Applications of Random Process Models to the Description of Spatial Distributions of Qualitative Geologic Variables

1976 ◽  
pp. 124-134 ◽  
Author(s):  
P. Switzer
Keyword(s):  
Random Process ◽  
Process Models ◽  
Spatial Distributions

Determination of Gegenbauer-type random process models

1997 ◽  
Vol 63 (1) ◽  
pp. 73-90 ◽  
Author(s):  
P.M. Lapsa
Keyword(s):  
Random Process ◽  
Process Models

New Metrics for Validation of Data-Driven Random Process Models in Uncertainty Quantification

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
Hongyi Xu ◽  
Zhen Jiang ◽  
Daniel W. Apley ◽  
Wei Chen
Keyword(s):  
Uncertainty Quantification ◽  
Random Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Experimental Tests ◽  
Process Models ◽  
Data Driven ◽  
Gaussian Copula ◽  
High Dimensional ◽  
Marginal Distributions

Data-driven random process models have become increasingly important for uncertainty quantification (UQ) in science and engineering applications, due to their merit of capturing both the marginal distributions and the correlations of high-dimensional responses. However, the choice of a random process model is neither unique nor straightforward. To quantitatively validate the accuracy of random process UQ models, new metrics are needed to measure their capability in capturing the statistical information of high-dimensional data collected from simulations or experimental tests. In this work, two goodness-of-fit (GOF) metrics, namely, a statistical moment-based metric (SMM) and an M-margin U-pooling metric (MUPM), are proposed for comparing different stochastic models, taking into account their capabilities of capturing the marginal distributions and the correlations in spatial/temporal domains. This work demonstrates the effectiveness of the two proposed metrics by comparing the accuracies of four random process models (Gaussian process (GP), Gaussian copula, Hermite polynomial chaos expansion (PCE), and Karhunen–Loeve (K–L) expansion) in multiple numerical examples and an engineering example of stochastic analysis of microstructural materials properties. In addition to the new metrics, this paper provides insights into the pros and cons of various data-driven random process models in UQ.

scholarly journals PHYSICISTS ATTEMPT TO SCALE THE IVORY TOWERS OF FINANCE

2000 ◽  
Vol 03 (03) ◽  
pp. 311-333 ◽  
Author(s):  
J. DOYNE FARMER
Keyword(s):  
Random Process ◽  
Agent Based Modeling ◽  
Statistical Properties ◽  
Process Models ◽  
Price Dynamics ◽  
Agent Based ◽  
Practical Applications

Physicists have recently begun doing research in finance, and even though this movement is less than five years old, interesting and useful contributions have already emerged. This article reviews these developments in four areas, including empirical statistical properties of prices, random-process models for price dynamics, agent-based modeling, and practical applications.

Stationary and cyclostationary random process models

2002 ◽  
Author(s):  
B.J. Skinner ◽  
F.M. Ingels ◽  
J.P. Donohoe
Keyword(s):  
Random Process ◽  
Process Models

Modelling Shallow-Water Waves: Truncated Hermite Models and the ShallowWave Routine

2015 ◽  
Author(s):  
Steven R. Winterstein ◽  
Sverre Haver
Keyword(s):  
Random Process ◽  
Water Waves ◽  
Statistical Modelling ◽  
Finite Depth ◽  
Ocean Waves ◽  
Process Models ◽  
Wave Heights ◽  
Wave Models ◽  
Non Gaussian ◽  
Limiting Values

Statistical modelling of ocean waves is complicated by their nonlinearity, which leads in turn to non-Gaussian statistical behavior. While non-Gaussianity is present even in deep-water applications, its effects are especially pronounced as water depths decrease. We apply two types of wave models here: (1) local models of extreme wave heights/periods and breaking limits, and (2) random process models of the entire non-Gaussian wave surface. For the random process approach, we derive a new “truncated” Hermite model, which can reflect four moments and both upper- and lower-bound limiting values due to breaking and finite-depth effects. Results are calibrated and compared with an extensive model test series, comprising up to 23 hrs of histories across 19 seastates, at depths from 15–67m (full scale).

scholarly journals Gibbs Point Process Model for Young Star Clusters in M33

2020 ◽  
Author(s):  
Dayi Li ◽  
Pauline Barmby
Keyword(s):  
Point Process ◽  
Process Model ◽  
Function Analysis ◽  
Cluster Formation ◽  
Process Models ◽  
Spatial Distributions ◽  
Galactocentric Distance ◽  
Stellar Cluster ◽  
Positive Effects ◽  
Gibbs Point Process

Abstract We demonstrate the power of Gibbs point process models from the spatial statistics literature when applied to studies of resolved galaxies. We conduct a rigorous analysis of the spatial distributions of objects in the star formation complexes of M33, including giant molecular clouds (GMCs) and young stellar cluster candidates (YSCCs). We choose a hierarchical model structure from GMCs to YSCCs based on the natural formation hierarchy between them. This approach circumvents the limitations of the empirical two-point correlation function analysis by naturally accounting for the inhomogeneity present in the distribution of YSCCs. We also investigate the effects of GMCs’ properties on their spatial distributions. We confirm that the distribution of GMCs and YSCCs are highly correlated. We found that the spatial distributions of YSCCs reaches a peak of clustering pattern at ∼250 pc scale compared to a Poisson process. This clustering mainly occurs in regions where the galactocentric distance ≳ 4.5 kpc. Furthermore, the galactocentric distance of GMCs and their mass have strong positive effects on the correlation strength between GMCs and YSCCs. We outline some possible implications of these findings for our understanding of the cluster formation process.

The effect of decay of the amplitude of oscillation on random process models for QPO X-ray stars

1987 ◽  
Vol 322 ◽  
pp. 831 ◽  
Author(s):  
N. Shibazaki ◽  
R. F. Elsner ◽  
M. C. Weisskopf
Keyword(s):  
Random Process ◽  
Process Models ◽  
X Ray

A Study of Power Spectral Density Models of Earthquake Ground Motion

2011 ◽  
Vol 90-93 ◽  
pp. 1503-1510
Author(s):  
Fu Jun Liu ◽  
Yu Hua Zhu ◽  
Xiao Hui Ma
Keyword(s):  
Random Process ◽  
Ground Motion ◽  
Process Model ◽  
Least Square Method ◽  
Least Square ◽  
Process Models ◽  
Earthquake Ground Motion ◽  
Power Spectral ◽  
Proposed Model ◽  
Power Spectral Densities

In this paper, a modified random process model of earthquake ground motion based on the model proposed by JinPing Ou is presented. The parameters in the model except the factor S0 are determined by using the least square method and the power spectral densities of 361 earthquake records. Then the method for determining the parameter S0 is proposed. The good performance of the proposed model in this paper in modeling the earthquake ground motion on firm ground is demonstrated by comparing it with other random process models.

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