标题： 通过贝叶斯广义融合套索进行空间数据分析的信息准则开发 显示英文标题

标题： Developing an information criterion for spatial data analysis through Bayesian generalized fused lasso

摘要： 在空间数据分析领域，允许回归系数按区域变化并灵活捕捉空间异质性的空间变化系数（SVC）模型，一直在多个方向上持续发展。 此外，贝叶斯广义融合Lasso通常作为一种在自然假设下高效提供估计的方法，该假设认为相邻区域的回归系数倾向于取相同值。 在大多数贝叶斯方法中，先验分布的选择是一个关键问题，在贝叶斯广义融合Lasso的SVC模型设置中，确定先验分布类别的复杂性也是一个具有挑战性的方面，进一步加剧了问题的难度。 例如，已成为贝叶斯模型选择标准的广泛适用信息准则（WAIC），并不针对确定复杂性。 因此，在本研究中，我们将一个称为先验强化信息准则（PIIC）的准则适应到这种设置中。 具体而言，在保留先验分布影响的渐近设定下，即在故意不提供选择一致性的渐近设定下，我们推导了广义融合Lasso估计量的渐近性质。 然后，基于这些性质，我们构建了一个信息准则，作为预测风险的渐近偏差校正估计量。 在数值实验中，我们确认PIIC在降低预测风险方面优于WAIC，在实际数据分析中，我们观察到两种准则产生了显著不同的结果。 显示英文摘要

摘要： In the field of spatial data analysis, spatially varying coefficients (SVC) models, which allow regression coefficients to vary by region and flexibly capture spatial heterogeneity, have continued to be developed in various directions. Moreover, the Bayesian generalized fused lasso is often used as a method that efficiently provides estimation under the natural assumption that regression coefficients of adjacent regions tend to take the same value. In most Bayesian methods, the selection of prior distribution is an essential issue, and in the setting of SVC model with the Bayesian generalized fused lasso, determining the complexity of the class of prior distributions is also a challenging aspect, further amplifying the difficulty of the problem. For example, the widely applicable information criterion (WAIC), which has become standard in Bayesian model selection, does not target determining the complexity. Therefore, in this study, we adapted a criterion called the prior intensified information criterion (PIIC) to this setting. Specifically, under an asymptotic setting that retains the influence of the prior distribution, that is, under an asymptotic setting that deliberately does not provide selection consistency, we derived the asymptotic properties of our generalized fused lasso estimator. Then, based on these properties, we constructed an information criterion as an asymptotically bias-corrected estimator of predictive risk. In numerical experiments, we confirmed that PIIC outperforms WAIC in the sense of reducing the predictive risk, and in a real data analysis, we observed that the two criteria give rise to substantially different results.