The University of Montana

Department of Mathematical Sciences

Technical report #25/2009

Reduction and identification of dynamic models. Simple example: generic receptor model.

**Heikki Haario*, Leonid Kalachev**, and Marko Laine*****

*Lappeenranta University of Technology, Lappeenranta, Finland

**University of Montana, Missoula, MT, USA

***Finnish Meteorological institute, Helsinki, Finland

**Abstract**

We consider a general scheme for reduction and identification of dynamic models using available experimental data. Analysis of reliability regions for estimated parameter values is performed using Markov Chain Monte Carlo simulation methods. In cases where some of the model parameters are not reliably defined, and when the values of certain model parameters turn out to be small (or large), asymptotic reduction techniques are used to reduce the models (i.e., to reduce the number of equations, number of reliably identifiable parameter, etc.). Consecutive application of parameters estimation (together with their reliability regions) and asymptotic reduction procedures will produce the new simpler model with the smallest number of parameters reliably identifiable by the available data (i.e., the model that is optimal with respect to available data). The ideas are illustrated using a simple example related to biomedical applications: a model of a generic receptor.

**Keywords:** Model identification, asymptotic methods, Boundary Function Method,
model reduction, Markov chain Monte Carlo (MCMC)

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