scholarly journals Global statistical tests for clustered earthquake pattern discovery in Italy

2012 ◽  
Vol 2 (2) ◽  
pp. 9 ◽  
Author(s):  
Renata Rotondi ◽  
Elisa Varini
Keyword(s):  
Point Processes ◽  
Statistical Tests ◽  
Stress Transfer ◽  
Eastern Alps ◽  
Space Time ◽  
Data Sets ◽  
Seismogenic Sources ◽  
Time Interaction ◽  
Time Space ◽  
Stochastic Point Processes

It is a widely shared opinion that not only secondary earthquakes (aftershocks) but also main earthquakes tend to occur in time-space clusters. The importance of this assumption requires the application of statistical tools to objectively evaluate its coherence with the reality at different scales of size-space-time. Global tests allow us to select the data sets with significant space-time clustering in order to perform more in-depth analyses to detect cluster locations. According to different fixed magnitude thresholds, we perform two global statistical tests, the Knox test and the Jacquez test, based on the space-time distance between pairs of earthquakes under the null hypothesis of uniform distribution in time and space, and evaluate the significance of the possible clusters. We analyze subsets of historical Italian earthquakes drawn from the Parametric Catalog of Italian Earthquakes (CPTI04) with magnitude thresholds 4.5, 5.3 and 6.0, associated with the composite seismogenic sources of the Database of Individual Seismogenic Sources. Each subset is related to one of the eight tectonically homogeneous macroregions in which the Italian territory has been divided. Significant space-time clustering is found for all sets with a magnitude threshold of 4.5. This tendency decreases drastically or disappears when the cut off rises to 5.3, with the exception of two macroregions located in the Eastern Alps and the Calabrian Arc, respectively, where evidence of space-time interaction may refer to stress transfer among consecutive or adjacent faults. The link between clustering effect and tectonic behavior could guide the choice of different stochastic point processes to model the seismic activity.

scholarly journals Statistical properties of earthquakes clustering

2008 ◽  
Vol 15 (2) ◽  
pp. 333-338 ◽  
Author(s):  
A. Vecchio ◽  
V. Carbone ◽  
L. Sorriso-Valvo ◽  
C. De Rose ◽  
I. Guerra ◽  
...  
Keyword(s):  
Point Processes ◽  
Sequence Data ◽  
Temporal Distribution ◽  
Statistical Properties ◽  
Poisson Processes ◽  
Data Sets ◽  
Variable Rate ◽  
Poisson Statistics ◽  
Stochastic Point Processes

Abstract. Often in nature the temporal distribution of inhomogeneous stochastic point processes can be modeled as a realization of renewal Poisson processes with a variable rate. Here we investigate one of the classical examples, namely, the temporal distribution of earthquakes. We show that this process strongly departs from a Poisson statistics for both catalogue and sequence data sets. This indicate the presence of correlations in the system probably related to the stressing perturbation characterizing the seismicity in the area under analysis. As shown by this analysis, the catalogues, at variance with sequences, show common statistical properties.

scholarly journals Analysis, Synthesis, and Estimation of Fractal-Rate Stochastic Point Processes

Fractals ◽  
1997 ◽  
Vol 05 (04) ◽  
pp. 565-595 ◽  
Author(s):  
Stefan Thurner ◽  
Steven B. Lowen ◽  
Markus C. Feurstein ◽  
Conor Heneghan ◽  
Hans G. Feichtinger ◽  
...  
Keyword(s):  
Point Process ◽  
Action Potentials ◽  
Point Processes ◽  
Computer Network ◽  
Amorphous Semiconductors ◽  
Data Sets ◽  
Different Types ◽  
Design Values ◽  
Low Jitter ◽  
Stochastic Point Processes

Fractal and fractal-rate stochastic point processes (FSPPs and FRSPPs) provide useful models for describing a broad range of diverse phenomena, including electron transport in amorphous semiconductors, computer-network traffic, and sequences of neuronal action potentials. A particularly useful statistic of these processes is the fractal exponent α, which may be estimated for any FSPP or FRSPP by using a variety of statistical methods. Simulated FSPPs and FRSPPs consistently exhibit bias in this fractal exponent, however, rendering the study and analysis of these processes non-trivial. In this paper, we examine the synthesis and estimation of FRSPPs by carrying out a systematic series of simulations for several different types of FRSPP over a range of design values for α. The discrepancy between the desired and achieved values of α is shown to arise from finite data size and from the character of the point-process generation mechanism. In the context of point-process simulation, reduction of this discrepancy requires generating data sets with either a large number of points, or with low jitter in the generation of the points. In the context of fractal data analysis, the results presented here suggest caution when interpreting fractal exponents estimated from experimental data sets.

