Reducing the number of MC runs with antithetic and common random fields

Stoch Environ Res Risk Assess

2023

Self Cite

Dependencies between variables are often very complex, and may for high values, be different from that of the low values. As the normal distribution and the corresponding copula behave symmetrically for low and high values the frequent application of the normal copula for the description of the dependence may be inappropriate. In this contribution a new way of defining high dimensional multivariate distributions with changing correlations is presented. The method can also be used for a flexible definition of tail dependence. Examples of copulas with linear changing correlations illustrate the methodology. Parameter estimation methods and simulation procedures are discussed. A five dimensional example using groundwater quality data and another four dimensional one using air pollution data, are used to illustrate the methodology.

Section: Distributions With Value Dependent Correlationsmentioning

confidence: 99%

Changing correlations: a flexible definition of non-Gaussian multivariate dependence

Stoch Environ Res Risk Assess

2023

Self Cite

“…All fields were generated as common random fields (Guthke & Bárdossy, 2012), using the same random numbers for the simulation. Thus, the fields are similar but one can also see the differences depending on the corresponding model.…”

Section: Examplesmentioning

confidence: 99%

Definition of Spatial Copula Based Dependence Using a Family of Non‐Gaussian Spatial Random Fields

Water Resources Research

Hörning

2023

Self Cite

Spatial structures of natural variables are often very complex due to the different physical chemical or biological processes which contributed to the emergence of the fields. These structures often show non‐Gaussian spatial dependence. Unfortunately, there are only a limited number of approaches that can explicitly consider non‐Gaussian behavior. In this contribution, a very flexible way of defining non‐Gaussian spatial dependence is presented. The approach is based on a kind of continuous deformation of fields with different Gaussian spatial dependence. Theoretical examples illustrate the methodology for a wide variety of non‐Gaussian structures. A real‐life example of groundwater quality parameters shows the practical applicability of the geostatistical model.

“…The basic idea behind the construction of the distribution is to gradually change the dependence structure depending on the values of a variables. As described in [11] one can obtain very similar spatial fields if one uses the same set of random numbers to generate them. A similar methodology was used in [12] to exchange correlation structures of simulated precipitation.…”

Section: Distributions With Value Dependent Correlationsmentioning

confidence: 99%

“…As a first example consider a bi-variate distribution with correlation matrices Σ(0) = 1 0.2 0.2 1 Σ(1) = 1 0.9 0.9 1 (11) with normal marginals and linearly changing correlation matrices according to (6). The Pearson correlation of the two variables (with normal marginals) is 0.60.…”

Section: Examplesmentioning

confidence: 99%

Value dependent correlations: A flexible definition of non-Gaussian multivariate dependence

2022

Preprint

Dependencies between variables are often very complex, and may for high values be different from that of the low values. As the normal distribution and the corresponding copula behaves symmetrically for low and high values the frequent application of the normal copula for the description of the dependence may be inappropriate. In this contribution a new way of defining high dimensional multivariate distributions with changing correlations is presented. The method can also be used for a flexible definition of tail dependence. Examples of copulas with linear changing correlations illustrate the methodology. Parameter estimation methods and simulation procedures are discussed. A five dimensional example using groundwater quality data and another four dimensional using air pollution data are used to illustrate the methodology.