Maximum Probability and Relative Entropy Maximization. Bayesian Maximum Probability and Empirical Likelihood

Details Maximum Probability and Relative Entropy Maximization. Bayesian Maximum Probability and Empirical Likelihood Maximum Probability and Relative Entropy Maximization. Bayesian Maximum Probability and Empirical Likelihood

2008-04-24

arxiv.org/abs/0804.3926v1

Mathematics

Statistics Theory

Intnl. Workshop on Applied Probability 2008, Compiegne, France

Scientific paper

Works, 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.

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