*If you are currently using a smoothing function, here
is a way to test it. Smooth your data. Then smooth it
again. If the second smoothing changes the result of the first smoothing, then
you should think about using a better function.*

Smoothing algorithms have one of two goals: to make the data
look better; or, to reveal data partially obscured by noise. We view the former
as a corruption of the data; it cannot be justified from the formal principles
of Maximum Likelihood (ML) data analysis. We do not offer this option. On the
other hand, the separation of signal from noise is a legitimate goal of an ML
process. How might one carry it out?

First, one must bring information to the operation which
is not explicit in the data, and which differentiates signals from noise. One
immediately thinks first of *peakshapes*, the signature of the signal, and
then of *statistics*, the characteristic amplitude distribution in the data
in the absence of a signal. These two discriminants, encoded into a suitable
algorithm, can select signal-like features from data, discarding noise-like
features along the way. So we ask the user to specify: (1) Does the noise
follows Poisson (counting, or signal-dependent) or Gaussian (additive,
signal-independent) statistics? (2) What does the narrowest data peak look like?
We then solve the following problem: Given these two constraints, what is the
most likely spectrum one would see if there were no noise?

Experimentally, that answer may be obtained by averaging
very many identically prepared data sets together - a process not usually
practicable, either because of the time required, or because the data source is
not that stable. However, Maximum Likelihood and Maximum Entropy methods may be
utilized to calculate the most probable spectra that such averaging would
produce if one could carry it out. The additional constraints described above
make such a calculation possible. (The theory and equations are fully
described in "Maximum Likelihood smoothing of noisy data", published
in American Laboratory, March 1990, as well as in all Razor manuals).