Statistical analysis proved to be significant in determining the errors of theoretical models, assessing the risk of extrapolation and the sensitivity of the model to changes, as well as in the description of instabilities in the models. However, the importance of applying the analysis of the unreliability of individual parameters in the form of nuclear energy density functionals has only recently been recognized, where one of the main problems of error analysis of the parameters of those models is the possible sloppiness of some parameters or their combinations. This was precisely the motivation for using methods of reducing the number of model parameters based on information geometry - an interdisciplinary field that applies the ideas of differential geometry to statistical problems that have recently found application in the physical description of various systems in physics, chemistry and biology. Since in nuclear physics the manifold boundary approximation method (MBAM) has recently proved useful for the classification and reduction of complex models such as EDF models of the atomic nucleus, the statistical nature of determining the unreliability by the MBAM method was investigated in more detail using the example of the DD-PC1 functional. Also, using automatic differentiation in the code of the DD-PC1 functional and the MBAM method, a more thorough and precise analysis of the unreliability of the parameters itself is obtained, which enabled the optimization of time and numerical precision. Considering the novelty of the MBAM method itself, stability tests of the conclusions obtained by MBAM geodesics based on differential geometry techniques in the field of classical statistics and Bayesian statistics in the form of the Markov Chain Monte Carlo method were conducted.