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Herbert Lee
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.
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What's inside
Syllabus
Probability and Bayes' Theorem
In this module, we review the basics of probability and Bayes’ theorem. In Lesson 1, we introduce the different paradigms or definitions of probability and discuss why probability provides a coherent framework for dealing with uncertainty. In Lesson 2, we review the rules of conditional probability and introduce Bayes’ theorem. Lesson 3 reviews common probability distributions for discrete and continuous random variables.
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Syllabus
Probability and Bayes' Theorem
In this module, we review the basics of probability and Bayes’ theorem. In Lesson 1, we introduce the different paradigms or definitions of probability and discuss why probability provides a coherent framework for dealing with uncertainty. In Lesson 2, we review the rules of conditional probability and introduce Bayes’ theorem. Lesson 3 reviews common probability distributions for discrete and continuous random variables.
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Covers the core principles and concepts underlying Bayesian methods of statistical inference
Instructed by Herbert Lee, a respected expert and author in the domain of Bayesian statistics
Students have the option of using the popular Excel software or open-source statistical software R for computational exercises
Emphasizes the philosophical foundations, along with the practical implementation of Bayesian techniques
Teaches data analysis skills from a Bayesian perspective, highlighting the benefits of uncertainty quantification, interpretability, and explicit assumption specification
Prior knowledge in probability theory and frequentist statistics may enhance understanding of Bayesian concepts
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Reviews summary
Bayesian statistics concepts and analysis
According to learners, this course offers a strong conceptual introduction to Bayesian statistics, effectively explaining the philosophy and contrasting it with the Frequentist approach. Many students found the lectures clear and helpful for grasping foundational ideas. While the inclusion of both R and Excel options for data analysis is a notable feature, some reviewers felt the practical coding examples, particularly in R, lacked sufficient depth for real-world application. A significant point raised is that the course requires a solid background in mathematics and statistics, making it challenging for absolute beginners without prior quantitative knowledge. Despite the difficulty, those with the necessary prerequisites or willingness to put in extra effort often found the course rewarding and insightful.
Highlights differences with Frequentist stats.
"The comparison between Bayesian and Frequentist statistics throughout the course was incredibly insightful."
"I really liked how the course constantly contrasted Bayesian methods with the Frequentist ones I learned before."
"Understanding the key differences between the two statistical paradigms was a major takeaway for me."
Explains Bayesian concepts clearly.
"The course gave me a really solid conceptual grounding in Bayesian thinking and how it differs from Frequentist methods."
"I found the lectures excellent at explaining the core ideas behind Bayesian statistics. It clarified many points for me."
"This course provided a fantastic theoretical foundation for understanding Bayesian statistics. The concepts were well-explained."
Exercises can be difficult or unclear.
"Some of the homework assignments felt much harder than the lecture material and required outside research."
"I found the quizzes and exercises sometimes inconsistent or confusingly worded, making them a source of frustration."
"The assignments definitely test your understanding, but sometimes the leap from lecture to problem was quite large."
Coding examples could be improved.
"The R examples felt very basic and didn't prepare me well for applying Bayesian methods to complex datasets."
"I appreciated the R/Excel choice, but I wish there were more detailed, hands-on coding labs beyond the simple examples."
"While the theory is good, the practical application felt a bit weak. The R scripts were sometimes hard to follow or inconsistent with the lectures."
Requires strong math/stats prerequisites.
"Be warned: this course is much harder than it looks. You really need a strong math background to keep up."
"I struggled because I didn't have a solid statistics foundation. The course assumes you know quite a bit already."
"While the concepts are explained, the underlying math and statistical theory felt quite challenging without prior study."
Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Bayesian Statistics: From Concept to Data Analysis with these
activities:
Recall Basic Programming Concepts
Show steps
As some of the assignments involve programming, it would be beneficial to refresh your basic programming concepts to ensure a smooth learning experience.
Browse courses on
Programming
Show steps
-
Review your notes or textbooks from previous programming courses.