scholarly journals Monitoring Murder Crime in Namibia Using Bayesian Space-Time Models

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Isak Neema ◽  
Dankmar Böhning
Keyword(s):  
Relative Risk ◽  
Population Density ◽  
Temporal Trends ◽  
Space Time ◽  
Time Interaction ◽  
Time Space ◽  
Northern Regions ◽  
Gibbs Sampling Algorithm ◽  
Population Sizes ◽  
Regional Clustering

This paper focuses on the analysis of murder in Namibia using Bayesian spatial smoothing approach with temporal trends. The analysis was based on the reported cases from 13 regions of Namibia for the period 2002–2006 complemented with regional population sizes. The evaluated random effects include space-time structured heterogeneity measuring the effect of regional clustering, unstructured heterogeneity, time, space and time interaction and population density. The model consists of carefully chosen prior and hyper-prior distributions for parameters and hyper-parameters, with inference conducted using Gibbs sampling algorithm and sensitivity test for model validation. The posterior mean estimate of the parameters from the model using DIC as model selection criteria show that most of the variation in the relative risk of murder is due to regional clustering, while the effect of population density and time was insignificant. The sensitivity analysis indicates that both intrinsic and Laplace CAR prior can be adopted as prior distribution for the space-time heterogeneity. In addition, the relative risk map show risk structure of increasing north-south gradient, pointing to low risk in northern regions of Namibia, while Karas and Khomas region experience long-term increase in murder risk.

CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

2011 ◽  
Vol 20 (02) ◽  
pp. 161-168 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
M. DEHGHANI
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Robin Boundary Condition ◽  
Momentum Tensor ◽  
Space Time ◽  
Conformally Invariant ◽  
Time Space ◽  
Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

An analysis of the Pólya point process

1983 ◽  
Vol 15 (01) ◽  
pp. 39-53 ◽  
Author(s):  
Ed Waymire ◽  
Vijay K. Gupta
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Critical Value ◽  
General Representation ◽  
Infinitely Divisible ◽  
Generating Functional ◽  
Representation Problem ◽  
Polya Process ◽  
Pólya Process ◽  
Stochastic Point Processes

The Pólya process is employed to illustrate certain features of the structure of infinitely divisible stochastic point processes in connection with the representation for the probability generating functional introduced by Milne and Westcott in 1972. The Pólya process is used to provide a counterexample to the result of Ammann and Thall which states that the class of stochastic point processes with the Milne and Westcott representation is the class of regular infinitely divisble point processes. So the general representation problem is still unsolved. By carrying the analysis of the Pólya process further it is possible to see the extent to which the general representation is valid. In fact it is shown in the case of the Pólya process that there is a critical value of a parameter above which the representation breaks down. This leads to a proper version of the representation in the case of regular infinitely divisible point processes.

On Updating Algorithms and Inference for Stochastic Point Processes

1975 ◽  
Vol 12 (S1) ◽  
pp. 239-259 ◽  
Author(s):  
D. Vere-Jones
Keyword(s):  
Stochastic Process ◽  
Maximum Likelihood ◽  
Stochastic Approximation ◽  
Approximation Theory ◽  
Point Processes ◽  
Maximum Likelihood Estimates ◽  
Doubly Stochastic ◽  
Stochastic Point Processes ◽  
Asymptotically Efficient ◽  
Estimation And Filtering

This paper is an attempt to interpret and extend, in a more statistical setting, techniques developed by D. L. Snyder and others for estimation and filtering for doubly stochastic point processes. The approach is similar to the Kalman-Bucy approach in that the updating algorithms can be derived from a Bayesian argument, and lead ultimately to equations which are similar to those occurring in stochastic approximation theory. In this paper the estimates are derived from a general updating formula valid for any point process. It is shown that almost identical formulae arise from updating the maximum likelihood estimates, and on this basis it is suggested that in practical situations the sequence of estimates will be consistent and asymptotically efficient. Specific algorithms are derived for estimating the parameters in a doubly stochastic process in which the rate alternates between two levels.

