Workshop on Systems Biology, Fri, 09 Nov, 2007
Speaker: Mats Jirstrand
Abstract
We consider system identification of biological and biochemical systems described by differential equations. Parameter estimation is an integral part of the system identification process and since measurement data often is sampled at discrete points in time we are faced with a mixed continuous-discrete parameter estimation problem. A common way of addressing this problem is to add Gaussian measurement noise to the measured variables and perform a maximum likelihood estimation of the unknown parameters. This leads to an objective function to be minimized that consists of a possibly weighted sum-of-squares of the error between the measurement data and simulated response. However, the underlying assumption that there is no uncertainty in the proposed differential equations for the system under study is often not that realistic. A formal way of introducing a measure of this uncertainty is to consider stochastic differential equations, which also incorporates noise terms or disturbances to account for unknown or non mechanistically modeled effects. A formal treatment of the problem in a maximum likelihood setting gives a modified objective function that consists of a weighted sum-of-squares of the prediction error, i.e., the differences between measurement data and predicted response of the system. Note that a predicted response of the system also allows to include measurement data collected prior to the point in time when the system output is to be predicted. In this way the optimization problem has been observed to be more well behaved, which to some extent can be explained by that the predicted solution in many cases remains close to the measurement data also in the initial steps of the optimization algorithm despite the fact that the initial guess of the parameter vector is largely incorrect. In this talk we will introduce the parameter estimation by prediction error minimization method and show its applicability on some biochemical examples.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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