-
Work through online tutorials or coding challenges.
-
Practice writing simple programs to reinforce your understanding.
Review Probability and Statistics Concepts
Show steps
Refresh your memory on the fundamental concepts of probability and statistics, which are essential for understanding Bayesian statistics.
Browse courses on
Probability
Show steps
-
Review your notes or textbooks from previous probability and statistics courses.
-
Go through online tutorials or videos to reinforce your understanding.
-
Solve practice problems to test your proficiency.
Read 'Bayesian Data Analysis' by Andrew Gelman et al.
Show steps
Expand your knowledge of Bayesian statistics by reading a经典textbook that provides a comprehensive overview of the subject.
View
Bayesian Data Analysis (Chapman & Hall/CRC...
on Amazon
Show steps
-
Read the book thoroughly.
-
Take notes and highlight key concepts.
-
Attempt the exercises and problems to test your understanding.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Implement Bayes' Theorem for Discrete Data
Show steps
Reinforce your understanding of Bayes' theorem by practicing its application in various discrete probability scenarios.
Browse courses on
Bayes' Theorem
Show steps
-
Review the fundamentals of Bayes' theorem.
-
Work through examples of applying Bayes' theorem to calculate posterior probabilities for discrete events.
-
Solve practice problems involving the use of Bayes' theorem in real-world situations.
Develop a Tutorial on Bayesian Hypothesis Testing
Show steps
Solidify your comprehension of Bayesian hypothesis testing by creating a tutorial that explains the concepts and demonstrates its application.
Show steps
-
Research and gather information on Bayesian hypothesis testing.
-
Organize your material into a logical flow.
-
Write clear and concise explanations, providing examples to illustrate the concepts.
-
Include interactive elements to enhance engagement and understanding.
Estimate Parameters of Continuous Distributions Using Bayesian Inference
Show steps
Develop proficiency in estimating parameters of continuous distributions using Bayesian inference techniques.
Browse courses on
Bayesian Inference
Show steps
-
Familiarize yourself with the principles of Bayesian inference for continuous distributions.
-
Practice applying Bayesian inference methods to estimate parameters of normal and exponential distributions.
-
Work through examples involving the use of conjugate priors for parameter estimation.
Build a Bayesian Model for a Real-World Problem
Show steps
Apply your knowledge of Bayesian modeling to solve a real-world problem, showcasing your ability to use the technique effectively.
Browse courses on
Bayesian Modeling
Show steps
-
Identify a suitable real-world problem that can be addressed using Bayesian modeling.
-
Gather and preprocess the necessary data.
-
Develop a Bayesian model for the problem.
-
Implement the model and analyze the results.
-
Write a report summarizing your findings and insights.
Perform Bayesian Analysis with Regression Models
Show steps
Gain hands-on experience in performing Bayesian analysis with regression models, enhancing your understanding of regression techniques.
Browse courses on
Bayesian Regression
Show steps
-
Review the basics of Bayesian linear regression.
-
Apply Bayesian linear regression to real-world datasets.
-
Compare the results of Bayesian regression with those of frequentist regression methods.
Recall Basic Programming Concepts
Show steps
As some of the assignments involve programming, it would be beneficial to refresh your basic programming concepts to ensure a smooth learning experience.
Browse courses on
Programming
Show steps
Show steps
Show steps
- Review your notes or textbooks from previous programming courses.
- Work through online tutorials or coding challenges.
- Practice writing simple programs to reinforce your understanding.
Review Probability and Statistics Concepts
Show steps
Refresh your memory on the fundamental concepts of probability and statistics, which are essential for understanding Bayesian statistics.
Browse courses on
Probability
Show steps
Show steps
Show steps
- Review your notes or textbooks from previous probability and statistics courses.
- Go through online tutorials or videos to reinforce your understanding.
- Solve practice problems to test your proficiency.
Read 'Bayesian Data Analysis' by Andrew Gelman et al.
Show steps
Expand your knowledge of Bayesian statistics by reading a经典textbook that provides a comprehensive overview of the subject.
