We consider the problem of clustering grouped data with possibly non-exchangeable groups whose dependencies can be characterized by a known directed acyclic graph. To allow the sharing of clusters among the non-exchangeable groups, we propose a Bayesian nonparametric approach, termed graphical Dirichlet process, that jointly models the dependent group-specific random measures by assuming each random measure to be distributed as a Dirichlet process whose concentration parameter and base probability measure depend on those of its parent groups. The resulting joint stochastic process respects the Markov property of the directed acyclic graph that links the groups. We characterize the graphical Dirichlet process using a novel hypergraph representation as well as the stick-breaking representation, the restaurant-type representation, and the representation as a limit of a finite mixture model. We develop an efficient posterior inference algorithm and illustrate our model with simulations and a real grouped single-cell data set.

Multivariate zero-inflated count data arise in a wide range of areas such as economics, social sciences, and biology. To infer causal relationships in zero-inflated count data, we propose a new zero-inflated Poisson Bayesian network (ZIPBN) model. We show that the proposed ZIPBN is identifiable with cross-sectional data. The proof is based on the well-known characterization of Markov equivalence class which is applicable to other distribution families. For causal structural learning, we introduce a fully Bayesian inference approach which exploits the parallel tempering Markov chain Monte Carlo algorithm to efficiently explore the multi-modal network space. We demonstrate the utility of the proposed ZIPBN in causal discoveries for zero-inflated count data by simulation studies with comparison to alternative Bayesian network methods. Additionally, real single-cell RNA-sequencing data with known causal relationships will be used to assess the capability of ZIPBN for discovering causal relationships in real-world problems.

Differential gene expression testing is an analysis commonly applied to RNA-Seq data. These statistical tests identify genes that are significantly different across phenotypes. We extend this testing paradigm to multivariate gene interactions from a classification perspective with the goal to detect novel gene interactions for the phenotypes of interest. This is achieved through our novel computational framework comprised of a hierarchical statistical model of the RNA-Seq processing pipeline and the corresponding optimal Bayesian classifier. Through Markov Chain Monte Carlo sampling and Monte Carlo integration, we compute quantities where no analytical formulation exists. The performance is then illustrated on an expression dataset from a dietary intervention study where we identify gene pairs that have low classification error yet were not identified as differentially expressed. Additionally, we have released the software package to perform OBC classification on RNA-Seq data under an open source license and is available at http://bit.ly/obc_package.

Motivated by the problem of identifying correlations between genes or features of two related biological systems, we propose a model of feature selection in which only a subset of the predictors Xt are dependent on the multidimensional variate Y, and the remainder of the predictors constitute a “noise set” Xu independent of Y. Using Monte Carlo simulations, we investigated the relative performance of two methods: thresholding and singular-value decomposition, in combination with stochastic optimization to determine “empirical bounds” on the small-sample accuracy of an asymptotic approximation. We demonstrate utility of the thresholding and SVD feature selection methods to with respect to a recent infant intestinal gene expression and metagenomics dataset.

BACKGROUND: Developing and evaluating new technology that enables researchers to recover gene-expression levels of colonic cells from fecal samples could be key to a non-invasive screening tool for early detection of colon cancer. The current study, to the best of our knowledge, is the first to investigate and report the reproducibility of fecal microarray data. Using the intraclass correlation coefficient (ICC) as a measure of reproducibility and the preliminary analysis of fecal and mucosal data, we assessed the reliability of mixture density estimation and the reproducibility of fecal microarray data. Using Monte Carlo-based methods, we explored whether ICC values should be modeled as a beta-mixture or transformed first and fitted with a normal-mixture. We used outcomes from bootstrapped goodness-of-fit tests to determine which approach is less sensitive toward potential violation of distributional assumptions. RESULTS: The graphical examination of both the distributions of ICC and probit-transformed ICC (PT-ICC) clearly shows that there are two components in the distributions. For ICC measurements, which are between 0 and 1, the practice in literature has been to assume that the data points are from a beta-mixture distribution. Nevertheless, in our study we show that the use of a normal-mixture modeling approach on PT-ICC could provide superior performance. CONCLUSIONS: When modeling ICC values of gene expression levels, using mixture of normals in the probit-transformed (PT) scale is less sensitive toward model mis-specification than using mixture of betas. We show that a biased conclusion could be made if we follow the traditional approach and model the two sets of ICC values using the mixture of betas directly. The problematic estimation arises from the sensitivity of beta-mixtures toward model mis-specification, particularly when there are observations in the neighborhood of the the boundary points, 0 or 1. Since beta-mixture modeling is commonly used in approximating the distribution of measurements between 0 and 1, our findings have important implications beyond the findings of the current study. By using the normal-mixture approach on PT-ICC, we observed the quality of reproducible genes in fecal array data to be comparable to those in mucosal arrays.

MOTIVATION: The goal of the study is to obtain genetic information from exfoliated colonocytes in the fecal stream rather than directly from mucosa cells within the colon. The latter is obtained through invasive procedures. The difficulties encountered by this procedure are that certain probe information may be compromised due to partially degraded mRNA. Proper normalization is essential to obtaining useful information from these fecal array data. RESULTS: We propose a new two-stage semiparametric normalization method motivated by the features observed in fecal microarray data. A location-scale transformation and a robust inclusion step were used to roughly align arrays within the same treatment. A non-parametric estimated non-linear transformation was then used to remove the potential intensity-based biases. We compared the performance of the new method in analyzing a fecal microarray dataset with those achieved by two existing normalization approaches: global median transformation and quantile normalization. The new method favorably compared with the global median and quantile normalization methods. AVAILABILITY: The R codes implementing the two-stage method may be obtained from the corresponding author.