Background: Identifying differentially expressed genes between the same or different species is an urgent demand for biological and medical research. For RNA-seq data, systematic technical effects and different sequencing depths are usually encountered when conducting experiments. Normalization is regarded as an essential step in the discovery of biologically important changes in expression. The present methods usually involve normalization of the data with a scaling factor, followed by detection of significant genes. However, more than one scaling factor may exist because of the complexity of real data. Consequently, methods that normalize data by a single scaling factor may deliver suboptimal performance or may not even work.The development of modern machine learning techniques has provided a new perspective regarding discrimination between differentially expressed (DE) and non-DE genes. However, in reality, the non-DE genes comprise only a small set and may contain housekeeping genes (in same species) or conserved orthologous genes (in different species). Therefore, the process of detecting DE genes can be formulated as a one-class classification problem, where only non-DE genes are observed, while DE genes are completely absent from the training data. Results: In this study, we transform the problem to an outlier detection problem by treating DE genes as outliers, and we propose a scaling-free minimum enclosing ball (SFMEB) method to construct a smallest possible ball to contain the known non-DE genes in a feature space. The genes outside the minimum enclosing ball can then be naturally considered to be DE genes. Compared with the existing methods, the proposed SFMEB method does not require data normalization, which is particularly attractive when the RNA-seq data include more than one scaling factor. Furthermore, the SFMEB method could be easily extended to different species without normalization. Conclusions: Simulation studies demonstrate that the SFMEB method works well in a wide range of settings, especially when the data are heterogeneous or biological replicates. Analysis of the real data also supports the conclusion that the SFMEB method outperforms other existing competitors. The R package of the proposed method is available at https://bioconductor.org/packages/MEB.

In this paper, we propose a new multivariate Laplace distribution from normal variance mixture models, called as Type II multivariate Laplace distribution. Unlike the original multivariate Laplace distribution whose all components must have the same value for the mixing variate, the random components in the new distribution could have different value for its own mixing variate and are correlated only through the dependence structure of the normal random vector. Thus, it contains the multiplication of independently identical distribution univariate Laplace distributions as a special case if the normal covariance matrix is diagonal. A tractable stochastic representation is used to derive the probability density function and other statistical properties. The maximum likelihood estimates of parameters via an ECM (expectation/conditional maximization) algorithm and the Bayesian methods are derived. Some simulation studies are conducted to evaluate the performance of the proposed methods. Applications in two real data sets indicate that the Type II multivariate Laplace distribution could have a better performance and is distinct from the original one.

Under-dispersed count data often appear in clinical trials, medical studies, demography, actuarial science, ecology, biology, industry and engineering. Although the generalized Poisson (GP) distribution possesses the twin properties of under- and over-dispersion, in the past 50 years, many authors only treat the GP distribution as an alternative to the negative binomial distribution for modeling over-dispersed count data. To our best knowledge, the issues of calculating maximum likelihood estimates (MLEs) of parameters in GP model without covariates and with covariates for the case of under-dispersion were not solved up to now. In this paper, we first develop a new minimization–maximization (MM) algorithm to calculate the MLEs of parameters in the GP distribution with under-dispersion, and then we develop another new MM algorithm to compute the MLEs of the vector of regression coefficients for the GP mean regression model for the case of under-dispersion. Three hypothesis tests (i.e., the likelihood ratio, Wald and score tests) are provided. Some simulations are conducted. The Bangladesh demographic and health surveys dataset is analyzed to illustrate the proposed methods and comparisons with the existing Conway–Maxwell–Poisson regression model are also presented.