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

2008/04/24 by Grendar, M.
#62F10 #62G10 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.0804.3926

Abstract

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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