Over the years two ML estimation approaches have evolved (a) parameter estimation based an implicit formulation of the objective function and (b) parameter and state estimation or "error in variables" method based on an explicit formulation of the objective function. In the first approach only the parameters are estimated whereas in the second the true values of the state variables as well as the values of the parameters are estimated. In this section, we are concerned with the latter approach. [Pg.232]

We have presented applications of a parameter estimation technique based on Monte Carlo simulation to problems in polymer science involving sequence distribution data. In comparison to approaches involving analytic functions, Monte Carlo simulation often leads to a simpler solution of a model particularly when the process being modelled involves a prominent stochastic coit onent. [Pg.293]

The user supplied weighting constant, (>0), should have a large value during the early iterations of the Gauss-Newton method when the parameters are away from their optimal values. As the parameters approach the optimum, should be reduced so that the contribution of the penalty function is essentially negligible (so that no bias is introduced in the parameter estimates). [Pg.164]

Because the technical barriers previously outhned increase uncertainty in the data, plant-performance analysts must approach the data analysis with an unprejudiced eye. Significant technical judgment is required to evaluate each measurement and its uncertainty with respec t to the intended purpose, the model development, and the conclusions. If there is any bias on the analysts part, it is likely that this bias will be built into the subsequent model and parameter estimates. Since engineers rely upon the model to extrapolate from current operation, the bias can be amplified and lead to decisions that are inaccurate, unwarranted, and potentially dangerous. [Pg.2550]

When estimates of k°, k, k", Ky, and K2 have been obtained, a calculated pH-rate curve is developed with Eq. (6-80). If the experimental points follow closely the calculated curve, it may be concluded that the data are consistent with the assumed rate equation. The constants may be considered adjustable parameters that are modified to achieve the best possible fit, and one approach is to use these initial parameter estimates in an iterative nonlinear regression program. The dissociation constants K and K2 derived from kinetic data should be in reasonable agreement with the dissociation constants obtained (under the same experimental conditions) by other means. [Pg.290]

Thus, a list of 1 5 descriptors was calculated for these purposes, as described below. The partition coefficient log P (calculated by a method based on the Gho.sc/Crip-pen approach [11]) (see also Chapter X, Section 1.1 in the Handbook) was calculated because it affects the solubility dramatically [17, 18]. All the other descriptors were calculated with the program PETRA (Parameter Estimation for the Treatment of Reactivity Applications) [28. [Pg.498]

© 2019 chempedia.info