Abstract
The paper introduces a mathematical algorithm of curve-to-data best fit with robust Bayesian approach. Using Gaussian distribution as a background, one can find an outlier-resistant dedicated Bayesian probability distribution. With the use of a computational iterative method it can then be applied to find the best fit to experimental data points, including vertical and horizontal asymmetric uncertainties. The presented method was tested for constant fitting (so called Bayesian constant), linear regression as well as parabolic fitting for a number of outliers. Practical applications are also presented, e.g., the curves' fitting in radiation cytogenetic biodosimetry, in the financial quotations' trend detection as well as in the ecological study of human cancer mortality. The paper focuses also on other topics, including uncertainties of fitting parameters and the joint Gaussian and Bayesian probability distribution. This paper is an easy and useful tutorial (or technical note) dedicated for robust data analysis in both mathematical and non-mathematical interdisciplinary sciences.
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