 |
Center for Nonlinear Studies |
A main goal in science is to combine theoretical models with observations to learn something about the system under investigation. I will discuss a way to use measured data to estimate model parameters and states that cannot be directly measured. I will explain why state and parameter estimation is difficult in nonlinear systems, and show how synchronization of the model to the data stream can be used to reduce the difficulty. I will then move on to the stochastic case where a noise term is added to the model, and show how to formulate the probability distribution of the states and parameters of the model, conditioned on the observed data. State and parameter estimates can then be calculated, including uncertainties, by using a Monte Carlo integration method to evaluate path integrals through state and parameter space with the conditional probability distribution as a weight factor. I will also address the issue of how to find the number of observations required for a particular model.
Host: Robert Ecke