Bayesian Estimation of Negative Binomial Parameters with Applications to RNA-Seq Data

TL;DR

This paper introduces a Bayesian approach to estimate negative binomial parameters for RNA-Seq data, improving stability and reliability over traditional methods, and applies it to differential gene expression analysis.

Contribution

It develops a conjugate Bayesian hierarchical model for negative binomial overdispersion estimation and demonstrates its effectiveness in RNA-Seq data analysis.

Findings

Bayesian estimator outperforms MLE in controlling variance.

Proposed method is competitive with existing negative binomial procedures.

Application to real data illustrates the method's flexibility.

Abstract

RNA-Seq data characteristically exhibits large variances, which need to be appropriately accounted for in the model. We first explore the effects of this variability on the maximum likelihood estimator (MLE) of the overdispersion parameter of the negative binomial distribution, and propose instead the use an estimator obtained via maximization of the marginal likelihood in a conjugate Bayesian framework. We show, via simulation studies, that the marginal MLE can better control this variation and produce a more stable and reliable estimator. We then formulate a conjugate Bayesian hierarchical model, in which the estimate of overdispersion is a marginalized estimate and use this estimator to propose a Bayesian test to detect differentially expressed genes with RNA-Seq data. We use numerical studies to show that our much simpler approach is competitive with other negative binomial based procedures, and we use a real data set to illustrate the implementation and flexibility of the procedure.