Modelos geoestadísticos utilizando cópulas gaussianas
Date
2023-08-31
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Pontificia Universidad Católica del Perú
Abstract
La presente tesis busca aplicar una alternativa para el modelamiento de dependencia
espacial de puntos georeferenciados o también conocido como datos geoestadísticos. La metodología
con la que se busca abordar la autocorrelación espacial se basa en el uso de cópulas.
En particular, las cópulas gaussianas brindan un marco matemático que permite definir una
función de distribución conjunta acumulada a partir de la distribución marginal de la variable respuesta cuya distribución no es normal. A través de simulaciones se estudió la bondad
de ajuste de los modelos geoestadísticos usando cópulas gaussianas para datos no normales.
Finalmente, se aplicaron los modelos a dos bases de datos reales: i) para detectar yacimientos
petrolíferos y ii) para estimar el nivel de contaminación en el aire.
This thesis applies an alternative to modelling spatial dependence of geo-referenced points also known as geostatistics data. The methodology focus on the development of spatial auto- correlation is based on using copulas. In particular, Gaussian copulas allow a mathematical framework to define a joint cumulative distribution function based on the marginal distribution of the response variable that is non Gaussian. The goodness of fit of the geostatistical models using Gaussian copulas for non-normal data was studied through simulations. Finally, the models were applied to two real databases: i) to detect oil fields and ii) to estimate the level of air pollution.
This thesis applies an alternative to modelling spatial dependence of geo-referenced points also known as geostatistics data. The methodology focus on the development of spatial auto- correlation is based on using copulas. In particular, Gaussian copulas allow a mathematical framework to define a joint cumulative distribution function based on the marginal distribution of the response variable that is non Gaussian. The goodness of fit of the geostatistical models using Gaussian copulas for non-normal data was studied through simulations. Finally, the models were applied to two real databases: i) to detect oil fields and ii) to estimate the level of air pollution.
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Keywords
Geología--Métodos estadísticos, Cópulas (Estadística matemática), Procesos de Gauss
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