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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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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.
Read more
Statistical Inference
This module introduces concepts of statistical inference from both frequentist and Bayesian perspectives. Lesson 4 takes the frequentist view, demonstrating maximum likelihood estimation and confidence intervals for binomial data. Lesson 5 introduces the fundamentals of Bayesian inference. Beginning with a binomial likelihood and prior probabilities for simple hypotheses, you will learn how to use Bayes’ theorem to update the prior with data to obtain posterior probabilities. This framework is extended with the continuous version of Bayes theorem to estimate continuous model parameters, and calculate posterior probabilities and credible intervals.
Priors and Models for Discrete Data
In this module, you will learn methods for selecting prior distributions and building models for discrete data. Lesson 6 introduces prior selection and predictive distributions as a means of evaluating priors. Lesson 7 demonstrates Bayesian analysis of Bernoulli data and introduces the computationally convenient concept of conjugate priors. Lesson 8 builds a conjugate model for Poisson data and discusses strategies for selection of prior hyperparameters.
Models for Continuous Data
This module covers conjugate and objective Bayesian analysis for continuous data. Lesson 9 presents the conjugate model for exponentially distributed data. Lesson 10 discusses models for normally distributed data, which play a central role in statistics. In Lesson 11, we return to prior selection and discuss ‘objective’ or ‘non-informative’ priors. Lesson 12 presents Bayesian linear regression with non-informative priors, which yield results comparable to those of classical regression.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
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 statistical modeling
Learners say this course provides a largely positive introduction to Bayesian statistics, especially for those with at least a basic background in probability and statistics. Concepts are broken down into engaging assignments, readings, and quizzes covering a wide range of topics from basic introductions and binomial examples to challenging exams and real world examples of Bayesian applications. While some reviewers noted the course materials are well received and modules are well organized, others commented that they expected a course with more difficult exams and deeper explanations of the subject. The instructors have excellent communication and response times in the discussion forums. This course is recommended for students with a background in statistics or those who are eager to learn more about Bayesian statistics.
The instructors are knowledgeable and passionate about Bayesian statistics.
"excellent instructor, very lucid explanations of important concepts. "
"I had good background in probability and found this course enjoyable. "
"Herbert is clear, gives great examples, and is easy to follow."
The course includes a variety of assignments that help students apply their knowledge of Bayesian statistics.
"Useful guided quizzes with feedback: learning by doing principle."
"The quizzes-as-homework idea is great. Really liked the homework."
The lectures and assignments are all clear and understandable, even for beginners.
"This course provides a great introduction to Bayesian statistics."
"Excellent course.. short videos with lots of practice problems.. "
"Excellent videos and step-by-step instructions clearly explained."
The course could go into more depth on some of the topics covered.
"Not well organized.No sufficient materials, references, etc.Very short."
The course could benefit from more real-world examples of Bayesian statistics in practice.
"The course was good, but the math got me struggling"
"Good introduction, but there is no variety in the test questions"
"es una buena heramienta de aprendisaje pero tiene algunos errores"
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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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: From Concept to Data Analysis (viewing)
- Bayesian Statistics: Capstone Project
Good to know
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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