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.

翻译：本文源于量化人体对环境挑战的免疫应答的需求。具体而言，从血液样本中选定的细胞群基因组通过经典的聚合酶链式反应（PCR）加热冷却循环过程进行扩增，产生大量读段，数量约为3万至30万条。每条读段对应特定的V(D)J序列重排。最终观测数据为不同V(D)J序列对应的读段数量集合。不同V(D)J序列的潜在相对频率可由概率向量概括，其基数为血液中存在的不同V(D)J重排总数。统计学问题在于基于单一高维多类型观测对该概率向量的汇总参数进行推断。细胞群多样性的常用汇总指标包括克隆性与熵，更一般地是概率向量的某个适宜函数。此前已有研究提出基于同一血液样本多次重复实验的克隆性点估计方法。在获得特定函数的点估计量后，剩余挑战在于构建该参数的置信区间以恰当反映其不确定性。本文提出将实证贝叶斯方法与基于重抽样的校准程序相结合，为不同群体多样性参数构建稳健的置信区间。通过大量数值模拟和真实数据示例验证了该方法的有效性。