Locality hypothesis method

Molecular simulation methods have been applied to investigate the nucleation mechanism of gas hydrates in the bulk water phase (Baez and Clancy, 1994), and more recently at the water-hydrocarbon interface (Radhakrishnan and Trout, 2002 Moon et al., 2003). The recent simulations performed at the water-hydrocarbon interface provide support for a local structuring nucleation hypothesis, rather than the previously described labile cluster model. 

Many attempts have been made to quantify SIMS data by using theoretical models of the ionization process. One of the early ones was the local thermal equilibrium model of Andersen and Hinthome [36-38] mentioned in the Introduction. The hypothesis for this model states that the majority of sputtered ions, atoms, molecules, and electrons are in thermal equilibrium with each other and that these equilibrium concentrations can be calculated by using the proper Saha equations. Andersen and Hinthome developed a computer model, C ARISMA, to quantify SIMS data, using these assumptions and the Saha-Eggert ionization equation [39-41]. They reported results within 10% error for most elements with the use of oxygen bombardment on mineralogical samples. Some elements such as zirconium, niobium, and molybdenum, however, were underestimated by factors of 2 to 6. With two internal standards, CARISMA calculated a plasma temperature and electron density to be used in the ionization equation. For similar matrices, temperature and pressure could be entered and the ion intensities quantified without standards. Subsequent research has shown that the temperature and electron densities derived by this method were not realistic and the establishment of a true thermal equilibrium is unlikely under SIMS ion bombardment. With too many failures in other matrices, the method has fallen into disuse. 

To reduce the lost work in industrial process plants, the minimization of entropy production rates in process equipment is suggested as a strategy for future process design and optimization [81]. The method is based on the hypothesis that the state of operation that has a minimum total entropy production is characterized by equipartition of the local entropy production. In this context we need to quantify the entropy sources of the various irreversible unit operations that occur in the industrial system. 

In contrast to the hypothesis testing style of model selection/discrimination, the posterior predictive check (PPC) assesses the predictive performance of the model. This approach allows the user to reformulate the model selection decision to be based on how well the model performs. This approach has been described in detail by Gelman et al. (27) and is only briefly discussed here. PPC has been assessed for PK analysis in a non-Bayesian framework by Yano et al. (40). Yano and colleagues also provide a detailed assessment of the choice of test statistics. The more commonly used test statistic is a local feature of the data that has some importance for model predictions for example, the maximum or minimum concentration might be important for side effects or therapeutic success (see Duffull et al. (6)) and hence constitutes a feature of the data that the model would do well to describe accurately. The PPC can be defined along the fines that posterior refers to conditioning of the distribution of the parameters on the observed values of the data, predictive refers to the distribution of future unobserved quantities, and check refers to how well the predictions reflect the observations (41). This method is used to answer the question Does the observed data look plausible under the posterior distribution This method is therefore solely a check of internal consistency of the model in question. 

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