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Bayesian Statistics: From Concept to Data Analysis

Approx. 12 hours to complete

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Course Summary

This course covers the fundamentals of Bayesian statistics and their application to data analysis. Students will learn how to use Bayesian methods to solve problems in various fields such as finance, healthcare, and engineering.

Key Learning Points

Understand the principles of Bayesian statistics
Learn how to apply Bayesian methods to solve real-world problems
Gain practical skills in data analysis and decision-making

Job Positions & Salaries of people who have taken this course might have

Data Analyst
- USA: $65,000 - $120,000
- India: ₹6,00,000 - ₹16,00,000
- Spain: €30,000 - €50,000
Quantitative Analyst
- USA: $70,000 - $150,000
- India: ₹8,00,000 - ₹22,00,000
- Spain: €35,000 - €60,000
Risk Manager
- USA: $90,000 - $180,000
- India: ₹12,00,000 - ₹30,00,000
- Spain: €40,000 - €70,000

Learning Outcomes

Develop proficiency in using Bayesian methods to solve real-world problems
Understand the principles of Bayesian statistics and probability theory
Gain practical skills in data analysis and decision-making

Prerequisites or good to have knowledge before taking this course

Basic knowledge of probability theory and statistics
Familiarity with programming languages such as Python or R

Course Difficulty Level

Intermediate

Course Format

Self-paced
Video lectures
Assignments
Quizzes

Similar Courses

Applied Bayesian Statistics
Bayesian Statistics: Techniques and Models

Related Education Paths

Notable People in This Field

Andrew Gelman
David Spiegelhalter

Related Books

Description

This course introduces the Bayesian approach to statistics, starting with the concept of probability and moving to the analysis of data. We will learn about the philosophy of the Bayesian approach as well as how to implement it for common types of data. We will compare the Bayesian approach to the more commonly-taught Frequentist approach, and see some of the benefits of the Bayesian approach. In particular, the Bayesian approach allows for better accounting of uncertainty, results that have more intuitive and interpretable meaning, and more explicit statements of assumptions. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. For computing, you have the choice of using Microsoft Excel or the open-source, freely available statistical package R, with equivalent content for both options. The lectures provide some of the basic mathematical development as well as explanations of philosophy and interpretation. Completion of this course will give you an understanding of the concepts of the Bayesian approach, understanding the key differences between Bayesian and Frequentist approaches, and the ability to do basic data analyses.

Outline

Probability and Bayes' Theorem
Course introduction
Lesson 1.1 Classical and frequentist probability
Lesson 1.2 Bayesian probability and coherence
Lesson 2.1 Conditional probability
Lesson 2.2 Bayes' theorem
Lesson 3.1 Bernoulli and binomial distributions
Lesson 3.2 Uniform distribution
Lesson 3.3 Exponential and normal distributions
Module 1 objectives, assignments, and supplementary materials
Background for Lesson 1
Supplementary material for Lesson 2
Supplementary material for Lesson 3
Lesson 1
Lesson 2
Lesson 3.1
Lesson 3.2-3.3
Module 1 Honors

Statistical Inference
Lesson 4.1 Confidence intervals
Lesson 4.2 Likelihood function and maximum likelihood
Lesson 4.3 Computing the MLE
Lesson 4.4 Computing the MLE: examples
Introduction to R
Plotting the likelihood in R
Plotting the likelihood in Excel
Lesson 5.1 Inference example: frequentist
Lesson 5.2 Inference example: Bayesian
Lesson 5.3 Continuous version of Bayes' theorem
Lesson 5.4 Posterior intervals
Module 2 objectives, assignments, and supplementary materials
Background for Lesson 4
Supplementary material for Lesson 4
Background for Lesson 5
Supplementary material for Lesson 5
Lesson 4
Lesson 5.1-5.2
Lesson 5.3-5.4
Module 2 Honors

Priors and Models for Discrete Data
Lesson 6.1 Priors and prior predictive distributions
Lesson 6.2 Prior predictive: binomial example
Lesson 6.3 Posterior predictive distribution
Lesson 7.1 Bernoulli/binomial likelihood with uniform prior
Lesson 7.2 Conjugate priors
Lesson 7.3 Posterior mean and effective sample size
Data analysis example in R
Data analysis example in Excel
Lesson 8.1 Poisson data
Module 3 objectives, assignments, and supplementary materials
R and Excel code from example analysis
Lesson 6
Lesson 7
Lesson 8
Module 3 Honors

Models for Continuous Data
Lesson 9.1 Exponential data
Lesson 10.1 Normal likelihood with variance known
Lesson 10.2 Normal likelihood with variance unknown
Lesson 11.1 Non-informative priors
Lesson 11.2 Jeffreys prior
Linear regression in R
Linear regression in Excel (Analysis ToolPak)
Linear regression in Excel (StatPlus by AnalystSoft)
Conclusion
Module 4 objectives, assignments, and supplementary materials
Supplementary material for Lesson 10
Supplementary material for Lesson 11
Background for Lesson 12
R and Excel code for regression
Lesson 9
Lesson 10
Lesson 11
Regression
Module 4 Honors

Summary of User Reviews

Learn Bayesian Statistics on Coursera and gain a solid understanding of this powerful statistical approach. Students rave about the engaging instructors and easy-to-follow explanations in this course.

Key Aspect Users Liked About This Course

Many users appreciate the clear explanations and examples given by the instructors.

Pros from User Reviews

Engaging instructors
Easy-to-follow explanations
Interesting and relevant assignments
Good pacing of the course
Great introduction to Bayesian statistics

Cons from User Reviews

Some users found the course material to be too basic
A few users had technical issues with the platform
A few users found the assignments to be too challenging
Some users wished for more hands-on exercises
A few users felt that the course did not cover enough material

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