2021
DOI: 10.1002/mats.202100017
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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 method… Show more

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Cited by 5 publications
(4 citation statements)
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References 41 publications
(39 reference statements)
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“…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".…”
Section: Laboratory In Vitro Experimentsmentioning
confidence: 99%
“…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".…”
Section: Laboratory In Vitro Experimentsmentioning
confidence: 99%
“…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).…”
Section: Finding Local Minima With Pmalamentioning
confidence: 99%
“…We computed the likelihood function, denoting the probability density function in the event that fixed data are observed depending on the parameters, which is directly related to residual and measurement error. [14] The likelihood relates the residual to a probability by application of an inverse exponential function, motivated by the assumption of normally distributed measurement errors. Through the likelihood we obtained the posterior distribution, which denotes the probability density over all possible parameters given the observed data (the posterior is composed through the product of likelihood and prior distribution, which in our case was constant over the selected parameter domain and 0 outside this domain).…”
Section: Bayesian Approachmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%