Xiantao Li, The Pennsylvania State University
Room 306, No.5 Science Building
In practical applications, parameters in stochastic models often have to be determined from data. The problem becomes quite challenging when the equilibrium statistics is unknown or when some of the parameters are not involved in the equilibrium density. We will present a method based on the response properties, which arise when the system is under external perturbations. The approach formulates the parameter estimation problem of Itô drift diffusions as a nonlinear least-squares problem. This ensures that the stochastic model will respond `correctly’ to the external force. To avoid solving the model repeatedly when using an iterative scheme in solving the resulting least-squares problems, a polynomial chaos surrogate model is employed on appropriate response statistics with smooth dependence on the parameters. This is joint work with John Harlim and He Zhang.