Stationarity and inference in multistate promoter models of stochastic gene expression via stick-breaking measures

TL;DR

This paper introduces a novel stick-breaking method to explicitly derive and sample from the stationary distribution in multistate promoter models of gene expression, enabling improved inference and model selection.

Contribution

The authors develop a constructive stick-breaking approach for the stationary distribution in multistate gene expression models, extending previous restricted solutions.

Findings

Explicit stationary distribution derived using stick-breaking

Method enables direct sampling from the stationary distribution

Numerical Bayesian experiments demonstrate practical inference applications

Abstract

In a general stochastic multistate promoter model of dynamic mRNA/protein interactions, we identify the stationary joint distribution of the promoter state, mRNA, and protein levels through an explicit `stick-breaking' construction of interest in itself. This derivation is a constructive advance over previous work where the stationary distribution is solved only in restricted cases. Moreover, the stick-breaking construction allows to sample directly from the stationary distribution, permitting inference procedures and model selection. In this context, we discuss numerical Bayesian experiments to illustrate the results.