• Covariance matrix estimation;
  • Delta method;
  • EM algorithm;
  • Finite mixture model;
  • Mass spectrometry;
  • Secondary ion mass spectrometry


Secondary ion mass spectrometry is a popular physical technique that allows learning elemental and chemical compositions of various substances. In some cases, the mass spectrum of the sample studied is not observable without that of the liquid solution in which the investigated substance must be placed. To separate the informative part of the observed mixed spectrum from the irrelevant liquid solution part, we develop an approach that is based on finite mixtures. Finite mixture modelling is a statistical technique that is capable of accounting for various shapes and patterns in data. We discuss a mixture model constructed with bell-shaped discrete component distributions that can be employed in the mass spectrometry framework for extracting the informative part of the mixed spectrum of organic objects. The results for assessing variability in the mass spectrum extracted are derived. The procedure is thoroughly illustrated on simulated data sets and applied to several real life problems that are concerned with complex organic dyes placed in a glycerol liquid matrix. The results obtained have clear chemical interpretation and suggest that the approach proposed is very promising.