In demand of predicting new HIV diagnosis rates based on publicly available HIV data that is abundant in space but has few points in time, we propose a class of spatially varying autoregressive (SVAR) models compounded with conditional autoregressive (CAR) spatial correlation structures. We then propose to use the copula approach and a flexible CAR formulation to model the dependence between adjacent counties. These models allow for spatial and temporal correlation as well as space-time interactions and are naturally suitable for predicting HIV cases and other spatio-temporal disease data that feature a similar data structure. We apply the proposed models to HIV data over Florida, California and New England states and compare them to a range of linear mixed models that have been recently popular for modeling spatio-temporal disease data. The results show that for such data our proposed models outperform the others in terms of prediction.

中文翻译：

---

用于预测新的人类免疫缺陷病毒诊断的空间变化自回归模型。

为了根据可获取的公共HIV数据来预测新的HIV诊断率，这些数据在空间上很丰富，但时间点很少，因此我们提出了一类空间变化的自回归（SVAR）模型，并结合了条件自回归（CAR）空间相关结构。然后，我们建议使用copula方法和灵活的CAR公式来模拟相邻县之间的依存关系。这些模型允许时空相关以及时空相互作用，并且自然适用于预测具有相似数据结构的HIV病例和其他时空疾病数据。我们将拟议的模型应用于佛罗里达州，加利福尼亚州和新英格兰州的HIV数据，并将它们与最近在时空疾病数据建模中流行的一系列线性混合模型进行比较。