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Abstract

The preceding chapters have discussed many aspects of model design, variable selection, and how these variables are calculated or measured. Chapter 2 reviewed published porosity prediction models and showed that most are univariate or multivariate linear equations which contain one or several of the terms in the saturated linear model. Simpler univariate equations may provide sufficient accuracy for a particular application but are frequently limited in their range of applicability or robustness. Multivariate equations are usually more robust, but they often require larger data sets with greater ranges in the independent variables and a deeper understanding of controls. In addition, they may have diminished predictive accuracy due to the increase in the number of "latent" (e.g., minor, isolated, or unidentified) independent variables. All models represent a perceived optimal balance between budget, time, availability of data or sample material, complexity of the model, level of understanding of fundamental processes, and application requirements and conditions (required model accuracy and predictive confidence).

Linear models are generally the easiest to formulate, and are, therefore, the most common relational structures used. Consequently, the following discussion will concentrate on linear models (here linear does not mean that the data must correlate as a straight line but that the equations are linear with respect to the terms they contain). This in no way implies that other approaches cannot offer similar, or even greater, success. Other approaches, such as sequenced reaction kinetics-models, Monte Carlo analysis, Possibility analysis, neural networks, and non-linear regression analysis, may all provide accurate models.

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