Statistical Methods for Modelling Physical Systems
By Henrik Madsen.
Physical models are often identified by minimizing the sum of squared simulation errors. In the talk it will be explained why this approach does not lead to an efficient statistical approach for modelling. It will be argued that a full range of statistical tools can be enabled by instead considering state space models were the dynamics are described by stochastic differential equations while the observed data is described by a discrete time relationship. A maximum likelihood method for estimation of linear and non-linear stochastic differential equations using discrete time data will be described. The likelihood function is evaluated using state filtering techniques. By this approach both non-stationary and non-linear models can be identified. The method is useful for identifying physical models, since it allows for a combination of partial prior physical knowledge and information from data. For that reason the procedure is frequently called a grey box modelling approach. The method will be illustrated by identifying stochastic models for oxygen variations in a lake, and a non-linear stochastic Lotka-Volterra model for predator/prey relations.
The CEES seminar room has a coffee-machine – it is therefore recommended that you come a bit earlier and get yourself a good cup of coffee (for the price of 3 NOK).