标题： 一种用于空间细分的贝叶斯广义加性模型 显示英文标题

标题： A Bayesian Geoadditive Model for Spatial Disaggregation

摘要： 我们提出了一种新颖的贝叶斯空间细分模型，用于计数数据，在高分辨率下提供快速且灵活的推断。 首先，它使用惩罚样条来包含非线性协变量效应，这是一种灵活的方法，通常不包含在现有的空间细分方法中。 此外，它采用基于样条的低秩克里金近似来建模空间依赖性。 使用拉普拉斯近似相比传统的马尔可夫链蒙特卡洛（MCMC）方法具有计算优势，促进了对大规模数据集的可扩展性。 我们探索了两种估计策略：一种使用精确似然，另一种利用空间离散近似以提高计算效率。 模拟研究显示，两种方法表现良好，近似方法提供了显著的计算优势。 我们通过细分英国和比利时的疾病率来说明我们模型的适用性，展示了其生成高分辨率风险图的潜力。 通过结合协变量建模的灵活性、计算效率和易于实现，我们的方法为空间细分提供了一个实用而有效的框架。 显示英文摘要

摘要： We present a novel Bayesian spatial disaggregation model for count data, providing fast and flexible inference at high resolution. First, it incorporates non-linear covariate effects using penalized splines, a flexible approach that is not typically included in existing spatial disaggregation methods. Additionally, it employs a spline-based low-rank kriging approximation for modeling spatial dependencies. The use of Laplace approximation provides computational advantages over traditional Markov Chain Monte Carlo (MCMC) approaches, facilitating scalability to large datasets. We explore two estimation strategies: one using the exact likelihood and another leveraging a spatially discrete approximation for enhanced computational efficiency. Simulation studies demonstrate that both methods perform well, with the approximate method offering significant computational gains. We illustrate the applicability of our model by disaggregating disease rates in the United Kingdom and Belgium, showcasing its potential for generating high-resolution risk maps. By combining flexibility in covariate modeling, computational efficiency and ease of implementation, our approach offers a practical and effective framework for spatial disaggregation.