A parameter range reduction algorithm for ODE models: Time-series data representation and algorithm analysis

Parameter estimation techniques of ordinary differential equation models usually rely on an initial guess for the parameters which often results in convergence to a local rather than a global minimum. A parameter range reduction scheme was previously developed that reduces the parameter space. This scheme discretizes the model with a Linear Multistep (LMS) formula that preserves the monotonicity of the vector field with respect to the parameters and utilizes interval analysis to exclude regions of the parameter space. Each point in the time-series dataset to which the model is being fit is assumed to be replaced by an interval. An effective algorithm to achieve this last requirement is developed that encloses data in a continuous piecewise linear band. Analysis of a newly developed LMS is performed to determine its ability at reducing the parameter range of a simple vector field and whether accumulation of the LMS is beneficial at reducing parameters.