Statistical inference and residual analysis for the evaluation of datum transformation models developed on 3D coordinate data

Abstract

The evaluation of geoscience data is a far-reaching topic which cannot be systematically covered. The purpose of inferential statistics is to harness useful information from data for making decisions. This paper conducts in-depth statistical study for the Bursa-Wolf and Molodensky Badekas models of the three-dimensional transformation parameters. We also considered the combined and observation equations scenarios of these methods for the comparative study. Four key indicators are conducted to evaluate the performance of the two transformation models according to the residual results. These include root mean square error (RMSE), paired t-test, Wilcoxon signed-rank test and the Cohen’s d effect size measure. RMSE evaluation is based on the mean difference between model estimates and observed values. The correlations in the model results is investigated based on paired t-test. Wilcoxon signed-rank test assesses the statistical significance of the model’s paired differences. To estimate the effect size of the performance differences, Cohen’s d measures are computed. Further, the residuals of the estimated parameters are plotted according to their respective control points. The inference results of these tests generally show that Badekas transformation approach is more precise than Bursa-Wolf. Specifically, Badekas combined case is the most precise, followed by its observation case, then Bursa-Wolf combined and finally its observation case is the least performing model. The application of various data analysis and statistical verifications make the task of data interpretation and best model selection easier.