View
Bayesian Data Analysis (Chapman & Hall/CRC...
on Amazon
Show steps
Show steps
Show steps
- Read the book thoroughly.
- Take notes and highlight key concepts.
- Attempt the exercises and problems to test your understanding.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Implement Bayes' Theorem for Discrete Data
Show steps
Reinforce your understanding of Bayes' theorem by practicing its application in various discrete probability scenarios.
Browse courses on
Bayes' Theorem
Show steps
Show steps
Show steps
- Review the fundamentals of Bayes' theorem.
- Work through examples of applying Bayes' theorem to calculate posterior probabilities for discrete events.
- Solve practice problems involving the use of Bayes' theorem in real-world situations.
Develop a Tutorial on Bayesian Hypothesis Testing
Show steps
Solidify your comprehension of Bayesian hypothesis testing by creating a tutorial that explains the concepts and demonstrates its application.
Show steps
Show steps
Show steps
- Research and gather information on Bayesian hypothesis testing.
- Organize your material into a logical flow.
- Write clear and concise explanations, providing examples to illustrate the concepts.
- Include interactive elements to enhance engagement and understanding.
Estimate Parameters of Continuous Distributions Using Bayesian Inference
Show steps
Develop proficiency in estimating parameters of continuous distributions using Bayesian inference techniques.
Browse courses on
Bayesian Inference
Show steps
Show steps
Show steps
- Familiarize yourself with the principles of Bayesian inference for continuous distributions.
- Practice applying Bayesian inference methods to estimate parameters of normal and exponential distributions.
- Work through examples involving the use of conjugate priors for parameter estimation.
Build a Bayesian Model for a Real-World Problem
Show steps
Apply your knowledge of Bayesian modeling to solve a real-world problem, showcasing your ability to use the technique effectively.
Browse courses on
Bayesian Modeling
Show steps
Show steps
Show steps
- Identify a suitable real-world problem that can be addressed using Bayesian modeling.
- Gather and preprocess the necessary data.
- Develop a Bayesian model for the problem.
- Implement the model and analyze the results.
- Write a report summarizing your findings and insights.
Perform Bayesian Analysis with Regression Models
Show steps
Gain hands-on experience in performing Bayesian analysis with regression models, enhancing your understanding of regression techniques.
Browse courses on
Bayesian Regression
Show steps
Show steps
Show steps
- Review the basics of Bayesian linear regression.
- Apply Bayesian linear regression to real-world datasets.
- Compare the results of Bayesian regression with those of frequentist regression methods.
Career center
Learners who complete Bayesian Statistics: From Concept to Data Analysis will develop knowledge and skills
that may be useful to these careers:
Data Scientist
Data Scientist
Data Scientists use their knowledge of statistics, mathematics, and computer science to extract insights from data. The course, Bayesian Statistics: From Concept to Data Analysis, can help you develop the skills you need to be a successful Data Scientist. This course will give you the theoretical foundation and practical experience you need to excel in this field.
Statistician
Statistician
A Statistician uses their understanding of statistics and probability to collect, analyze, interpret, and present data. The course, Bayesian Statistics: From Concept to Data Analysis, will help you develop the skills you need to be successful in this field. This course will provide you with a solid foundation in the Bayesian approach to statistics, which is becoming increasingly popular in many areas of research and data analysis. Additionally, you will learn the key differences between the Bayesian approach and other methods of statistical inference.
Machine Learning Engineer
Machine Learning Engineer
The Bayesian approach is becoming increasingly popular in machine learning, as it can help to improve the accuracy and reliability of models. By taking the course, Bayesian Statistics: From Concept to Data Analysis, you will gain a strong foundation in Bayesian statistics, which will make you a more competitive candidate for Machine Learning Engineer roles.
Actuary
Actuary
Actuaries use their knowledge of probability and statistics to assess risk and uncertainty. The Bayesian approach is becoming increasingly popular in actuarial science, as it can help to improve the accuracy of risk assessments. By taking the course, Bayesian Statistics: From Concept to Data Analysis, you will gain a strong foundation in Bayesian statistics, which will make you a more competitive candidate for Actuary roles.
