Bayesian Analysis for miRNA and mRNA Interactions Using Expression Data

MicroRNAs (miRNAs) are small RNA molecules composed of 19-22 nt playing important regulatory roles in post-transcriptional gene regulation by inhibiting the translation of the mRNA into proteins or otherwise cleaving the target mRNA. Inferring miRNA targets provides useful information for understanding the roles of miRNA involving in biological processes which may result in diagnosing complex diseases. Statistical methodologies of point estimates such as the LASSO algorithm have been proposed to identify the interactions of miRNA and mRNA based on sequence and expression data. In this paper, we propose Bayesian LASSO and non-negative Bayesian LASSO to analyze the interactions between miRNA and mRNA using the expression data. The proposed Bayesian methods explore the posterior distributions for those parameters required in the model depicting the miRNA-mRNA interactions. For comparison purposes, we applied the Least Square Regression (LSR), Ridge Regression (RR), LASSO, non-negative LASSO (nLASSO), and the Bayesian approaches to four public data sets which have the known interaction pairs of miRNA and mRNA. Comparing to the point estimate algorithms, the Bayesian methods are able to infer more known interactions and are more meaningful to provide credible intervals to take into account the uncertainty of the interactions of miRNA and mRNA. The Bayesian approaches are useful for graphing the inferred eects of the miRNAs on the targets by plotting the posterior distributions of those parameters, and while the point estimate algorithm only provides a single estimate for those parameters.

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