多尺度随机过程的最优抽样策略
Optimal sampling strategies for multiscale stochastic processes
摘要：
在本文中，我们确定的固定大小的非随机抽样给出了最好的线性预测有限空间人口的总和。我们采用不同的多尺度超种群模型，并使用最小均方误差作为我们的最优性准则。在多尺度超种群树模型中，叶节点代表种群的单位，内结点代表种群的部分和，根节点代表种群的总和。我们证明了最佳抽样模式的变化显着的树节点的相关结构。虽然均匀采样对于"正相关进展“的树是最佳的，但它提供了”负相关进展“的最差可能采样。作为一种分析工具，我们引入并研究了一类自主创新树，它们本身就很有趣。我们推导出一个快速注水算法，以确定最佳抽样的叶子估计的根的独立创新树。
英文摘要：
In this paper, we determine which non-random sampling of fixed size gives the best linear predictor of the sum of a finite spatial population. We employ different multiscale superpopulation models and use the minimum mean-squared error as our optimality criterion. In multiscale superpopulation tree models, the leaves represent the units of the population, interior nodes represent partial sums of the population, and the root node represents the total sum of the population. We prove that the optimal sampling pattern varies dramatically with the correlation structure of the tree nodes. While uniform sampling is optimal for trees with ``positive correlation progression'', it provides the worst possible sampling with ``negative correlation progression.'' As an analysis tool, we introduce and study a class of independent innovations trees that are of interest in their own right. We derive a fast water-filling algorithm to determine the optimal sampling of the leaves to estimate the root of an independent innovations tree.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
