D-optimal designs for estimation of parameters in a simplex dispersion model with proportional data

2021 ◽  
Vol 215 ◽  
pp. 193-207
Author(s):  
Hsiang-Ling Hsu ◽  
Mong-Na Lo Huang
Keyword(s):  
Dispersion Model ◽  
Optimal Designs ◽  
Estimation Of Parameters ◽  
Proportional Data

Mathematical Models for Mixing and Dispersion in Forecasting and Management of Estuarine Water Quality

1987 ◽  
Vol 19 (9) ◽  
pp. 183-193 ◽  
Author(s):  
S. K. Bose ◽  
P. Ray ◽  
B. K. Dutta
Keyword(s):  
Water Quality ◽  
Dispersion Model ◽  
Water Quality Management ◽  
Field Studies ◽  
Accurate Estimation ◽  
Estuarine System ◽  
Estimation Of Parameters ◽  
Dispersion Parameters ◽  
Dispersion Coefficients ◽  
Dimensional Models

The dispersion or spread of a dissolved or suspended substance in an estuarine system occurs mainly due to the non-uniformity of velocity distribution, including turbulent fluctuations, shear stress at the boundary and surface stress caused by winds. The mixing and dispersion phenomena in rivers and estuaries are extremely important in water quality management and control. The development of a dispersion model in harmony with the nature of the flow field in a river or estuary is necessary in the estimation and correlation of dispersion parameters, called dispersion coefficients, which may, in general, be anisotropic in a multidimensional transport process. The earlier one-dimensional models have gradually given way to higher dimensional models for better description of the phenomena as well as for more accurate estimation of parameters. Field studies of dispersion of tracers have been the most important method of generating data for parameter estimation. A number of correlations for mixing and dispersion coefficients in terms of flow rates and other fundamental system parameters are available. The present study incorporates the analysis, assessment and applications of various dispersion and mixing models available. Also, a critical appraisal of the validity, inherent degree of uncertainty and the range of applications of different correlations has been incorporated.

Q-optimal experimental designs and close to them experimental designs for polynomial regression on the interval

2020 ◽  
Vol 86 (5) ◽  
pp. 65-72
Author(s):  
Yu. D. Grigoriev
Keyword(s):  
Optimal Design ◽  
Polynomial Regression ◽  
Direct Consequence ◽  
Experimental Designs ◽  
Optimal Designs ◽  
Software Systems ◽  
General Character ◽  
Support Points ◽  
Optimal Weights ◽  
Universal Expression

The problem of constructing Q-optimal experimental designs for polynomial regression on the interval [–1, 1] is considered. It is shown that well-known Malyutov – Fedorov designs using D-optimal designs (so-called Legendre spectrum) are other than Q-optimal designs. This statement is a direct consequence of Shabados remark which disproved the Erdős hypothesis that the spectrum (support points) of saturated D-optimal designs for polynomial regression on a segment appeared to be support points of saturated Q-optimal designs. We present a saturated exact Q-optimal design for polynomial regression with s = 3 which proves the Shabados notion and then extend this statement to approximate designs. It is shown that when s = 3, 4 the Malyutov – Fedorov theorem on approximate Q-optimal design is also incorrect, though it still stands for s = 1, 2. The Malyutov – Fedorov designs with Legendre spectrum are considered from the standpoint of their proximity to Q-optimal designs. Case studies revealed that they are close enough for small degrees s of polynomial regression. A universal expression for Q-optimal distribution of the weights pi for support points xi for an arbitrary spectrum is derived. The expression is used to tabulate the distribution of weights for Malyutov – Fedorov designs at s = 3, ..., 6. The general character of the obtained expression is noted for Q-optimal weights with A-optimal weight distribution (Pukelsheim distribution) for the same problem statement. In conclusion a brief recommendation on the numerical construction of Q-optimal designs is given. It is noted that in this case in addition to conventional numerical methods some software systems of symbolic computations using methods of resultants and elimination theory can be successfully applied. The examples of Q-optimal designs considered in the paper are constructed using precisely these methods.

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