In this contribution, we introduce, in analogy to penalized ambiguity resolution, the concept of penalized misclosure space partitioning, with the goal of directing the performance of the DIA-estimator towards its application-dependent tolerable risk objectives. We assign penalty functions to each of the decision regions in misclosure space and use the distribution of the misclosure vector to determine the optimal partitioning by minimizing the mean penalty. As each minimum mean penalty partitioning depends on the given penalty functions, different choices can be made, in dependence of the application. For the DIA-estimator, we introduce a special set of penalty functions that penalize its unwanted outcomes. It is shown how this set allows one to construct the optimal DIA-estimator, being the estimator that within its class has the largest probability of lying inside a user specified tolerance region. Further elaboration shows how these penalty functions are driven by the influential biases of the different hypotheses and how they can be used operationally. Hereby the option is included of extending the misclosure partitioning with an additional undecided region to accommodate situations when it will be hard to discriminate between some of the hypotheses or when identification is unconvincing. By extending the analogy with integer ambiguity resolution to that of integer-equivariant ambiguity resolution, we also introduce the maximum probability estimator within the similar larger class.

在这篇文章中，我们引入了与惩罚模糊度解决类似的惩罚闭合差空间划分的概念，其目标是将 DIA 估计器的性能引导至其依赖于应用程序的可容忍风险目标。我们将惩罚函数分配给闭合错误空间中的每个决策区域，并使用闭合错误向量的分布通过最小化平均惩罚来确定最佳划分。由于每个最小平均惩罚划分取决于给定的惩罚函数，因此可以根据应用做出不同的选择。对于 DIA 估计器，我们引入了一组特殊的惩罚函数来惩罚其不需要的结果。它显示了该集合如何允许人们构建最佳 DIA 估计器，即该估计器在其类别中具有位于用户指定的容差区域内的最大概率。进一步的阐述表明了这些惩罚函数是如何由不同假设的有影响力的偏差驱动的，以及如何在操作中使用它们。因此，包括用附加的未定区域来扩展闭合错误划分的选项，以适应难以区分某些假设或识别不令人信服的情况。通过将整数模糊度解析的类比扩展到整数等变模糊度解析，我们还在类似的较大类中引入了最大概率估计器。