2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159691Works, briefly surveyed here, are concerned with two basic methods: Maximum Probability and Bayesian Maximum Probability; as well as with their asymptotic instances: Relative Entropy Maximization and Maximum Non-parametric Likelihood. Parametric and empirical extensions of the latter methods - Empirical Maximum Maximum Entropy and Empirical Likelihood - are also mentioned. The methods are viewed as tools for solving certain ill-posed inverse problems, called Pi-problem, Phi-problem, respectively. Within the two classes of problems, probabilistic justification and interpretation of the respective methods are discussed.Intnl. Workshop on Applied Probability 2008, Compiegne, FranceStatistics TheoryProbabilityMethodology62F10; 62G10text