Estimation Theory

In this module, we move from describing data to inferring the underlying properties of the process that generated it. Estimation is the core of statistical inference and machine learning.

You will learn how to:

Construct estimators for unknown parameters.
Evaluate estimators based on bias, variance, and consistency.
Use powerful techniques like Maximum Likelihood Estimation (MLE) and Maximum A Posteriori (MAP).
Understand the fundamental Bias-Variance Tradeoff that governs all predictive models.

Module: 03 of 05 Difficulty: Intermediate Prerequisites: Probability Distributions, Calculus (Derivatives)

Module Contents

01. Maximum Likelihood & MAP Estimation

Discover the most widely used method for parameter estimation. Learn how to maximize the likelihood function and how to incorporate prior knowledge using Bayesian MAP estimation.

02. The Bias-Variance Tradeoff

Explore the central conflict in supervised learning. Understand how model complexity affects bias and variance, and learn to decompose the Mean Squared Error.

03. Method of Moments

Learn a simple yet powerful alternative to MLE. Match sample moments to population moments to derive consistent estimators for distribution parameters.