Indirect Hard Modeling (IHM) is the central method in spectral Hard Modeling. Here we address the fundamental questions about the method and its application.

In some cases, the "traditional" tools in chemometrics fail:

• Analysis of peak heights or areas fails in cases of strong peak overlap.
• Data-driven methods like Partial Least Squares (PLS) fail in cases of strong peak shifts and deformations, or require extraordinarily high calibration efforts.
• Frequently changing applications require fast and efficient calibration. Extrapolation into new concentration or temperature ranges should be of low effort, without the need of a full re-calibration.

Indirect Hard Modeling (IHM) uses a physically motivated model - hence, Hard Model -, to predict concentrationds from a mixture spectrum. Physics tell us that a mixture spectrum is composed of the contributions of the mixture components, and that the intensity of a component is linked to its concentration.

The spectrum of a component is composed of peak-shaped signals, expressed mathematically by (peak) functions.

This generates a spectral model in which all parameters have a physical meaning: describing at the same time the shape of spectra, with peak positions, peak width etc., and the mixture composition with Component Weights ω_k.

For the analysis of a mixture, the model gets fitted to the mixture spectrum by calculating the Component Weights. Peak shifts and other shape changes are compensated automatically.

For the individual use of IHM in PEAXACT, we are providing the following materials:

• a tutorial with test data
• a detailed method description linking to the underlying publications