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Introduction to Data Science (DS 215)
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Module 5
Maximum Likelihood and Least Squares Estimation
1
MLE for Common Distributions
Derive the Maximum Likelihood Estimators (MLE) for parameters of Normal, Exponential, and Poisson distributions.
2
Matrix Calculus for OLS Normal Equations
Derive the Normal Equations for Ordinary Least Squares (OLS) using matrix calculus.
3
Orthogonal Projection and Least Squares
Explain the geometric interpretation of Least Squares as an orthogonal projection onto a subspace.
4
Numerical MLE in Python
Implement a numerical Maximum Likelihood Estimator for a custom probability distribution in Python.
5
Invariance of MLEs
Analyze the invariance property of Maximum Likelihood Estimators.
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Foundations of Statistical Inference
Next module
Optimality and Performance of Estimators