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A Comprehensive Guide to Bayesian Statistics

Name: A Comprehensive Guide to Bayesian Statistics
Rating: 4.2 (118 reviews)

Bayesian Inference, Prior & Posterior Distn, Bayesian Interval Estimation, Bayesian Hypothesis Testing & Decision Theory

Created byTwinkle Sethi

Last updated 11/2020

English

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

Course content

7 sections • 50 lectures • 3h 13m total length

How exciting is Bayesian!3:51

What is Statistical Inference?1:48
What we already know about Probabilities?4:36
Explore how probabilities arise from well-defined experiments and the sample space, contrast frequentist inference with Bayesian updates via Bayes' theorem as unknowns become random variables with new data.
Frequentist vs Bayesian Statistics7:45
More illustrations for Bayesian Thinking1:39
Bayesian Applications Rippling Through1:14
Bayes Theorem4:21
Practical Application of Bayes Theorem: COVID-19 Screening8:37
Apply Bayesian reasoning to covid-19 screening by linking prior probability with sensitivity. Observe how sequential testing updates beliefs from 2 percent to 50 percent, then 98 percent, guided by specificity.
Understanding Prior & Posterior6:32
Bayesian Approach in All Aspects of Life2:16
Explore how Bayesian thinking updates beliefs by combining initial priors with new evidence, using Bayes' theorem to assess claims with observations and data.
Activity0:11
Practice Exercise0:14

Illustration for Prior2:04
Better Forecasting with Bayesian1:36
Types of Prior2:39
Numerical problems: Computing Posterior Distribution13:12
Compute posterior distributions for theta under Bernoulli and binomial data, using priors from uniform to beta; recognize natural conjugate priors and beta-binomial updates.
Jeffrey's Non-Informative Prior4:14
Derive Jeffreys non-informative prior from the Fisher information and illustrate with a normal model showing a uniform prior when sigma is known.
Practice Exercise0:14

Strategies for Parameter Estimation1:36
Bayesian Credible Intervals7:58
Interpretation of Confidence Interval & Credible Interval5:18
Computing Confidence Interval for Population Mean with known variance5:30
Computing Credible Interval0:39
Compute the credible interval with a lower and upper bound around a point estimate using standard error and credible value. State that a 95 percent credible interval has posterior probability 0.95.
Numerical Problem: Computing Credible Interval for Posterior Mean8:09
Explore computing a credible interval for the posterior mean with normal data and normal prior, derive the posterior, and compare bayesian credible intervals to frequentist confidence intervals.
Practice Exercise0:14
Practice the attached exercise to apply Bayesian statistics to new medical problems, and compare your results with the provided solutions.

Understanding Bayes Factor3:19
Analyze how Bayes factor informs hypothesis testing, showing how prior odds and posterior odds from data X update beliefs about the null hypothesis and its alternative.
Interpretation of Bayes Factor5:21
Numerical Problems: Obtaining Bayes Factor for two Competing Hypotheses6:49
Practice Exercise0:14
Engage with the attached practice exercise featuring new medical problems, try it out, and consult the provided solutions if you encounter challenges.

Decision Theory in Inference1:44
Basics of Bayesian Decision Theory4:42
Decision Theory Terminology7:36
Minimizing Expected Loss: Cancer Screening7:55
Types of Loss Functions1:22
Loss Functions in Real World0:54
Decision Making with Frequentist vs Bayesian approach13:21
Bayesian Expected Loss, Bayes Estimate & Frequentist Risk6:17
Admissibility of Decision Rules3:43
Understanding Bayes Risk2:12
Define the Bayes risk as the expected loss under the prior and data, and show that the Bayes rule minimizes base risk by choosing the action with minimal posterior loss.
Numericals: Using Normal Form of Analysis to find Bayes Estimate & Bayes Risk9:00
Numericals: Using Extensive Form of Analysis to find Bayes Estimate & Bayes Risk16:27
Practice Exercise0:14
Practice applying Bayesian methods with new medical problems using the attached exercise, tackle challenges, and compare your results with the provided solutions.

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

A Comprehensive Guide to Bayesian Statistics

What you'll learn

Explore related topics

Course content

Introduction1 lecture • 4min

Fundamentals of Bayesian Statistics11 lectures • 39min

Prior & Posterior Distribution with Numerical Problems6 lectures • 24min

Interval Estimation in Bayesian Statistics7 lectures • 29min

Bayesian Hypothesis Testing: Bayes Factor4 lectures • 16min

Bayesian Decision Theory13 lectures • 1hr 15min

Conclusion8 lectures • 6min

Requirements

Description

Who this course is for: