  Statistical modeling of physical laws connects experiments with mathematical
descriptions of natural phenomena. The modeling is based on the probability
density of measured variables expressed by experimental data via a kernel
estimator. As an objective kernel the scattering function determined by
calibration of the instrument is introduced. This function provides for a new
definition of experimental information and redundancy of experimentation in
terms of information entropy. The redundancy increases with the number of
experiments, while the experimental information converges to a value that
describes the complexity of the data. The difference between the redundancy and
the experimental information is proposed as the model cost function. From its
minimum, a proper number of data in the model is estimated. As an optimal,
nonparametric estimator of the relation between measured variables the
conditional average extracted from the kernel estimator is proposed. The
modeling is demonstrated on noisy chaotic data.
