Bayes' theorem provides a probabilistic framework for attacking the problem of data analysis. This framework is used to solve the unstable inverse problem of finding the lifetimes and their intensities present in a multi-exponential decay curve resulting from a lifetime measurement. The Maximum Entropy method provides a spectral decomposition of the lifetimes with errors and an estimation of the information contained in the data. No prior information about the number of components present is needed and satisfactory results can be obtained for reasonable statistics (> 1.10⁶). Two other approaches to the problem of regularization consisting of iterative use of firstly an optimal linear filter and secondly a Bayesian linear filter have also been developed and will be discussed. Simulations and analysis of real data are presented to illustrate the possibilities of these new methods.