Abstract
The purpose and statistical framework of the model-based approaches in the mathematical process and/or system modeling is presented. Mathematical background of the model parameter estimation as a systematic procedure for the model validation is reviewed. A novel statistical and numerical approach with notion of particles (i.e., particle filter) or population Monte Carlo is explained. Non-parametric numerical statistics is attempted with a general-purpose modeling platform (gPROMS) where empirical distribution functions are simulated based on the measured data. The significance of Bayesian statistical approaches is appreciated with a simple example where non-linear and dynamic models are investigated in terms of the predictive power of each theoretical/mathematical presentation. Model discrimination among the proposed mathematical formulae is attempted with the aid of information criterion statistics such as AIC (Akaike Information Criterion), BIC (Bayesian Information Criterion), or DIC (Deviance Information Criterion). These will not only tell us the best fit of the data but also provide us with the information on even better models.
