Inferring intrinsic and extrinsic noise from a dual fluorescent reporter

Dual fluorescent reporter constructs, which measure gene expression from two identical promoters within the same cell, allow total gene expression noise to be decomposed into an extrinsic component, roughly associated with cell-to-cell fluctuations in cellular component concentrations, and intrinsic noise, roughly associated with inherent stochasticity of the biochemical reactions involved in gene expression [1]. A recent paper by Fu and Pachter presented frequentist statistical estimators for intrinsic and extrinsic noise using data from dual reporters [2]. For comparison, I here present results of a Bayesian analysis of this problem. I show that the orthodox estimators suffer from pathologies such as predicting negative values for a manifestly non-negative quantity, i.e. variance, and show that the Bayesian estimators do not suffer from such pathologies. In addition, I show that the Bayesian analysis automatically identifies that optimal estimates of intrinsic and extrinsic noise depend on a subtle combination of two statistics of the data, allowing for accuracies that are up to twice the accuracy of the orthodox estimators in some parameter regimes. I hope up this little worked out example contrasting orthodox statistical analysis based on ad hoc estimators with estimators resulting from a Bayesian analysis, will be educational for others in the field. I distribute a Mathematica Notebook with this paper that allows users to easily reproduce all results and figures of the paper.