The Citrus tristeza virus (CTV) is one of the most economically devastating citrus diseases worldwide. The spread of CTV in eastern Spain was studied by Gottwald et al. with the goal of determining the spatio-temporal mechanisms of spread. Since the subjects in this study are individual trees, it is natural to think of infections as Bernoulli trials. This approach is difficult however, due to the spatial and temporal dependence of the observations. Consequently, a system of ordinary differential equations (ODE) was used to model the probabilities of infection as well as the spatial and temporal dependence. Given the parameters in the ODE, the probabilities of infection are treated as conditionally independent. Using the conditional independence we then specify the joint likelihood function as a Poisson binomial distribution. For the purpose of model selection and hypothesis testing we, employed accumulated prediction error (APE) which has connections to both Bayesian and frequentist frameworks. We demonstrated the robustness of our method in accounting for spatio-temporal dependencies in the data by accurately predicting the spatial distribution of the disease through Join Counts.

中文翻译：

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通过 ODE 和 Bernoulli 试验研究柑橘 tristeza 病毒的时空传播。

Citrus tristeza 病毒 (CTV) 是全球最具经济破坏性的柑橘病害之一。Gottwald 等人研究了 CTV 在西班牙东部的传播。目的是确定传播的时空机制。由于本研究中的受试者是个体树木，因此很自然地将感染视为伯努利试验。然而，由于观察的空间和时间依赖性，这种方法是困难的。因此，使用常微分方程 (ODE) 系统对感染概率以及空间和时间依赖性进行建模。给定 ODE 中的参数，感染概率被视为条件独立的。然后使用条件独立性将联合似然函数指定为泊松二项式分布。出于模型选择和假设检验的目的，我们采用了与贝叶斯和频率论框架都有联系的累积预测误差 (APE)。我们通过 Join Counts 准确预测疾病的空间分布，证明了我们的方法在考虑数据中的时空依赖性方面的稳健性。