Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples

Abstract

Two different approaches to parameter estimation (PE) in the context of polymerization are introduced, refined, combined, and applied. The first is classical PE where one is interested in finding parameters which minimize the distance between the output of a chemical model and experimental data. The second is Bayesian PE allowing for quantifying parameter uncertainty caused by experimental measurement error and model imperfection. Based on detailed descriptions of motivation, theoretical background, and methodological aspects for both approaches, their relation are outlined. The main aim of this article is to show how the two approaches complement each other and can be used together to generate strong information gain regarding the model and its parameters. Both approaches and their interplay in application to polymerization reaction systems are illustrated. This is the first part in a two‐article series on parameter estimation for polymer reaction kinetics with a focus on theory and methodology while in the second part a more complex example will be considered.

Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design

“…Here, the residual is the mean squared distance between ODE solution and data, summed over all four time series. The minimization was done using standard techniques for parameter estimation 27,28 , within the framework of the software PREDICI 29 . The resulting parameters values are shown in Table 2, third column termed "Parameter Estimation".…”

Understanding the romanization spreading on historical interregional networks in Northern Tunisia

“…The scalar step-size of the walker in MALA is replaced by a diagonal matrix, which is prescribed beforehand, and is dependent on the average length of the gradient and the average length of a step in each of the parameter directions τ . In this work, we only refer to how PMALA was used in the context of our minimization problem, for technical aspects we refer to Wulkow et al (2021).…”

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“…We fully agree with this statement, and therefore we will discuss the probability of parameters, as well as the probability that experimental data can be described using the estimated parameters based on the Bayesian approach. [14] 2 | EXPERIMENTAL SECTION 2.1 | Materials AA (BASF, ≥99.5%, water content <0.1%, diacrylic acid content <0.2%, stabilized with 200 ppm of hydroquinone monomethyl ether [MEHQ]), diacrylic acid (diAA, BASF, >96% stabilized with 405 ppm MeHQ), 2,2 0 -azobis (2-methylpropionamidine) dihydrochloride (V-50, Aldrich, 97%) were used as received.…”