, time-dependent seismicity models are…
In our paper published earlier we discussed forecasts of earthquake focal mechanism and ways to test the forecast efficiency. Several verification methods were proposed, but they were based on ad-hoc, empirical assumptions, thus their…
A study of the first four moments (mean, variance, skewness, and kurtosis) and their products ($\kappa\sigma^{2}$ and $S\sigma$) of the net-charge and net-proton distributions in Au+Au collisions at $\sqrt{\rm s_{NN}}$ = 7.7-200 GeV from…
Bayesian neural networks (BNN) are the probabilistic model that combines the strengths of both neural network (NN) and stochastic processes. As a result, BNN can combat overfitting and perform well in applications where data is limited.…
We develop and implement a new type of global earthquake forecast. Our forecast is a perturbation on a smoothed seismicity (Relative Intensity) spatial forecast combined with a temporal time-averaged (Poisson) forecast. A variety of…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
Earthquake occurrence is notoriously difficult to predict. While some aspects of their spatiotemporal statistics can be relatively well captured by point-process models, very little is known regarding the magnitude of future events, and it…
Kurtosis minus squared skewness is bounded from below by 1, but for unimodal distributions this parameter is bounded by 189/125. In some applications it is natural to compare distributions by comparing their kurtosis-minus-squared-skewness…
The distribution of inter-occurrence time between seismic events is a quantity of great interest in seismic risk assessment. We evaluate this distribution for different models of earthquakes occurrence and follow two distinct approaches:…
The concept of proper time, which is different from universal time, has been introduced into the physics of earthquakes. The global activity of strong earthquakes was chosen as the object of study. We consider the sequence of earthquakes as…
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…