! Calibration of Mathematical Models

Math models usually include constants. Calibration is the determination of the values of the constants. The calibration can be:

• Theoretical, i.e. the values are deduced by theory
• Empirical, i.e. the values are deduced from observing a process and measuring the inputs and outputs. Suitable measurements are Calibration DATA. The data are usually matched dependent & independent variable values. Fitting a random single variable model is essentially the selection of a mathematical distribution. Some discussion of this process is given in the lessons listed below.
For multivariate models there has to be at least two pairs of data unless the shape of the model is assumed. Fitting to one pair of data is essentially positioning a fixed shape model somewhere in two dimensional space. Discussion of fitting two or more dimensional models is given in the second lesson listed below.

Given calibration data some form of FITTING procedure can be used. It may be as simple as hand plotting of the data and hand fitting a straight or curved line, or as complicated as a non-linear fit using some criteria such as maximum likelihood or least squares, etc. Computer packages for statistical analysis include routines for 'fitting equations to data'

STATGRAPHICS, SASS, SPSS are some of the packages. STATGRAPHICS is compatible with MYSYS as it uses APL as its platform, was marketed by MANUGUISTICS which also marketed APL*PLUS/PC.

MYSYS includes notes on fitting functions, and the function FIT.

f60 ¦ FIT; Function fit for polynomial and exponential models.
f62 ¦ simplex; Simplex search technique for fitting models of any shape.
f216 ¦ lslfit; least squares linear fit of data array.