Supplementary Materials for “A statistical approach for identifying differential distributions in single-cell RNA-seq experiments”

Here we present a sensitivity analysis to evaluate several computational approaches to obtain an estimate of the maximum a priori (MAP) partition in the Dirichlet process mixture model framework. Specifically, we use simulated data from mixtures of normals to compare an agglomerative greedy search algorithm [Ward Jr, 1963, Wang and Dunson, 2011], a Polya urn Gibbs sampling scheme [MacEachern, 1994, Bush and MacEachern, 1996, MacEachern and Müller, 1998], an iterative stochastic search [Shotwell, 2013], as well as a simple BIC optimization [Fraley et al., 2012]. The latter is implemented in the R package Mclust. The first three methods are implemented in the R package profdpm by Shotwell [2013]. In this sensitivity analysis we evaluate the ability of each procedure to detect the existence of multiple components when they truly exist as well as its false positive rate in detecting multiple components when there is only one. Since the expected number of components in the Dirichlet process mixture model depends on the value of α (the Dirichlet concentration parameter) as well as the sample size J [Antoniak, 1974], we vary both of these parameters. For each procedure, we evaluate each choice of J ∈ (30, 50, 100, 200) and α ∈ (0.001, 0.01, 0.05, 0.10, 1, 5) under four scenarios: