A Comprehensive Guide to Bayesian Statistics

Genre: eLearning | MP4 | Video: h264, 1280x720 | Audio: aac, 48000 Hz
Language: English | Size: 812 MB | Duration: 3h 13m
What you'll 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 on 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
Requirements
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 the above concepts, a 'Prerequisite' document is provided in the first lecture of the course. Students are advised to go through it.
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, quiz, and much more . The course covers the basic theory behind probabilistic and Bayesian modelling, 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 understand the basics of Bayesian Statistics-

An overview on 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 Bayesian approach and think probabilistically. Enrolling in this course will make it easier for you to score well in your exams or apply Bayesian approach elsewhere.

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

Who this course is for:
Students currently pursuing Statistics and Probability
Anyone who wants to build a strong fundamental of Bayesian Statistics
Anyone who wants to apply Bayesian Statistics to other fields like ML, Artificial Intelligence, Business, Applied Sciences, Psychology etc.
Students of Machine Learning and Data Science
Data Scientists curious about Bayesian Statistics