Application of Bayesian Reasoning and the Maximum Entropy Method to Some Reconstruction Problems

The so-called Bayesian reasoning is applied whenever uncertainty has to be considered as serious factor in interpretation of results. The paper presents analysis of the impact of inaccurate data on the straight line and quadratic relation fittings. This type of analysis is particularly important when one tries to decide on the type of dependence. The paper also shows examples of the Maximum Entropy Methods applied to the reconstruction of the hyperfine parameters distribution from the measured Mössbauer spectra of $GaFeO_{3}$ and the electron-positron momentum distribution from the positron annihilation data of Gd.