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In principle, the objective of Bayesian estimation is to minimize the Bayes risk, which is defined to be the expected value of the cost. Within this framework, different cost functions would lead to different estimation methods. For example, if the cost function is defined to be the mean-squared error, the Bayesian estimation method leads to the minimum mean-squared error (MMSE) estimator, which turns out to be the conditional mean estimator. On the other hand, if the cost function is the a posteriori PDF, the resulting Bayesian estimator is the maximum a posteriori (MAP) estimator, which is obtained by maximizing the a posteriori PDF.

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Bayesian Estimation

  • 章节

  • 发表日期：

    2026年

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  • Yong Ching Lim,
  • Paulo S. R. Diniz,
  • Yih-Fang Huang

摘要

In principle, the objective of Bayesian estimation is to minimize the Bayes risk, which is defined to be the expected value of the cost. Within this framework, different cost functions would lead to different estimation methods. For example, if the cost function is defined to be the mean-squared error, the Bayesian estimation method leads to the minimum mean-squared error (MMSE) estimator, which turns out to be the conditional mean estimator. On the other hand, if the cost function is the a posteriori PDF, the resulting Bayesian estimator is the maximum a posteriori (MAP) estimator, which is obtained by maximizing the a posteriori PDF.