Time-Ordered Product Expansions for Computational Stochastic Systems Biology
- Eric Mjolsness
- Physical biology
Deterministic dynamical systems are used extensively for modeling in biological applications. Unfortunately, such models cannot take into account much of the stochastic behavior that arises in biological systems. Stochastic process models can capture the variance and higher moments that exist in noisy real data. But the use of stochastic process models is limited because of the formidable task of inferring the model parameters’ values from observations. In this chapter we discuss a parameter inference scheme for a family of stochastic processes that can be defined by generalized reactions or rewrite rules as they occur within the Stochastic Parameterized Grammars (SPGs) modeling framework. The chapter is organized as follows. Section 1 provides an overview of the related work on optimization techniques for both deterministic continuous models and stochastic processes. In Section 2 we introduce the SPG modeling framework and derive a sampling scheme for SPG models. The parameter inference problem is defined in Section 3. We describe the general Metropolis-Hastings algorithm in section 3.1, and demonstrate how to apply it to SPG models in 3.2. Section 4 presents the results for optimization in a stochastic model of chemical reactions. Possible extensions and comparison to related algorithms is discussed in Section 5.