Parameter discovery for stochastic biological models against temporal behavioral specifications using an SPRT based Metric for simulated annealing

Stochastic models are often used to study the behavior of biochemical systems and biomedical devices. While the structure of such models is often readily available from first principles, several quantitative features of the model are not easily determined. These quantitative features are often incorporated into the model as parameters. The algorithmic discovery of parameter values from experimentally observed facts (including extreme-scale data) remains a challenge for the computational systems biology community. In this paper, we present a new parameter discovery algorithm based on Wald´s sequential probability ratio test (SPRT). Our algorithm uses a combination of simulated annealing and sequential hypothesis testing to reduce the number of samples required for parameter discovery of stochastic models. We use probabilistic bounded linear temporal logic (PBLTL) to express the desired behavioral specification of a model. We also present theoretical results on the correctness of our algorithm, and demonstrate the effectiveness of our algorithm by studying a detailed model of glucose and insulin metabolism.