AI 中文总结
该研究针对空间统计中协方差函数选择不当的问题，提出基于伯恩斯坦多项式的半参数方法，经模拟和美洲知更鸟实际数据验证，具低偏差、高精度及强泛化能力，是稳健灵活的工具。
AI 中文摘要
在空间统计学中，若未正确选择合适的协方差函数，可能会导致推断错误和置信度低估。鉴于此类局限，我们引入并评估一种基于伯恩斯坦多项式估计空间协方差函数的灵活半参数方法。该公式具有通用性，适用于包含地理参考数据中潜在空间效应的模型类别，例如空间广义线性混合模型。通过蒙特卡洛模拟进行实证验证，模型拟合采用马尔可夫链蒙特卡洛的贝叶斯推断。模拟场景表明，该模型能够以低偏差和高参数精度恢复结构性协方差构型。利用北美繁殖鸟类调查中的美洲知更鸟（Turdus migratorius）实际丰度数据测试了该方法的实际适用性，具有负二项式结构的所提模型取得了令人满意的结果，有效捕捉了计数数据中固有的过度离散性。估计的范围参数为381.48公里，表明该物种的空间依赖性在区域尺度上运作，暗示未观测到的生态过程在该环境影响半径内均匀作用。此外，使用独立样本（n_pred = 34）的预测验证通过贝叶斯克里金法证明了模型的强泛化能力，生成的点预测与观测值高度匹配，且预测区间校准良好。结论表明，所提方法代表了一种稳健的方法学进展，确立了自身作为灵活高效工具的地位。
英文摘要
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.
Comments18 pages, 16 figures
