Parametrized Model

Table VI. Estimated Values of Energy Level Parameters for Parametric Model, in cm-1.

Hamiltonian operators, correction for parametric model for actinide... 

In calibration, the number of degrees of freedom depends on the number of parameters estimated by the given model. In case of the two-parametric model (Eq. 6.6) v = n — 2, in case of linear calibration through the coordinate origin (a = 0) v = n — 1, and in case of a three-parametric nonlinear calibration model... 

Neural networks are extensively used to develop nonparametric models and are now the method of choice when electronic noses are used to analyze complex mixtures, such as wines and oils.5 Judgments made by the neural network cannot rely on a parametric model that the user has supplied because no model is available that correlates chemical composition of a wine to the wine s taste. Fortunately, the network can build its own model from scratch, and such models often outperform humans in determining the composition of oils, perfumes, and wines. 

G. D. Hawkins, C. J. Cramer, and C. D. Truhlar, Parametrized models of aqueous free... 

To demonstrate the applicability of the described approach to a system of a reasonable complexity, we briefly consider a (parametric) model of the CO2-assimilating Calvin cycle. In particular, we seek to detect and quantify the possible dynamic regimes of the model without specifying a set of explicit differential equations. 

To investigate these two questions, a parametric model of the Jacobian of human erythrocytes was constructed, based on the earlier explicit kinetic model of Schuster and Holzhiitter [119]. The model consists of 30 metabolites and 31 reactions, thus representing a metabolic network of reasonable complexity. Parameters and intervals were defined as described in Section VIII, with approximately 90 saturation parameters encoding the (unknown) dependencies on substrates and products and 10 additional saturation parameters encoding the (unknown) allosteric regulation. The metabolic state is described by the concentration and fluxes given in Ref. [119] for standard conditions and is consistent with thermodynamic constraints. 

Figure 45. The distribution of the real parts of the eigenvalues sampled from the parametric model of the human erythrocyte. (A) The ensemble of models with Creg and without regulation Cnoreg- ( ) Comparing the distributions associated with two metabolic states normal conditions (Cyivo) and increased energy drain (Catp). The data are adapted from Ref. 296.

J.C. Amphlett, et al., "The Operation of a Solid Polymer Fuel Cell A Parametric Model," Royal Military College of Canada. 

The models used can be either fixed or adaptive and parametric or non-parametric models. These methods have different performances depending on the kind of fault to be treated i.e., additive or multiplicative faults). Analytical model-based approaches require knowledge to be expressed in terms of input-output models or first principles quantitative models based on mass and energy balance equations. These methodologies give a consistent base to perform fault detection and isolation. The cost of these advantages relies on the modeling and computational efforts and on the restriction that one places on the class of acceptable models. 

The high quality numerical data on physical and chemical properties of atoms, molecules, and compounds present a good starting point for the development of a knowledgebase. The task is to condense the information contained in a series of individual data into a quantitative parametric model which will reproduce the primary data with a certain accuracy. If this is successful it can be used to predict new, as yet unknown data for which the same kind of accuracy can be expected. Furthermore, the parameters could also be of use in other models which in turn give new types of data. 

If a multitude of individual waveguides is eontained in a complex eireuitry, then parametric models for basic entities are preferentially used, whieh apply to the optieal signal level, i.e. to complex (mode) amplitudes. 

Just another approach is to calculate e.g. the temperature distribution within a separate program like ANSYS, figure 14, and to transfer the temperature induced index change to the 10 design. If the refractive index change due to the heater can be represented in a parametric model of a... 

In order to optimise individual structures in the lO-design the definition of parameter-loops and scanning routines is required. In combination with this, post-processing of BPM-runs to evaluate channel-specific mode amplitudes, system transmission etc. is necessary, as well, which is assisted by eommercial lO-design tools, naturally. This facilitates the generation of parametric models for any optical sub-system, cf. figures 11 and 12, which at the end is a prerequisite for an efficient system design. 

Briggs A, Nixon R, Dixon S, Thompson S. Parametric modelling of cost data some simulation evidence. Health Econ 2005 14 421-8. 

Therefore, the limitations of the parametrization models should reflect the relative extents of additivity on which they are based, which are also related to their generality. 

A fully parametric model/estimator provides consistent, efficient, and comparatively precise results. The semiparametric model/estimator, by comparison, is relatively less precise in general terms. But, the payoff to this imprecision is that the semiparametric formulation is more likely to be robust to failures of the assumptions of the parametric model. Consider, for example, the binary probit model of Chapter 21, which makes a strong assumption of normality and homoscedasticity. If the assumptions are coirect, the probit estimator is the most efficient use of the data. However, if the normality assumption or the homoscedasticity assumption are incorrect, then the probit estimator becomes inconsistent in an unknown fashion. Lewbel s semiparametric estimator for the binary choice model, in contrast, is not very precise in comparison to the probit model. But, it will remain consistent if the normality assumption is violated, and it is even robust to certain kinds of heteroscedasticity. 

Leontaritis and Billings, 1985] Leontaritis, I. J. and Billings, S. A. (1985). Input-output parametric models for non-linear systems, part I deterministic non-linear systems part II Stochastic non-linear systems. Int. J. Control, 41(2) 303-344. 

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