The inherently nonlinear phenomenon of hysteresis is notoriously difficult to model. Of notable interest are the inverse models of hysteresis which identify the parameters of a particular model to closely match experimental data. Two major models of hysteresis are the Preisach and Bouc-Wen models. As researchers typically deal with solely one model for their analyses, this thesis initially develops techniques to convert from the Bouc-Wen model to the Preisach model, using first a least squares fit followed by using artificial neural networks. The parameters of each of the two models are investigated in further detail, with emphasis on how each parameter affects the loop and how to arrive at an adequate initial estimate for the identification problem algorithms. The techniques are then evaluated and compared against several sets of experimental data for hysteresis loops supplied by the Air Force Research Lab. Their optimized solutions are compared to assess the flexibility and viability of each model. Generally, it is found that, while both models are successful, the Preisach model is more flexible in fitting different types of experimental loops. Lastly, both experimental loops and theoretical loops subjected to white noise are identified using Transitional Markov Chain Monte Carlo (TMCMC) algorithms via the Preisach model. These results show promise for the TMCMC method being applied on data, particularly when the loop is induced by white noise.