Lecture-0(Part-1): From Classical to Bayesian Inference(Classical Estimation)

Описание: 📘 Lecture 0: From Classical to Bayesian Inference – Classical Estimation Techniques & MLE

This introductory lecture builds the foundation for the entire Bayesian Inference series by first revisiting Classical (Frequentist) Estimation Methods, especially the Maximum Likelihood Estimation (MLE) approach.

Before understanding Bayesian methods, it is essential to understand how classical inference works — its strengths, assumptions, and limitations.

🔎 What You Will Learn:

✔️ Difference between Classical and Bayesian inference
✔️ Concept of parameter estimation
✔️ Likelihood function and its construction
✔️ Maximum Likelihood Estimation (MLE) – theory and intuition
✔️ Derivation of MLE for common distributions
✔️ Properties of MLE (Consistency, Efficiency, Asymptotic Normality)
✔️ Limitations of classical estimation
✔️ Why Bayesian inference becomes necessary

📊 Topics Covered:

• Likelihood principle
• Log-likelihood function
• Score function and information matrix
• Bias and variance of estimators
• Large sample properties
• Comparison: Classical vs Bayesian philosophy

🎯 By the End of This Lecture:

You will be able to:

Construct likelihood functions

Derive MLEs step-by-step

Understand theoretical properties of estimators

Identify limitations of classical methods

Appreciate the motivation for Bayesian inference

📚 Recommended for:
Statistics | Econometrics | Data Science | Machine Learning | Research Scholars | Applied Mathematics

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