Modelo bayesiano geoestadístico beta-inflacionado utilizando NNGP con aplicación a datos de cobertura forestal
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Date
2020-09-29
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Pontificia Universidad Católica del Perú
Abstract
En esta tesis proponemos un nuevo modelo geoestadístico beta inflacionado en ceros y unos utilizando NNGP (del inglés Nearest Neighbor Gaussian Process). La ventaja principal de modelar los efectos espaciales utilizando NNGP es la reducción del elevado tiempo computacional que con lleva modelar un proceso gaussiano, ya que no necesita trabajar con todos los vecinos sino solo con un grupo reducido. La estimación de los parámetros se llevó a cabo desde una perspectiva bayesiana. Además, se llevó a cabo un estudio de simulación en el cual se hicieron pruebas con diferentes cantidades de vecinos para evaluar en términos de RMSE y tiempo computacional la ganancia en la estimación del modelo al agregar más vecinos. Finalmente, se modeló la proporción de cobertura forestal en Hiroshima utilizando el modelo geoestadístico desarrollado, obteniendo buenos resultados.
In this thesis, we propose a new geostatistical beta inflated zero-one model using NNGP (Nearest Neighbor Gaussian Process). The main advantage of using NNGP in the modeling of spatial effects is the reduction of the large computing time it takes to model a Gaussian process since it does not need to work with all the neighbors, but only with a small group. The estimation of the parameters is done from a bayesian perspective since the posterior distribution does not have a known shape. In addition, a simulation studywas carried out inwhich testswere donewith different amounts of neighborstoevaluateintermsofRMSEandcomputational timethegaininthemodels whenaddingmore neighbors.Finally, the proportionof forest cover inHiroshimawas modeled using the developed geostatistical model, obtaining good results.
In this thesis, we propose a new geostatistical beta inflated zero-one model using NNGP (Nearest Neighbor Gaussian Process). The main advantage of using NNGP in the modeling of spatial effects is the reduction of the large computing time it takes to model a Gaussian process since it does not need to work with all the neighbors, but only with a small group. The estimation of the parameters is done from a bayesian perspective since the posterior distribution does not have a known shape. In addition, a simulation studywas carried out inwhich testswere donewith different amounts of neighborstoevaluateintermsofRMSEandcomputational timethegaininthemodels whenaddingmore neighbors.Finally, the proportionof forest cover inHiroshimawas modeled using the developed geostatistical model, obtaining good results.
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Deforestación, Estadística bayesiana, Geografía matemática
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