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A Comprehensive Guide to Bayesian Statistics

Features Includes:
  • Self-paced with Life Time Access
  • Certificate on Completion
  • Access on Android and iOS App

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  • Categories

    Academics

  • Duration

    03:13:51

  • 0 Students Enrolled

Description

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 Statistics

  • An 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 Prior

Section 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 Mean

Section 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 hypotheses

Section 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
  • Bayesian Expected Loss
  • Risk: Frequentist Risk/Risk Function, Bayes Estimate, and Bayes Risk
  • Admissibility of Decision Rules
  • Procedures to find Bayes Estimate & Bayes Risk: Normal & Extensive Form of Analysis
  • Solved numerical problems of computing Bayes Estimate and Bayes Risk for different Loss Functions

Section 6: This section includes:

  • Bayesian's Defense & Critique
  • Applications of Bayesian Statistics in various fields
  • Additional Resources
  • Bonus Lecture and a Quiz

At the end of the course, you will have a complete understanding of Bayesian concepts from scratch. You will know how to effectively use the Bayesian approach and think probabilistically. Enrolling in this course will make it easier for you to score well in your exams or apply the Bayesian approach elsewhere.

Complete this course, master the principles, and join the queue of top Statistics students all around the world.



Basic knowledge

Basic knowledge of Probability and Statistics

  • You should be comfortable with concepts of conditional and marginal probability, all probability distributions, and basics of Statistical Inference
  • You will need concepts of differentiation and integration to solve the problems, so if you have that foundation, you'll be well prepared for this course
  • To brush up on the above concepts, a 'Prerequisite' document is provided in the first lecture of the course. Students are advised to go through it

What will you learn
  • An Overview on Statistical Inference
  • Frequentist vs Bayesian approach to Statistical Inference
  • Clearly understand Bayes Theorem and its application in Bayesian Statistics
  • Build a good intuitive understanding of Bayesian Statistics with real-life illustrations
  • Master the key concepts of Prior and Posterior Distribution
  • Solve exam-style numerical problems of computing Posterior Distribution for Population Parameter with different types of Prior
  • Understand Conjugate Prior and Jeffrey's Prior
  • Interval Estimation in Bayesian Statistics: Credible Intervals
  • Distinguish and work with Confidence Intervals and Credible Intervals
  • Solve problems of computing Credible Interval for Posterior Mean
  • Bayesian Hypothesis Testing: Bayes Factor
  • Learn to Interpret Bayes Factor
  • Solve numerical problems of computing Bayes Factor for two competing hypotheses
  • Build a solid understanding of Bayesian Decision Theory with examples
  • Decision Theory Terminology: State/Parameter Space, Decision Rule, Action Space, Loss Function
  • Minimizing Expected Loss
  • Real Life Illustrations of Bayesian Decision Theory
  • Use different Loss Functions: Squared Error Loss, Absolute Error Loss, 0-1 Loss
  • Decision Making with Frequentist vs Bayesian
  • Understand Bayesian Expected Loss, Frequentist Risk, and Bayes Risk
  • Admissibility of Decision Rules
  • Procedures to find Bayes Estimate & Bayes Risk: Normal & Extensive Form of Analysis
  • Solve numerical problems of computing Bayes Estimate and Bayes Risk for different Loss Functions
  • Bayesian's Defense & Critique
  • Applications of Bayesian Inference in various fields
Course Curriculum
Number of Lectures: 50 Total Duration: 03:13:51
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