Optimal designs for the Arrhenius equation

Rodríguez-Aragón, Licesio J.; López–Fidalgo, Jesús

doi:10.1016/j.chemolab.2004.06.007

Cited by 37 publications

(15 citation statements)

References 18 publications

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“…Estimation of Arrhenius parameters A and E using the logarithmic form of the Arrhenius equation was investigated by Klička and Kubáček [5], and by Sundberg [6], based on different assumptions for the errors of the measured rate coefficients. Rodríguez-Aragón and López-Fidalgo [7] discussed the determination of the Arrhenius parameters from the point of view of experimental design theory. Schwaab et al [8,9] studied the question of the selection of the optimum reference temperature to decrease the correlation between the parameters of the reparameterized Arrhenius equation.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty of Arrhenius parameters

Nagy

Turányi

2011

Int J of Chemical Kinetics

103

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Chemical kinetics databases for many elementary gas-phase reactions provide the recommended values of the Arrhenius parameters, the temperature range of their validity, and the temperature dependence of the uncertainty of the rate coefficient k. An analytical expression is derived that describes the temperature dependence of the uncertainty of k as a function of the elements of the covariance matrix of the Arrhenius parameters. Based on this analytical expression, the various descriptions of the temperature dependence of the uncertainty of k used in the combustion, and in the IUPAC and JPL atmospheric chemical databases are analyzed in detail. Recommendations are given for an improved representation of the uncertainty information in future chemical kinetics databases using the covariance matrix of the Arrhenius parameters. Utilization of the joint uncertainty of the Arrhenius parameters is needed for a correct uncertainty analysis in varying temperature chemical kinetic systems. A method is suggested for the determination of the covariance matrix and the joint probability density function of the Arrhenius parameters from the present uncertainty information given in the kinetics databases. The method is demonstrated on seven gas kinetic reactions exhibiting different types of uncertainty representation. C

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Section: Introductionmentioning

confidence: 99%

Uncertainty of Arrhenius parameters

Nagy

Turányi

2011

Int J of Chemical Kinetics

103

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“…to be in a uniform, geometric or harmonic progression (see e.g. [11,13,14]). The uniform law is likely the most common in practice [4].…”

Section: Suboptimal Sequence Designsmentioning

confidence: 99%

Experimental designs for the Adair model

López–Fidalgo

Rodríguez–Hernández

2014

Chemometrics and Intelligent Laboratory Systems

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The Adair equation is used to model biological macro-molecule reactions. This equation relates the saturation rate to the free ligand concentration. But, the latter is not a variable completely under the control of the experimenter. The ligand is a random variable depending on an initial ligand added by the experimenter, which can be designed, but the dependence of the saturation rate on the initial ligand has not been considered in the literature. In this paper a transformed model based on the Adair model of first order (monomer) is derived in order to obtain a proper model that depends on the initial ligand. This model will allow proper fitting and optimal designs using the initial ligand. It will be called the transformed Adair model (TAM). Optimal designs as well as seven-point quasi-optimal designs forced to follow a harmonic, geometric or uniform progression, are computed. The parameters are estimated and compared for simulated data from these designs. A sensitivity analysis against the choice of nominal values of the parameters is also performed for the TAM. The analytic version of the transformed model is only possible for the first class model. But the good efficiencies of the optimal designs obtained directly from the monomer model for fitting the TAM justify doing something similar for the second order model (dimer). Designs were computed numerically in this case.

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“…. , kr n−2 ) with 0 <r 1 and we shall refer to this as a GPD (see also [23]). Within this class, k is a positive normalization constant due to the constraint (6), i.e.…”

Section: The Gpdmentioning

confidence: 99%

“…Consider a general setup in which a continuous process Y (·) is to be observed at a discrete set of sites, which can be chosen by the experimenter from a compact domain X. Let y(x) denote the as Geometric Progression Design (GPD), recently taken into account by Rodríguez-Aragóna and López-Fidalgo [23]. This family of designs depends on a tuning parameter, which can be chosen by the experimenter in order to achieve a suitable trade-off between the precision in estimation of the trend and the correlation, especially when the observations are strongly correlated.…”

Section: Introductionmentioning

confidence: 99%

Optimal designs for parameter estimation of the Ornstein–Uhlenbeck process

Zagoraiou

Antognini

2008

Appl Stoch Models Bus & Ind

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This paper deals with optimal designs for Gaussian random fields with constant trend and exponential correlation structure, widely known as the Ornstein-Uhlenbeck process. Assuming the maximum likelihood approach, we study the optimal design problem for the estimation of the trend and the correlation parameter using a criterion based on the Fisher information matrix. For the problem of trend estimation, we give a new proof of the optimality of the equispaced design for any sample size (see Statist. Probab. Lett. 2008; 78:1388-1396. We also show that for the estimation of the correlation parameter, an optimal design does not exist. Furthermore, we show that the optimal strategy for conflicts with the one for , since the equispaced design is the worst solution for estimating the correlation. Hence, when the inferential purpose concerns both the unknown parameters we propose the geometric progression design, namely a flexible class of procedures that allow the experimenter to choose a suitable compromise regarding the estimation's precision of the two unknown parameters guaranteeing, at the same time, high efficiency for both.

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Optimal designs for the Arrhenius equation

Cited by 37 publications

References 18 publications

Uncertainty of Arrhenius parameters

Uncertainty of Arrhenius parameters

Experimental designs for the Adair model

Optimal designs for parameter estimation of the Ornstein–Uhlenbeck process

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