Maximum Likelihood Estimation: Statistical Parameter Fitting for Beginners

How do we find the exact parameters that make a statistical model best fit our real-world data? Maximum Likelihood Estimation (MLE) is the foundational framework that powers modern machine learning algorithms and statistical modeling. This text-based course guides you through the core mathematical intuition and practical application of MLE. You will progress from basic probability concepts to deriving estimates for Gaussian distributions and implementing numerical optimization techniques. What you'll learn: Understand the fundamental concepts of likelihood, probability, and parameter estimation; Derive the log-likelihood function step-by-step for single and multi-variable models; Apply MLE to Gaussian distributions to find optimal mean and variance; Explore how MLE connects directly to modern machine learning loss functions; Implement gradient-based optimization methods to find maximums when analytical solutions are not possible. You will start with essential terminology and the conceptual difference between probability and likelihood. Then, you will work through written derivations and step-by-step optimization logic to build a solid mathematical foundation. This course is designed for aspiring data scientists, analysts, and students who want a clear, beginner-friendly introduction to statistical estimation. Read, practice, and master the core engine of statistical modeling today.