Hybrid Pathwise Sensitivity Methods for Discrete Stochastic Models of Chemical Reaction Systems

TL;DR

This paper introduces hybrid pathwise sensitivity methods for biochemical CTMC models, combining existing techniques to efficiently and unbiasedly estimate parameter sensitivities across a broad range of models.

Contribution

The paper presents a novel hybrid approach that unifies different sensitivity estimation methods, offering unbiased, efficient, and broadly applicable techniques for biochemical stochastic models.

Findings

Methods are unbiased for many problems

Applicable to nearly all biochemical CTMC models

Demonstrated efficiency in numerical examples

Abstract

Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations of model output quantities with respect to model parameters, are useful in this setting for a variety of applications. In this paper, we introduce a class of hybrid pathwise differentiation methods for the numerical estimation of parametric sensitivities. The new hybrid methods combine elements from the three main classes of procedures for sensitivity estimation, and have a number of desirable qualities. First, the new methods are unbiased for a broad class of problems. Second, the methods are applicable to nearly any physically relevant biochemical CTMC model. Third, and as we demonstrate on several numerical examples, the new methods are quite efficient, particularly if one wishes to estimate the full gradient of parametric sensitivities. The methods are rather intuitive and utilize the multilevel Monte Carlo philosophy of splitting an expectation into separate parts and handling each in an efficient manner.