论文标题
部分可观测时空混沌系统的无模型预测
An Empirical Bayes Approach for Constructing the Confidence Intervals of Clonality and Entropy
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
This paper is motivated by the need to quantify human immune responses to environmental challenges. Specifically, the genome of the selected cell population from a blood sample is amplified by the well-known PCR process of successive heating and cooling, producing a large number of reads. They number roughly 30,000 to 300,000. Each read corresponds to a particular rearrangement of so-called V(D)J sequences. In the end, the observation consists of a set of numbers of reads corresponding to different V(D)J sequences. The underlying relative frequencies of distinct V(D)J sequences can be summarized by a probability vector, with the cardinality being the number of distinct V(D)J rearrangements present in the blood. Statistical question is to make inferences on a summary parameter of the probability vector based on a single multinomial-type observation of a large dimension. Popular summary of the diversity of a cell population includes clonality and entropy, or more generally, is a suitable function of the probability vector. A point estimator of the clonality based on multiple replicates from the same blood sample has been proposed previously. After obtaining a point estimator of a particular function, the remaining challenge is to construct a confidence interval of the parameter to appropriately reflect its uncertainty. In this paper, we have proposed to couple the empirical Bayes method with a resampling-based calibration procedure to construct a robust confidence interval for different population diversity parameters. The method has been illustrated via extensive numerical study and real data examples.
