Bayesian inference applied to linear regression model and spatial model: An approach on the covariance structure between geostatistical data
Keywords:Spatial Statistics; Geostatistics; Bayesian inference; Markov chains Monte Carlo; DIC; Linear Regression Model; Mean square error.
Statistical models serve to describe the probabilistic behavior of phenomena of interest, allowing them to be analyzed, predicted and made relevant decisions. Linear regression models are widely used in several areas. These models have strong assumptions such as independence between errors that in general do not fit spatial data, since these data allow dependence on the error covariance structure. Therefore, linear regression models can be compared with spatial models. Spatial data can be divided into 3 types: dot pattern, area data and geostatistical data. This work aims to evaluate linear regression models initially and later to compare them to spatial models for geostatistical data through the exponential covariance function. Unknown parameters are found in these models and the inference adopted in this work is Bayesian for allowing the expert's initial belief to be incorporated into the modeling, increasing the amount of information evaluated and therefore improving the estimates. When adjusting the models under simulated data sets, it is possible to verify the ability of the adjustments to recover the true values of the parameters and select the true model. This article is the result of an interest in analyzing the adjustment of the linear regression model with a set of artificial data with spatial dependence and comparing this to the adjustment of the spatial model, more specifically, based on geostatistical data.
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