Extensions in Semiparametric Geostatistical Models

Abstract

In spatial statistics, the incorrect selection of an appropriate covariance function may lead to inference errors and confidence underestimation. Motivated by such restrictions, we introduce and evaluate a flexible semiparametric approach for estimating spatial covariance functions based on Bernstein polynomials. The proposed formulation is general and applicable to classes of models that incorporate latent spatial effects in georeferenced data, such as Spatial Generalized Linear Mixed Models. Empirical validation was conducted via Monte Carlo simulations, and model fitting was performed using Bayesian inference via Markov chain Monte Carlo. Simulated scenarios demonstrated the model's ability to recover structural covariance configurations with low bias and high parameter precision. The practical applicability of the methodology was tested using real abundance data for American Robin (Turdus migratorius) from the North American Breeding Bird Survey. The proposed model, featuring a Negative Binomial structure, yielded satisfactory results, efficiently capturing the overdispersion inherent in the count data. The estimated range parameter of 381.48 km revealed that the species' spatial dependence operates at a regional scale, suggesting that unobserved ecological processes act homogeneously within this radius of environmental influence. Additionally, predictive validation using an independent sample (n_pred = 34) demonstrated the model's strong generalization capability via Bayesian Kriging, producing point projections that closely matched observed values and well-calibrated prediction intervals. It is concluded that the proposed approach represents a robust methodological advancement, establishing itself as a flexible and efficient tool.