scholarly journals Monte Carlo Simulations for the Analysis of Non-linear Parameter Confidence Intervals in Optimal Experimental Design

Author(s):  
Niels Krausch ◽  
Tilman Barz ◽  
Annina Sawatzki ◽  
Mathis Gruber ◽  
Sarah Kamel ◽  
...  
1992 ◽  
Vol 19 (3) ◽  
pp. 188-189 ◽  
Author(s):  
John F. Walsh

Courses in statistics and experimental design can be enhanced through use of crafted data sets. The use of examples highlights the interface between data and statistical routine. FORTRAN programs utilizing the International Mathematical and Statistical Library subroutines permit the user to control the variance—covariance structure of multivariate normal variables and build data sets that have instructional value. Scale transformations and Monte Carlo simulations of the data can be performed as well.


Water ◽  
2018 ◽  
Vol 10 (2) ◽  
pp. 166 ◽  
Author(s):  
Roberto Flowers-Cano ◽  
Ruperto Ortiz-Gómez ◽  
Jesús León-Jiménez ◽  
Raúl López Rivera ◽  
Luis Perera Cruz

2017 ◽  
Vol 66 (2) ◽  
pp. 333-346 ◽  
Author(s):  
Patrycja Wyszkowska

Abstract The determination of the accuracy of functions of measured or adjusted values may be a problem in geodetic computations. The general law of covariance propagation or in case of the uncorrelated observations the propagation of variance (or the Gaussian formula) are commonly used for that purpose. That approach is theoretically justified for the linear functions. In case of the non-linear functions, the first-order Taylor series expansion is usually used but that solution is affected by the expansion error. The aim of the study is to determine the applicability of the general variance propagation law in case of the non-linear functions used in basic geodetic computations. The paper presents errors which are a result of negligence of the higher-order expressions and it determines the range of such simplification. The basis of that analysis is the comparison of the results obtained by the law of propagation of variance and the probabilistic approach, namely Monte Carlo simulations. Both methods are used to determine the accuracy of the following geodetic computations: the Cartesian coordinates of unknown point in the three-point resection problem, azimuths and distances of the Cartesian coordinates, height differences in the trigonometric and the geometric levelling. These simulations and the analysis of the results confirm the possibility of applying the general law of variance propagation in basic geodetic computations even if the functions are non-linear. The only condition is the accuracy of observations, which cannot be too low. Generally, this is not a problem with using present geodetic instruments.


Pharmaceutics ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1087
Author(s):  
Cyril Leven ◽  
Sacha Schutz ◽  
Marie-Pierre Audrezet ◽  
Emmanuel Nowak ◽  
Laurent Meijer ◽  
...  

Roscovitine (Seliciclib), a new protein kinase inhibitor, was administered orally to adult patients with cystic fibrosis for the first time in the ROSCO-CF trial, a dose-escalation, phase IIa, randomized, controlled trial. Extensive pharmacokinetic sampling was performed up to 12 h after the first oral dose. Roscovitine and its main metabolite M3 were quantified by liquid chromatography coupled with tandem mass spectrometry. The pharmacokinetics analyses were performed by non-linear mixed effects modelling. Monte Carlo simulations were performed to assess the impact of dose on the pharmacokinetics of oral roscovitine. Twenty-three patients received oral doses ranging from 200 to 800 mg of roscovitine and 138 data points were available for both roscovitine and M3 concentrations. The pharmacokinetics was best described by a two-compartment parent-metabolite model, with a complex saturable absorption process modelled as the sum of Gaussian inverse density functions. The Monte Carlo simulations showed a dose-dependent and saturable first-pass effect leading to pre-systemic formation of M3. The treatment with proton-pump inhibitors reduced the rate of absorption of oral roscovitine. The pharmacokinetics of oral roscovitine in adult patients with cystic fibrosis was non-linear and showed significant inter-individual variability. A repeat-dose study will be required to assess the inter-occasional variability of its pharmacokinetics.


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