Exploring behaviors of SDE models of biological systems using change of measures

We introduce a method for solving the following problem: given a Stochastic Differential Equation (SDE) model describing the dynamics of a biological system, algorithmically decide whether the model satisfies a given high-level behavioral specification. Our proposed solution uses a combination of Bayesian statistical hypothesis testing, Girsanov's theorem for change of measures, and independent but non-identically distributed (i.i.d.) sampling algorithms. Our use of non-i.i.d. sampling contributes to the state of the art in statistical verification of stochastic systems by providing an effective means for exposing rare events, while retaining the ability to compute bounds on the probability that those events occur.