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.

翻译：在空间数据分析领域，允许回归系数随区域变化并灵活捕捉空间异质性的空间变系数模型，已在多个方向持续发展。此外，贝叶斯广义融合LASSO常被用作一种在相邻区域回归系数倾向于取相同值的自然假设下，能高效提供估计的方法。在大多数贝叶斯方法中，先验分布的选择是一个核心问题，而在采用贝叶斯广义融合LASSO的空间变系数模型设定中，确定先验分布族的复杂度同样具有挑战性，这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方法的广泛适用信息准则，并不以确定复杂度为目标。因此，在本研究中，我们将一种称为先验强化信息准则的指标适配于此设定。具体而言，在保留先验分布影响的渐近设定下，即刻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。随后，基于这些性质，我们构建了一个作为预测风险渐近偏差校正估计量的信息准则。在数值实验中，我们证实了在降低预测风险的意义上，先验强化信息准则优于广泛适用信息准则；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。