Calibration space

When we plot the sample concentrations in this way, we begin to see that each sample with a unique combination of component concentrations occupies a unique point in this concentration space. (Since this is the concentration space of a training set, it sometimes called the calibration space.) If we want to construct a training set that spans this concentration space, we can see that we must do it in the multivariate sense by including samples that, taken as a set, will occupy all the relevant portions of the concentration space. 

The random approach involves randomly selecting samples throughout the calibration space. It is important that we use a method of random selection that does not create an underlying correlation among the concentrations of the components. As long as we observe that requirement, we are free to choose any randomness that makes sense. 

Inlier detection methods, n - statistical tests which are conducted to determine if a spectmm resides within a region of the multivariate calibration space which is sparsely populated. 

Nearest neighbor distance inlier, n - a spectrum residing within a significant gap in the multivariate calibration space, the result for which is subject to possible interpolation error across the sparsely populated calibration space. 

A second challenge was to rapidly develop real models as soon as possible after plant start-up, in spite of the relatively small variation in composition expected at a given process point. This challenge was solved by modelling all three process points (esterifier exit, pipeline reactor exit, and prepolymerizer exit) together. Inclusion of the process variability due to the start-up itself also helped. The calibration space for the first calibration set is shown in Figure 15.7. 

Figure 15.7 Calibration space covered by the first calibration set. The x-axis is lab carboxyl ends in meq/kg and the y-axis is DP in repeat units. The samples are labelled by process point 1 - esterifier, 2 - pipeline reactor and 3 - prepolymerizer. Reprinted with permission from Brearley and Hernandez (2000). ...

The conclusion is that the model appears to be acceptable. This graph also provides information about how well the method will predict future samples. It is expected that the errors in prediction for component B will be 0.06. This conclu.sion is only possible because the validation set contains many samples that adequately span the calibration space (see Habit 1). A conclusion about the prediction errors for component A will be evaluated after resolving the issue with the unusual sample. 

The use of more calibration data can result in improved model performance, especially if the additional calibration data result in an improved representation of the sample states that need to be covered for calibration. Referring to the earlier plot of interference error and estimation error versus model complexity (Figure 8.18), an improved representation of the calibration space corresponds to a general drop in the level of the estimation error curve. This results in lower overall prediction error. 

Difficult calibration space between electrodes must be representative for entire column little experience... 

Then it may be debated given the specific application what is meant by such a test-set should it allow for extrapolatirm of the calibration space Is the assumptirm that the model shall be robust towards change in sample matrix, raw materials, chemical reagents, etc. These sources of variation that are in principle unknown for future objects can be to some extent quantified by several approaches. 

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