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Introduction to Data Science (DS 215)
·
Module 7
Principles of Bayesian Inference
1
Gaussian-Gaussian Conjugate Priors
Derive the posterior distribution for a model with a Gaussian likelihood and Gaussian prior (conjugate priors).
2
MMSE Estimator as Posterior Mean
Derive the Minimum Mean Square Error (MMSE) estimator as the mean of the posterior distribution.
3
MAP Estimation: Mode of the Posterior
Derive the Maximum A Posteriori (MAP) estimator as the mode of the posterior distribution.
4
MAP, MLE, and L2 Regularization: A Relationship Explained
Explain the relationship between MAP, MLE, and L2 regularization.
5
Sequential Bayesian Estimation for Coin Bias
Project: Implement a Bayesian estimator to sequentially update beliefs about a coin's bias as new data arrives.
Previous module
Optimality and Performance of Estimators
Next module
Hypothesis Testing and Statistical Significance