Risk Analyst
Risk Analyst
Risk Analysts use their understanding of probability and statistics to assess and manage risk. The Bayesian approach is becoming increasingly popular in risk management, as it can help to improve the accuracy of risk assessments. By taking the course, Bayesian Statistics: From Concept to Data Analysis, you will gain a strong foundation in Bayesian statistics, which will make you a more competitive candidate for Risk Analyst roles.
Financial Analyst
Financial Analyst
Financial Analysts use their understanding of statistics and economics to analyze financial data and make investment recommendations. The Bayesian approach is becoming increasingly popular in financial analysis, as it can help to improve the accuracy of investment decisions. By taking the course, Bayesian Statistics: From Concept to Data Analysis, you will gain a strong foundation in Bayesian statistics, which will make you a more competitive candidate for Financial Analyst roles.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use their understanding of probability and statistics to solve complex problems in business and industry. The Bayesian approach is becoming increasingly popular in operations research, as it can help to improve the accuracy of decision-making. By taking the course, Bayesian Statistics: From Concept to Data Analysis, you will gain a strong foundation in Bayesian statistics, which will make you a more competitive candidate for Operations Research Analyst roles.
Market Researcher
Market Researcher
Market Researchers use their understanding of probability and statistics to collect and analyze data about consumer behavior. The Bayesian approach is becoming increasingly popular in market research, as it can help to improve the accuracy of market forecasts. By taking the course, Bayesian Statistics: From Concept to Data Analysis, you will gain a strong foundation in Bayesian statistics, which will make you a more competitive candidate for Market Researcher roles.
Biostatistician
Biostatistician
Biostatisticians use their understanding of probability and statistics to analyze biological and medical data. The Bayesian approach is becoming increasingly popular in biostatistics, as it can help to improve the accuracy of medical diagnoses and treatments. By taking the course, Bayesian Statistics: From Concept to Data Analysis, you will gain a strong foundation in Bayesian statistics, which will make you a more competitive candidate for Biostatistician roles.
Epidemiologist
Epidemiologist
Epidemiologists use their understanding of probability and statistics to study the distribution and causes of disease. The Bayesian approach is becoming increasingly popular in epidemiology, as it can help to improve the accuracy of disease modeling. By taking the course, Bayesian Statistics: From Concept to Data Analysis, you will gain a strong foundation in Bayesian statistics, which will make you a more competitive candidate for Epidemiologist roles.
Policy Analyst
Policy Analyst
Policy Analysts use their understanding of probability and statistics to analyze public policy issues. The Bayesian approach is becoming increasingly popular in policy analysis, as it can help to improve the accuracy of policy decisions. By taking the course, Bayesian Statistics: From Concept to Data Analysis, you will gain a strong foundation in Bayesian statistics, which will make you a more competitive candidate for Policy Analyst roles.
Quantitative Analyst
Quantitative Analyst
In this role, you will leverage your knowledge of mathematics, statistics, and probability to make financial decisions and manage risk. The course, Bayesian Statistics: From Concept to Data Analysis, can help you understand the fundamentals of Bayesian statistics, which is a valuable technique in this field. This course will help you make more informed decisions and manage risk more effectively.
Consultant
Consultant
Consultants provide advice and expertise to businesses and organizations. The Bayesian approach is becoming increasingly popular in consulting, as it can help to improve the accuracy of decision-making. By taking the course, Bayesian Statistics: From Concept to Data Analysis, you will gain a strong foundation in Bayesian statistics, which will make you a more competitive candidate for Consultant roles.
Data Analyst
Data Analyst
A Data Analyst uses their understanding of probability and statistics to transform raw data into insights that can inform business decisions. Taking the course, Bayesian Statistics: From Concept to Data Analysis, will help you understand probability and Bayes' Theorem, statistical inference, priors and models for discrete data, and models for continuous data. This knowledge will give you the foundation you need to succeed in the role.