Belief Movement, Uncertainty Reduction, and Rational Updating*

2021 ◽  
Author(s):  
Ned Augenblick ◽  
Matthew Rabin
Keyword(s):  
Statistical Tests ◽  
Uncertainty Reduction ◽  
The State ◽  
Data Sets ◽  
New Information ◽  
The World ◽  
Core Concepts ◽  
Market Beliefs ◽  
Over Time

Abstract When a Bayesian learns new information and changes her beliefs, she must on average become concomitantly more certain about the state of the world. Consequently, it is rare for a Bayesian to frequently shift beliefs substantially while remaining relatively uncertain, or, conversely, become very confident with relatively little belief movement. We formalize this intuition by developing specific measures of movement and uncertainty reduction given a Bayesian’s changing beliefs over time, showing that these measures are equal in expectation and creating consequent statistical tests for Bayesianess. We then show connections between these two core concepts and four common psychological biases, suggesting that the test might be particularly good at detecting these biases. We provide support for this conclusion by simulating the performance of our test and other martingale tests. Finally, we apply our test to data sets of individual, algorithmic, and market beliefs.

The coincidence approach to stochastic point processes

1975 ◽  
Vol 7 (1) ◽  
pp. 83-122 ◽  
Author(s):  
Odile Macchi
Keyword(s):  
Poisson Process ◽  
Probability Space ◽  
Point Processes ◽  
Counting Process ◽  
Regular Point ◽  
General Point ◽  
Completely Regular ◽  
Photon Process ◽  
Stochastic Point Processes

The structure of the probability space associated with a general point process, when regarded as a counting process, is reviewed using the coincidence formalism. The rest of the paper is devoted to the class of regular point processes for which all coincidence probabilities admit densities. It is shown that their distribution is completely specified by the system of coincidence densities. The specification formalism is stressed for ‘completely’ regular point processes. A construction theorem gives a characterization of the system of coincidence densities of such a process. It permits the study of most models of point processes. New results on the photon process, a particular type of conditioned Poisson process, are derived. New examples are exhibited, including the Gauss-Poisson process and the ‘fermion’ process that is suitable whenever the points are repulsive.

scholarly journals Organic aerosol source apportionment in London 2013 with ME-2: exploring the solution space with annual and seasonal analysis

2016 ◽  
Vol 16 (24) ◽  
pp. 15545-15559 ◽  
Author(s):  
Ernesto Reyes-Villegas ◽  
David C. Green ◽  
Max Priestman ◽  
Francesco Canonaco ◽  
Hugh Coe ◽  
...  
Keyword(s):  
Source Apportionment ◽  
Statistical Tests ◽  
Solution Space ◽  
Organic Aerosol ◽  
Data Sets ◽  
Environmental Implications ◽  
Data Set ◽  
Diesel Vehicles ◽  
Heavy Duty Diesel ◽  
Paul Scherrer

Abstract. The multilinear engine (ME-2) factorization tool is being widely used following the recent development of the Source Finder (SoFi) interface at the Paul Scherrer Institute. However, the success of this tool, when using the a value approach, largely depends on the inputs (i.e. target profiles) applied as well as the experience of the user. A strategy to explore the solution space is proposed, in which the solution that best describes the organic aerosol (OA) sources is determined according to the systematic application of predefined statistical tests. This includes trilinear regression, which proves to be a useful tool for comparing different ME-2 solutions. Aerosol Chemical Speciation Monitor (ACSM) measurements were carried out at the urban background site of North Kensington, London from March to December 2013, where for the first time the behaviour of OA sources and their possible environmental implications were studied using an ACSM. Five OA sources were identified: biomass burning OA (BBOA), hydrocarbon-like OA (HOA), cooking OA (COA), semivolatile oxygenated OA (SVOOA) and low-volatility oxygenated OA (LVOOA). ME-2 analysis of the seasonal data sets (spring, summer and autumn) showed a higher variability in the OA sources that was not detected in the combined March–December data set; this variability was explored with the triangle plots f44 : f43 f44 : f60, in which a high variation of SVOOA relative to LVOOA was observed in the f44 : f43 analysis. Hence, it was possible to conclude that, when performing source apportionment to long-term measurements, important information may be lost and this analysis should be done to short periods of time, such as seasonally. Further analysis on the atmospheric implications of these OA sources was carried out, identifying evidence of the possible contribution of heavy-duty diesel vehicles to air pollution during weekdays compared to those fuelled by petrol.

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