On spatial statistical methods and applications for large datasets

Abstract

El interés de la tesis es la aplicación de modelos innovadores para el análisis del índice de biomasa de anchovetas en el espacio y tiempo, así como desenvolver un nuevo proceso espacial gaussiano adecuado para el análisis de grandes bancos de datos.

The focus of this work is on the application of novelty models for the spatio-temporal analysis of large anchovy biomass dataset, and the development of a new Gaussian random field suitable for the analysis of large datasets. The first paper presents an advance application of spatio-temporal modeling through the Stochastic Partial Differential Equation (SPDE) for estimating and predicting anchovy biomass off the coast of Peru. We introduce a complete, and computationally efficient, flexible Bayesian hierarchical spatio-temporal modeling for zero-inflated positive continuous, accounting for spatial or spatio-temporal dependencies in the data. The models are capable of performing predictions of anchovy presence and abundance, in particular,in particular, when the set of observed sites is large (> 500) and different across the temporal domain. They are based on the fact that Gaussian Matérn field can be viewed as solutions to a certain SPDE, which combined with Integrated Nested Laplace Approximations (INLA) improves the computational efficiency. The second paper is devoted to extend the newly proposed Nearest Neighbor Gaussian Process (NNGP). A new class of Gaussian random field process is constructed and, it is showed its applicability to simulated data with small or large spatial dependences. The key idea behind this new spatial process (or random field) is to subdivide the spatial domain into several blocks which are dependent on some of the “past” blocks. The new spatial process recovers the NNGP and independent blocks approach. Moreover, The reduction in computational complexity is achieved through the sparsity of the precision matrices and parallelization of many computations for blocks of data. It is useful for large spatial data sets where traditional methods are too computationally intensive to be used efficiently. Finally, to perform inference we adopt a Bayesian framework, we use Markov chain Monte Carlo (MCMC) algorithms and demonstrate the full inferential capabilities of the modeling including the new spatial process, in terms of estimation, prediction and goodness of fit.