  MicroRNAs (miRNAs) are small RNA molecules composed of 19-22 nt, which play
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 in biological processes that are potentially
involved in complex diseases. Statistical methodologies for point estimation,
such as the Least Absolute Shrinkage and Selection Operator (LASSO) algorithm,
have been proposed to identify the interactions of miRNA and mRNA based on
sequence and expression data. In this paper, we propose using the Bayesian
LASSO (BLASSO) and the non-negative Bayesian LASSO (nBLASSO) to analyse the
interactions between miRNA and mRNA using expression data. The proposed
Bayesian methods explore the posterior distributions for those parameters
required to model the miRNA-mRNA interactions. These approaches can be used to
observe the inferred effects of the miRNAs on the targets by plotting the
posterior distributions of those parameters. For comparison purposes, the Least
Squares Regression (LSR), Ridge Regression (RR), LASSO, non-negative LASSO
(nLASSO), and the proposed Bayesian approaches were applied to four public
datasets. We concluded that nLASSO and nBLASSO perform best in terms of
sensitivity and specificity. Compared to the point estimate algorithms, which
only provide single estimates for those parameters, the Bayesian methods are
more meaningful and provide credible intervals, which take into account the
uncertainty of the inferred interactions of the miRNA and mRNA. Furthermore,
Bayesian methods naturally provide statistical significance to select
convincing inferred interactions, while point estimate algorithms require a
manually chosen threshold, which is less meaningful, to choose the possible
interactions.
