A new development of Bayesian prediction using saddlepoint equalities

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The likelihood maximization and the Shannon entropy maximization are two of the most fundamental principles in statistics. Focusing attention on a common mathematical structure between Bayesian prediction and thermodynamics, this research revealed a very interesting relationship, which should be called duality, between these two principles. Under a certain loss function the Shannon entropy maximization derives the best prediction while the likelihood maximizatiton leads to the worst prediction. Under a dual loss function the roles of these two principles are reversed, and the likelihood maximization derives the best prediction and the Shannon entropy maximization leads to the worst prediction.