Bayesian Maximum A Posteriori Estimation - Extending Maximum Likelihood Estimation

Learn Bayesian Maximum A Posteriori (MAP) estimation as an extension of Maximum Likelihood Estimation that incorporates prior information to improve parameter estimation, particularly valuable when working with sparse or expensive data such as in seismic inversion applications. Explore the fragility of MLE when dealing with poor quality data and discover how Bayesian priors can provide more robust estimates. Master the mathematical derivation of the MAP optimizer and understand how it balances observed data with prior knowledge to produce better parameter estimates. Examine practical applications where MAP estimation outperforms traditional MLE approaches, especially in scenarios with limited data availability, and gain insights into this fundamental technique in distribution estimation and Bayesian inference.