Professor
Professor
A Professor teaches and conducts research in their field of expertise. If you are interested in a career in academia, taking the course, Bayesian Statistics: From Concept to Data Analysis, will give you a strong foundation in Bayesian statistics, which will help you to be more successful in your research and teaching.
For more career information including salaries, visit:
OpenCourser.com/course/wyyoxe/bayesian
Reading list
We've selected 17 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Bayesian Statistics: From Concept to Data Analysis.
Provides a more in-depth look at Bayesian statistics, complementing the course's introduction to the subject. It offers an accessible and practical guide to Bayesian modeling using R and Stan.
This practical guide provides a step-by-step approach to Bayesian data analysis using R, JAGS, and Stan. It valuable resource for students and practitioners who want to learn how to apply Bayesian methods to their own research.
Introduces graphical models for representing and analyzing complex probabilistic relationships, providing a theoretical foundation for advanced Bayesian methods.
Save
Presents Bayesian statistical inference in French, providing a valuable resource for students and researchers in various scientific disciplines.
This classic textbook comprehensive resource on Bayesian data analysis. It covers a wide range of topics, from basic concepts to advanced modeling techniques. While it valuable reference tool, it may be too advanced for beginners.
This classic textbook provides a comprehensive introduction to Bayesian statistics from a foundational perspective. It valuable resource for students and practitioners who want to deeply understand the theoretical foundations of Bayesian statistics.
This introductory text provides a comprehensive overview of Bayesian statistics. It covers a wide range of topics, including probability, inference, and modeling. It useful resource for students who are new to the subject.
Provides a practical introduction to Bayesian analysis using Python. It valuable resource for students and practitioners who want to learn how to use Python to perform Bayesian data analysis.
Provides a humorous and engaging introduction to Bayesian statistics. It valuable resource for students and practitioners who want to learn the basics of Bayesian statistics in a fun and accessible way.
Provides a comprehensive overview of Bayesian reasoning for machine learning. It covers both theoretical and practical aspects of Bayesian modeling, with a focus on applications in machine learning.
Provides a comprehensive introduction to Bayesian statistics and Markov chain Monte Carlo. It valuable resource for students and practitioners who want to learn the theoretical foundations of Bayesian statistics and how to apply these foundations to perform Bayesian data analysis.
Provides a comprehensive introduction to Bayesian nonparametrics. It valuable resource for students and practitioners who want to learn the theoretical foundations of Bayesian statistics and how to apply these foundations to perform Bayesian data analysis on nonparametric models.
Provides a comprehensive introduction to Bayesian statistical methods. It valuable resource for students and practitioners who want to learn the theoretical foundations of Bayesian statistics and how to apply these foundations to perform Bayesian data analysis.
Provides a comprehensive overview of biostatistical analysis. It useful resource for learners who are interested in applying statistical methods to biological problems, including Bayesian methods.
Provides a comprehensive overview of mathematical statistics. It useful resource for learners who are interested in understanding the mathematical foundations of statistics and Bayesian statistics.
Provides a comprehensive overview of mathematical statistics. It useful resource for learners who are interested in understanding the mathematical foundations of statistics and Bayesian statistics.
Save
Provides a concise overview of statistical inference. It useful resource for learners who are interested in understanding the fundamental concepts of statistical inference, including Bayesian inference.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/wyyoxe/bayesian
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Effort
Four weeks of study, two-five hours/week depending on your familiarity with mathematical statistics.
Level
Intermediate
Via
Coursera
Institution
University of California, Santa Cruz
Instructor
Herbert Lee
Language
English
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This course belongs to a
collection
called
Bayesian Statistics. It's comprised of five courses:
- Bayesian Statistics: Mixture Models
- Bayesian Statistics: Time Series Analysis
- Bayesian Statistics: Techniques and Models
- Bayesian Statistics: Capstone Project
- Bayesian Statistics: From Concept to Data Analysis (viewing)
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