A Comprehensive Guide to Bayesian Statistics

This course is a comprehensive guide to Bayesian Statistics. It includes video explanations along with real-life illustrations, examples, numerical problems, take away notes, practice exercise workbooks, quizzes, and much more. The course covers the basic theory behind probabilistic and Bayesian modeling, and their applications to common problems in data science, business, and applied sciences.The course is divided into the following sections:Section 1 and 2: These two sections cover the concepts that are crucial to understanding the basics of Bayesian StatisticsAn overview of Statistical Inference/Inferential Statistics
Introduction to Bayesian Probability
Frequentist/Classical Inference vs Bayesian Inference
Bayes Theorem and its application in Bayesian Statistics
Real Life Illustrations of Bayesian Statistics
Key concepts of Prior and Posterior Distribution
Types of Prior
Solved numerical problems addressing how to compute the posterior probability distribution for population parameters
Conjugate Prior
Jeffrey's Non-Informative PriorSection 3: This section covers Interval Estimation in Bayesian Statistics:Confidence Intervals in Frequentist Inference vs Credible Intervals in Bayesian Inference
Interpretation of Confidence Intervals & Credible Intervals
Computing Credible Interval for Posterior MeanSection 4: This section covers Bayesian Hypothesis Testing:Introduction to Bayes Factor
Interpretation of Bayes Factor
Solved Numerical problems to obtain Bayes factor for two competing hypothesesSection 5: This section caters to Decision Theory in Bayesian Statistics:Basics of Bayesian Decision Theory with examples
Decision Theory Terminology: State/Parameter Space, Action Space, Decision Rule. Loss Function
Real Life Illustrations of Bayesian Decision Theory
Classification Loss Matrix
Minimizing Expected Loss
Decision making with Frequentist vs Bayesian approach
Types of Loss Functions: Squared Error Loss, Absolute Error Loss, 0-1 Loss