
Chapter 3
Mathematical and Statistical
Aspects of Inverse Problems
In inverse or parameter estimation problems, as discussed in the Introduc-
tion, an important but practical question is how successful the mathematical
model is in describing the physical or biological pheno mena represe nted by
the experimental data. In general, it is very unlikely that the residual sum of
squares (RSS) in the least-squa res formulation is zero. Indeed, due to mea-
surement noise as well as modeling error, there may not be a “true ” set of
parameters so that the mathematical model will provide an exact fit to the
experimental data.
Even if one begins with a deterministic ...