The main goal of the whole transcriptome analysis is to correctly identify all expressed transcripts within a specific cell/tissue - at a particular stage and condition - to determine their structures and to measure their abundances. RNA-seq data promise to allow identification and quantification of transcriptome at unprecedented level of resolution, accuracy and low cost. Several computational methods have been proposed to achieve such purposes. However, it is still not clear which promises are already met and which challenges are still open and require further methodological developments.

Gene expression levels in a given cell can be influenced by different factors, namely pharmacological or medical treatments. The response to a given stimulus is usually different for different genes and may depend on time. One of the goals of modern molecular biology is the high-throughput identification of genes associated with a particular treatment or a biological process of interest. From methodological and computational point of view, analyzing high-dimensional time course microarray data requires very specific set of tools which are usually not included in standard software packages. Recently, the authors of this paper developed a fully Bayesian approach which allows one to identify differentially expressed genes in a 'one-sample' time-course microarray experiment, to rank them and to estimate their expression profiles. The method is based on explicit expressions for calculations and, hence, very computationally efficient.

The objective of the present paper is to develop a truly functional Bayesian method specifically designed for time series microarray data. The method allows one to identify differentially expressed genes in a time-course microarray experiment, to rank them and to estimate their expression profiles. Each gene expression profile is modeled as an expansion over some orthonormal basis, where the coefficients and the number of basis functions are estimated from the data. The proposed procedure deals successfully with various technical difficulties that arise in typical microarray experiments such as a small number of observations, non-uniform sampling intervals and missing or replicated data. The procedure allows one to account for various types of errors and offers a good compromise between nonparametric techniques and techniques based on normality assumptions. In addition, all evaluations are performed using analytic expressions, so the entire procedure requires very small computational effort. The procedure is studied using both simulated and real data, and is compared with competitive recent approaches. Finally, the procedure is applied to a case study of a human breast cancer cell line stimulated with estrogen. We succeeded in finding new significant genes that were not marked in an earlier work on the same dataset.

This article proposes a nonlinear block shrinkage method in the wavelet domain for estimating an unknown function in the presence of Gaussian noise. This shrinkage uses an empirical Bayesian blocki...