2021
DOI: 10.1002/mats.202170012
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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 2 publications
(2 citation statements)
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“…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: Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…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: Resultsmentioning
confidence: 99%
“…Since their results show that different methods—using the same set of data—result in different reactivity ratios, they assessed that “It is impossible to know which value is most accurate, and true values have no independent method of verification since all methods are based on the same foundational copolymer equation and its assumptions.” 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 ]…”
Section: Introductionmentioning
confidence: 99%