Fisher-Pitman permutation tests based on nonparametric Poisson mixtures with application to single cell genomics
This work addresses the need for robust statistical tests in genomics, particularly for single-cell data analysis, though it is incremental as it extends existing permutation test frameworks to Poisson mixtures.
The paper tackles the problem of testing equality of unknown Poisson mixture distributions, developing Fisher-Pitman permutation tests based on nonparametric maximum likelihood estimators, which are shown to be consistent and adapt to complex count data structures. Applied to single-cell RNA-seq data from autism and control brain samples, the methods identify differentially expressed genes missed by common tests, with theoretical rate optimality established.
This paper investigates the theoretical and empirical performance of Fisher-Pitman-type permutation tests for assessing the equality of unknown Poisson mixture distributions. Building on nonparametric maximum likelihood estimators (NPMLEs) of the mixing distribution, these tests are theoretically shown to be able to adapt to complicated unspecified structures of count data and also consistent against their corresponding ANOVA-type alternatives; the latter is a result in parallel to classic claims made by Robinson (Robinson, 1973). The studied methods are then applied to a single-cell RNA-seq data obtained from different cell types from brain samples of autism subjects and healthy controls; empirically, they unveil genes that are differentially expressed between autism and control subjects yet are missed using common tests. For justifying their use, rate optimality of NPMLEs is also established in settings similar to nonparametric Gaussian (Wu and Yang, 2020a) and binomial mixtures (Tian et al., 2017; Vinayak et al., 2019).