Exploring behaviors of stochastic differential equation models of biological systems using change of measures

BMC Bioinformatics

Research

Christopher James Langmead¹  Sumit Kumar Jha² 

[1] Computer Science Department, Carnegie Mellon University, 15213, Pittsburgh, PA, USA;Lane Center for Computational Biology, Carnegie Mellon University, 15213, Pittsburgh, PA, USA;Electrical Engineering and Computer Science Department, University of Central Florida, 32816, Orlando, FL, USA;

关键词: Probability Measure;    Stochastic Differential Equation;    Testing Strategy;    Importance Sampling;    Bernoulli Random Variable;   

DOI  :  10.1186/1471-2105-13-S5-S8

来源: Springer

【 摘 要 】

Stochastic Differential Equations (SDE) are often used to model the stochastic dynamics of biological systems. Unfortunately, rare but biologically interesting behaviors (e.g., oncogenesis) can be difficult to observe in stochastic models. Consequently, the analysis of behaviors of SDE models using numerical simulations can be challenging. We introduce a method for solving the following problem: given a SDE model and a high-level behavioral specification about the dynamics of the model, algorithmically decide whether the model satisfies the specification. While there are a number of techniques for addressing this problem for discrete-state stochastic models, the analysis of SDE and other continuous-state models has received less attention. Our proposed solution uses a combination of Bayesian sequential hypothesis testing, non-identically distributed samples, and Girsanov's theorem for change of measures to examine rare behaviors. We use our algorithm to analyze two SDE models of tumor dynamics. Our use of non-identically distributed samples sampling contributes to the state of the art in statistical verification and model checking of stochastic models by providing an effective means for exposing rare events in SDEs, while retaining the ability to compute bounds on the probability that those events occur.

【 授权许可】

CC BY   
© Jha and Langmead; licensee BioMed Central Ltd. 2012