Optimal prediction space

Since a CSTR operates at or close to uniform conditions of temperature and composition, its kinetic and product parameters can usually be predicted more accurately and controlled with greater ease. The CSTR can often be operated at a selected conversion level to optimize space-time yield, or where a particular product parameter is especially favored. 

We have discussed our theoretical calculations on metals ranging from very accurate ab initio studies of diatomic and triatomic systems to model studies of larger clusters. Recent improvements in the accuracy to which we can represent both the one-particle and n-particle spaces has significantly improved the reliability of theoretical calculations on small molecules. For example, we are able to predict definitively that AI2 has a Hu ground state even though the state lies within 200 cm . Calculations on clusters indicate that their geometry varies dramatically with cluster size, and that rather large clusters are required before the bulk structure becomes optimal. Since clusters are more... 

Once a model has been fitted to the available data and parameter estimates have been obtained, two further possible questions that the experimenter may pose are How important is a single parameter in modifying the prediction of a model in a certain region of independent variable space, say at a certain point in time and, moreover. How important is the numerical value of a specific observation in determining the estimated value of a particular parameter Although both questions fall within the domain of sensitivity analysis, in the following we shall address the first. The second question is addressed in Section 3.6 on optimal design. 

A new idea has recently been presented that makes use of Monte Carlo simulations [60,61], By defining a range of parameter values, the parameter space can be examined in a random fashion to obtain the best model and associated parameter set to characterize the experimental data. This method avoids difficulties in achieving convergence through an optimization algorithm, which could be a formidable problem for a complex model. Each set of simulated concentration-time data can be evaluated by a goodness-of-fit criterion to determine the models that predict most accurately. 

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