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3. The Gaussian kernel

3. The Gaussian kernel "Everybody believes in the exponential law of errors: the experimenters, because they think it can be proved by mathematics; and the mathematicians, because they believe it has been established by observation" (Lippman in [Whittaker1967, p. 179]). The Gaussian kernelThe Gaussian (better Gau ian) kernel is named after Carl Friedrich Gau (1777-1855), a brilliant Germanmathematician. This chapter discusses many of the nice and peculiar properties of the Gaussian kernel .<<FEVinit ;<<FEVF unctions ;Show@ The Gaussian kernel is apparent on every German banknote of DM 10,- where it is depictednext to its famous inventor when he was 55 years old.

The Gaussian kernel is defined in 1-D, 2D and N-D respectively as ... process of observation s can never become zero. For, this would imply making an observation through an infinitesimally small aperture, which is impossible. The factor of 2 in the exponent is a matter of convention,

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