Implementing two dimensional segment inversions with inversion-conforming data sets processing being rendered to include generalized composite weight factors in the processing of error-affected multivariate data samples

Abstract

Representations of data inversions are generated by alternate forms of maximum likelihood estimating and associated least-squares and regression analysis which are rendered in correspondence with either single component residual deviations or projections between data samples and inversion-conforming data sets. Deficiencies in representing likelihood as related to errors-in-variables data and heterogeneous precision are compensated by composite weighting of likelihood elements. Composite weight factors employ both normalization to establish non-skewed homogeneous likelihood elements and fundamental weighting to compensate for associated non-linearly and establish common units for combining orthogonal coordinate-oriented data-point projections. Respective weight factors are related to alternately considered fundamental variables. Variance or alternate representation, as related to statistically independent sampling, is utilized as assumed applicable or replaced by composite variability representing single coordinate variations as affected by orthogonal coordinate sampling dispersions. Statistical rendition is generated as a replacement for unquantifiable dependent variable representation.