Many analysis algorithms for high-dimensional remote sensing data require that the remotely sensed radiance spectra be transformed to approximate reflectance to allow comparison with a library of laboratory reflectance spectra. In maximum likelihood classification, however, the remotely sensed spectra are compared to training samples, thus a transformation to reflectance may or may not be helpf...

Because of the presence of Jacobian terms, determinants which arose as a result of a transformation of variables, many common likelihood functions have singularities. This fact has several implications for maximum likelihood estimation. The most interesting of these is that singularities often correspond with economically meaningful restrictions, and they can be used to impose the latter. Sever...