SUMMARYVariational approximations facilitate approximate inference for the parameters in complex statistical models and provide fast, deterministic alternatives to Monte Carlo methods. However, much of the contemporary literature on variational approximations is in Computer Science rather than Statistics, and uses terminology, notation and examples from the former field. In this article we explain variational approximation in statistical terms. In particular, we illustrate the ideas of variational approximation using examples that are familiar to statisticians.

Concerted examination of multiple collections of single-cell RNA sequencing (RNA-seq) data promises further biological insights that cannot be uncovered with individual datasets. Here we present scMerge, an algorithm that integrates multiple single-cell RNA-seq datasets using factor analysis of stably expressed genes and pseudoreplicates across datasets. Using a large collection of public datasets, we benchmark scMerge against published methods and demonstrate that it consistently provides improved cell type separation by removing unwanted factors; scMerge can also enhance biological discovery through robust data integration, which we show through the inference of development trajectory in a liver dataset collection.

SummaryAn exposition on the use of O'Sullivan penalized splines in contemporary semiparametric regression, including mixed model and Bayesian formulations, is presented. O'Sullivan penalized splines are similar to P-splines, but have the advantage of being a direct generalization of smoothing splines. Exact expressions for the O'Sullivan penalty matrix are obtained. Comparisons between the two types of splines reveal that O'Sullivan penalized splines more closely mimic the natural boundary behaviour of smoothing splines. Implementation in modern computing environments such as MATLAB, R and BUGS is discussed.