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Interactive Visually-Assisted Fitting of Histograms and Vectors


Fitting histograms and vectors is a difficult computational problem. In many cases the underlying minimization problem has numerous local minima and, therefore, the minimization program can miss the global minimum. Even for a relatively simple case of fitting a double-peak histogram with the sum of two Gaussians, as shown in the figure below, the minimizing program fails to converge to the correct solution unless good initial values of the fit function parameters are given.

Often, the user has semantic knowledge of his fitting problem, which the minimizing program lacks. Using the scales and input fields on the panel, the user can set a good initial estimate observing the fit function and the histogram on the screen.

The histogram fit panel (see Figure below) can be opened from PAW++ command line when the histo/fit command has option M, from the Browser popup menu, or from a graphics window pop-up menu. The vector fit panel looks similar to the histogram fit panel, except for the upper line which has text fields for the names of a vector pair to fit instead of the histogram identifier.

The full functionality of MINUIT is accessible from both panels, including save/restore, computing and plotting contours and one-dimensional cross-sections, computing Minos errors, Hessians, correlations, eigenvalues. The panels will be put into the NEW area of CERNLIB by the end of December.

Histogram Fit Panel

Janne Saarela
Tue May 23 09:56:57 METDST 1995