Inferencia bayesiana aproximada del modelo espacio-temporal usando NNGP
Date
2023-08-23
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Pontificia Universidad Católica del Perú
Abstract
Los modelos espacio-temporales nos permiten estudiar la distribución espacial de una
variable en el tiempo. Por ejemplo, se puede estudiar la distribución espacial del material
particulado en un país a través de los años, dado que las concentraciones de material particulado
en estaciones cercanas pueden ser similares y la concentración en una estación en
un año puede depender de la concentración en la misma estación el año anterior anterior.
En esta tesis se propone usar un modelo espacio-temporal a través del proceso gaussiano de
vecinos más cercanos. Para implementar este modelo y aplicarlo en grandes bases de datos se
propone usar inferencia bayesiana a través del método de integración aproximada de Laplace
(INLA). La bondad de ajuste del modelo y su eficiencia se estudia a través de simulaciones.
Finalmente se aplica el modelo implementado a una base de datos reales.
Spatio-temporal models allow us to study the spatial distribution of a variable over time. For example, we can study the spatial distribution of particulate matter in a country through the years, given that the concentrations of particulate matter in nearby stations can be similar and the concentration in a station in a year can depend on the concentration in the same station in the previous year. In this thesis, we proposed to use a spatio-temporal model through the nearest neighbor Gaussian process. In order to implement and apply the hierarchical model in large databases, it is proposed to use Bayesian inference through Integrated nested Laplace approximation(INLA). The goodness of fit and efficiency of the model is studied through simulations. Finally, the model is applied to real data set.
Spatio-temporal models allow us to study the spatial distribution of a variable over time. For example, we can study the spatial distribution of particulate matter in a country through the years, given that the concentrations of particulate matter in nearby stations can be similar and the concentration in a station in a year can depend on the concentration in the same station in the previous year. In this thesis, we proposed to use a spatio-temporal model through the nearest neighbor Gaussian process. In order to implement and apply the hierarchical model in large databases, it is proposed to use Bayesian inference through Integrated nested Laplace approximation(INLA). The goodness of fit and efficiency of the model is studied through simulations. Finally, the model is applied to real data set.
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Estadística bayesiana, Geografía matemática, Modelos matemáticos
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