Maximal information analysis: I—various Wayne State plots and the most common likelihood principle

Statistical analysis using all moments of the likelihood L ( y | α ) (y being the data and α being the fit parameters) is presented. The relevant plots for various data fitting situations are presented. The goodness of fit (GOF) parameter (currently the χ 2 ) is redefined as the isoprobability level in a multidimensional space. Many useful properties of statistical analysis are summarized in a new statistical principle which states that the most common likelihood, and not the tallest, is the best possible likelihood, when comparing experiments or hypotheses.