This volume contains the proceedings of the Fifteenth International Workshop on Maximum Entropy and Bayesian Methods, held in Sante Fe, New Mexico, USA, from July 31 to August 4, 1995. Maximum entropy and Bayesian methods are widely applied to statistical data analysis and scientific inference in the natural and social sciences, engineering and medicine. Practical applications include: parametric model fitting and model selection; ill-posed inverse problems; image reconstruction; signal processing; decision making; and spectrum estimation. Fundamental applications include the common foundations for statistical inference, statistical physics and information theory. Specific sessions during the workshop focused on time series analysis, machine learning, deformable geometric models, and data analysis of Monte Carlo simulations, as well as reviewing the relation between maximum entropy and information theory.