Representations of data inversions are generated by alternate forms of maximum likelihood estimating which are rendered in correspondence with dependent coordinate mappings of path-oriented displacements. The dependent coordinate mappings are alternately considered to represent either path coincident deviations, path-oriented data-point projections. Normal displacements are rendered in normalized coordinates as a shortest distance between respective data samples and successive fitting function approximations. Deficiencies in representing likelihood as related to nonlinearities and heterogeneous precision are compensated by essential weighting of respectively mapped path-oriented displacements.