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Omics techniques have changed the way we depict the molecular features of a cell. The integrative and quantitative analysis of omics data raises unprecedented expectations for understanding biological systems on a global scale. However, its inherently noisy nature, together with limited knowledge of potential sources of variation impacting health and disease, require the use of proper mathematical and computational methods for its analysis and integration. Bayesian inference of probabilistic models allows propagation of the uncertainty from the experimental data to our beliefs of the model parameters, allowing us to appropriately answer complex biological questions. In this chapter, we build probabilistic models of gene expression from RNA-seq data and make inference about their parameters using Bayesian methods. We present models of increasing complexity, from the quantification of a single gene expression to differential gene expression for a whole transcriptome, comparing them to the available tools for analysis of gene expression data. We provide Stan scripts that introduce the reader into the implementation of Bayesian statistics for omics data. The rationale that we apply for transcriptomics data may be easily extended to model the particularities of other omics data and to integrate the different regulatory layers.
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