Solution 3.4 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant

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  • Published: Jan 1, 2000
  • Channels: Chemometrics & Informatics

1. The probability vectors are as follows.

2. Graphs of the three models are as follows.

3. Positive values are expected because spectra are positive in nature.

4. The entropy calculation is presented below, using logarithms to the base 10 (any base is possible) and remembering that 0log(0) equals 0.

5. Model C has the most positive entropy. This is the flattest model. No other information has been given, so the maximum entropy solution is the one with least features and which is most spread out and even.

6. Normally there is some experimental data, so the least squares fit of each model to the data is important. If all three models had equal least squares fit to the observed data, then model C would be chosen. However there is generally a balance between the least squares fit, which tries to find structure, and the entropy which choses the model with least structure.

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