Stochastic Parameter Search for Events
Results We have developed a novel parameter estimation algorithm—Stochastic Parameter Search for Events (SParSE)—that automatically computes parameter configurations for propagating the system to produce an event of interest at a user-specified success rate and error tolerance. Our method is highly automated and parallelizable. In addition, computational complexity does not scale linearly with the number of unknown parameters; all reaction rate parameters are updated concurrently at the end of each iteration in SParSE. We apply SParSE to three systems of increasing complexity: birth-death, reversible isomerization, and Susceptible-Infectious-Recovered-Susceptible (SIRS) disease transmission. Our results demonstrate that SParSE substantially accelerates computation of the parametric solution hyperplane compared to uniform random search. We also show that the novel heuristic for handling over-perturbing parameter sets enables SParSE to compute biasing parameters for a class of rare events that is not amenable to current algorithms that are based on importance sampling.
Ensemble result for the birth-death process. SParSE required a total of 131 samples (30 initial, 71 intermediate, and 30 final). The green dashed line denotes the exact solution and the green dotted lines represent ±0.05 absolute error tolerance band. Initial reaction rates are represented by orange squares, intermediate reaction rates by white squares, and k?s by red squares. Orange dashed lines connect any two subsequent reaction rates originated from the same k(0). White dashed lines represent the parameter ranges specified prior to simulation.
Conclusions SParSE provides a novel, efficient, event-oriented parameter estimation method for computing parametric configurations that can be readily applied to any stochastic systems obeying chemical master equation (CME). Its usability and utility do not diminish with large systems as the algorithmic complexity for a given system is independent of the number of unknown reaction rate parameters.