We characterize D-optimal designs in the two-dimensional Poisson regression model with synergetic interaction and provide an explicit proof. The proof is based on the idea of reparameterization of the design region in terms of contours of constant intensity. This approach leads to a substantial reduction in complexity as properties of the sensitivity can be treated along and across the contours separately. Furthermore, some extensions of this result to higher dimensions are presented.

中文翻译：

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具有协同相互作用的Poisson回归的D最优设计

我们在具有协同作用的二维Poisson回归模型中表征D最优设计，并提供了明确的证明。该证明基于以恒定强度的轮廓对设计区域进行重新参数化的想法。该方法导致复杂度的显着降低，因为可以分别沿着轮廓线和穿过轮廓线来处理灵敏度的属性。此外，提出了将该结果扩展到更高维度的一些方法。