论文标题
离散分布的最小覆盖区域和最高密度区域
Smallest covering regions and highest density regions for discrete distributions
论文作者
论文摘要
本文研究了计算任意离散概率分布的规范最小覆盖区域的问题。这个优化问题类似于经典的0-1背包问题，但它涉及对可能无限无限的集合的优化，从而引发了使问题不乏味的计算挑战。为了解决问题，我们提出的定理为优化区域提供了有用的条件，并开发了一种迭代的一次性计算方法来计算规范最小的覆盖区域。我们展示了如何在伪代码中对其进行编程，并研究了方法的性能。我们将该算法与统计计算软件包中可用的其他算法进行比较以计算HDR。我们发现，我们的方法是唯一一种准确计算HDR用于任意离散分布的方法。
This paper examines the problem of computing a canonical smallest covering region for an arbitrary discrete probability distribution. This optimisation problem is similar to the classical 0-1 knapsack problem, but it involves optimisation over a set that may be countably infinite, raising a computational challenge that makes the problem non-trivial. To solve the problem we present theorems giving useful conditions for an optimising region and we develop an iterative one-at-a-time computational method to compute a canonical smallest covering region. We show how this can be programmed in pseudo-code and we examine the performance of our method. We compare this algorithm with other algorithms available in statistical computation packages to compute HDRs. We find that our method is the only one that accurately computes HDRs for arbitrary discrete distributions.
