Model-building methods

Model building remains a useful technique for situations where the data are not amenable to solution in any other way, and for which existing related crystal structures can be used as a starting point. This usually happens because of a combination of structural complexity and poor data quality. For recent examples of this in the structure solution of polymethylene chains see Dorset [21] and [22]. It is interesting to note that model building methods for which there is no prior information are usually unsuccessful because the data are too insensitive to the atomic coordinates. This means that the recent advances in structure solution from powder diffraction data (David et al. [23]) in which a model is translated and rotated in a unit cell and in which the torsional degrees of freedom are also sampled by rotating around bonds which are torsionally free will be difficult to apply to structure solution with electron data. 

Finally, the specific methods discussed below were chosen based on their utility for PAT applications and their availability in current commercial software packages. For those who are interested in a more complete list of quantitative model building methods, further details can be found in the following references [1,46-56]. 

Figure 12.9 The NIR transmission spectra of 70 different styrene-butadiene copolymers over the range 1570-1850nm, for use in demonstrating the quantitative model building methods.

Conventional model building methods have enabled elucidation of the framework structures of Montesommaite [57], ZSM-18 [58], ZSM-57 [59], A1P04-52 [60] and A1P04-54 [61]. The structure... 

Model Building Method". Paper presented at Princeton Symposium on Statistics, 1966. 

The principal reason that a test set is necessary for validation is that empirical model-building methods cannot readily distinguish between noise and information in data sets, so the methods are prone to adjusting the model parameters to reduce error beyond the point warranted by the information contained in the data. This problem is called overtraining and can be countered by a variety of techniques such as descriptor reduction and early stopping, and readers interested in those topics are referred to the more detailed reviews of numerical methods cited in each of the following sections. 

G. W. Small et al., Evaluation of Data Pretreatment and Model Building Methods for the Determination of Glucose from Near-Infrared Single-Beam Spectra, Appl. Spectrosc., 53(4), 402 (1999). 

Conventional model building methods have, however, recently enabled elucidation of the framework stroctures of Montesommaite [46], ZSM-18 [47], ZSM-57 [48], A1P04-52 [49] and VPI-5 [50]. The stracture of ZSM-18 had perplexed zeolite crystallographers for many years. Its solution by the model building approach, like the related structures of beryllophosphate-H (BPH) and Linde type Q (BPH), was made possible by the determination of the related APS and AFY framework stractures by ctmventional difiiaction teclmiques. 

Allpossible regressions is a model-building method, when all possible variable combinations are examined in the model. 

In order to assess the potential toxicological effects of onchidal from a predictive standpoint, the author subjected the two-dimensional molecular structure of onchidal (1) to an in silica QSAR computational analysis. Details regarding the approach of the software, including procedures and model building methods, have been described in recent publications (e.g., Choi et al., 2013 Valencia et al., 2013). The in silica analysis of the molecular structure of onchidal produced predictive information on nonclinical toxicities. The computational QSAR models included bacterial mutagenicity (Salmanella h/pln/murium mutagenicity (Ames) assay), and phospholipidosis (Table 30.3). 

Thi.s method of cstabli.shing a rclation.ship between a molcculai structure and it.s properties is inductive. It depends on a set of compounds with know n properties or activities whicli is used for model building. 

The method of building predictive models in QSPR/QSAR can also be applied to the modeling of materials without a unique, clearly defined structure. Instead of the connection table, physicochemical data as well as spectra reflecting the compound s structure can be used as molecular descriptors for model building,... 

A structure descriptor is a mathematical representation of a molecule resulting from a procedure transforming the structural information encoded within a symbolic representation of a molecule. This mathematical representation has to be invariant to the molecule s size and number of atoms, to allow model building with statistical methods and artificial neural networks. 

The abbreviation QSAR stands for quantitative structure-activity relationships. QSPR means quantitative structure-property relationships. As the properties of an organic compound usually cannot be predicted directly from its molecular structure, an indirect approach Is used to overcome this problem. In the first step numerical descriptors encoding information about the molecular structure are calculated for a set of compounds. Secondly, statistical methods and artificial neural network models are used to predict the property or activity of interest, based on these descriptors or a suitable subset. A typical QSAR/QSPR study comprises the following steps structure entry or start from an existing structure database), descriptor calculation, descriptor selection, model building, model validation. 

Much of the study of kinetics constitutes a study of catalysis. The first goal is the determination of the rate equation, and examples have been given in Chapters 2 and 3, particularly Section 3.3, Model Building. The subsection following this one describes the dependence of rates on pH, and most of this dependence can be ascribed to acid—base catalysis. Here we treat a very simple but widely applicable method for the detection and measurement of general acid-base or nucleophilic catalysis. We consider aqueous solutions where the pH and p/f concepts are well understood, but similar methods can be applied in nonaqueous media. 

A machine-learning method was proposed by Klon et al. [104] as an alternative form of consensus scoring. The method proved unsuccessful for PKB, but showed promise for the phosphatase PTPIB (protein tyrosine phosphatase IB). In this approach, compounds were first docked into the receptor and scored using conventional means. The top scoring compounds were then assumed to be active and used to build a naive Bayes classification model, all compounds were subsequently re-scored and ranked using the model. The method is heavily dependent upon predicting accurate binding... 

Part I comprises three chapters that motivate the study of optimization by giving examples of different types of problems that may be encountered in chemical engineering. After discussing the three components in the previous list, we describe six steps that must be used in solving an optimization problem. A potential user of optimization must be able to translate a verbal description of the problem into the appropriate mathematical description. He or she should also understand how the problem formulation influences its solvability. We show how problem simplification, sensitivity analysis, and estimating the unknown parameters in models are important steps in model building. Chapter 3 discusses how the objective function should be developed. We focus on economic factors in this chapter and present several alternative methods of evaluating profitability. 

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