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Bayesian Statistics

Mine Çetinkaya-Rundel, David Banks, Merlise A Clyde, and Colin Rundel

This course describes Bayesian statistics, in which one's inferences about parameters or hypotheses are updated as evidence accumulates. You will learn to use Bayes’ rule to transform prior probabilities into posterior probabilities, and be introduced to the underlying theory and perspective of the Bayesian paradigm. The course will apply Bayesian methods to several practical problems, to show end-to-end Bayesian analyses that move from framing the question to building models to eliciting prior probabilities to implementing in R (free statistical software) the final posterior distribution. Additionally, the course will introduce credible regions, Bayesian comparisons of means and proportions, Bayesian regression and inference using multiple models, and discussion of Bayesian prediction.

We assume learners in this course have background knowledge equivalent to what is covered in the earlier three courses in this specialization: "Introduction to Probability and Data," "Inferential Statistics," and "Linear Regression and Modeling."

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Syllabus

About the Specialization and the Course

This short module introduces basics about Coursera specializations and courses in general, this specialization: Statistics with R, and this course: Bayesian Statistics. Please take several minutes read this information. Thanks for joining us in this course!

Welcome! Over the next several weeks, we will together explore Bayesian statistics.

In this module, we will work with conditional probabilities, which is the probability of event B given event A. Conditional probabilities are very important in medical decisions. By the end of the week, you will be able to solve problems using Bayes' rule, and update prior probabilities.

Please use the learning objectives and practice quiz to help you learn about Bayes' Rule, and apply what you have learned in the lab and on the quiz.

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Taught by Mine Çetinkaya-Rundel, David Banks, Merlise A Clyde, Colin Rundel, who are recognized for their work in statistics and probability

Examines Bayesian statistics, which is highly relevant to data science, machine learning, and other fields

Provides end-to-end Bayesian analyses, moving from framing the question to building models to eliciting prior probabilities to implementing in R

Develops skills in credible regions, Bayesian comparisons of means and proportions, Bayesian regression, and inference using multiple models

Requires background knowledge equivalent to what is covered in earlier courses in this specialization: "Introduction to Probability and Data," "Inferential Statistics," and "Linear Regression and Modeling."

Assumes learners have a strong foundation in probability and statistics

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Reviews summary

Challenging introduction to bayesian statistics

According to students, this course offers a solid introduction to the Bayesian paradigm, particularly appreciated by those looking to build upon prior statistical knowledge from the specialization. Many learners found the exploration of Bayes' rule and updating beliefs valuable. While the course is generally well-regarded for its theoretical depth, some students highlight it as challenging and stress that having strong prerequisites is crucial for success. Feedback is mixed regarding the clarity of lectures and the practical aspects of R implementation, with some wishing for more hands-on application. The final data analysis project is frequently mentioned as a worthwhile component that reinforces learning.

Final project is challenging and helps apply concepts.

"The project was challenging but very useful."

"The final project was a good test of understanding."

"Found the data analysis project valuable for applying what I learned."

"The final project consolidates the knowledge gained effectively."

Integrates well with prior courses in the series.

"It builds nicely on the previous courses in the specialization."

"Appreciated how this course followed logically from the others."

"Taking the prerequisite courses was definitely helpful for this one."

"Seamless progression from the earlier statistics courses in the series."

Provides a good foundation in Bayesian statistics.

"Excellent course covering the fundamentals of Bayesian statistics."

"A good introduction to Bayesian methods."

"Really helped solidify my understanding of the Bayesian paradigm basics."

"Provides a strong theoretical foundation for Bayesian statistics."

R examples could be improved for practical application.

"Sometimes the R implementation felt a bit rushed."

"The R code examples were not always well explained."

"Wish there were more hands-on R exercises connecting theory to data."

"More practical coding examples in R would be very beneficial."

Explanations are sometimes unclear for complex topics.

"The lectures could be clearer, especially for the more complex topics like model averaging."

"Sometimes explanations felt a bit dense and required rewatching."

"While basics were clear, advanced ideas were harder to follow in lectures."

"Some topics were not explained well, especially decision making theory."

Course is challenging, requires strong prior knowledge.

"Okay course, but definitely difficult. The prerequisites are essential; if you don't have a solid grasp of linear regression, you'll struggle."

"Requires a strong stats background, as mentioned."

"Found this course very challenging; prior stats knowledge is a must."

"The course was much more challenging than expected, definitely need solid stats background."

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 with these activities:

Solve Bayes' Rule problems on Khan Academy

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Sharpen your problem-solving skills and solidify your understanding of Bayes' Rule.

Browse courses on Bayesian Statistics

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Visit the Khan Academy website and select the 'Bayes' Theorem' topic.
Work through the practice exercises and videos to master the concepts.
Attempt the challenge problems to test your abilities.

Work through Bayesian statistics exercises on DataCamp

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Reinforce your understanding of Bayesian concepts through interactive exercises and simulations.

Browse courses on Bayesian Statistics

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Create an account on DataCamp and select the 'Bayesian Statistics' track.
Complete the exercises and quizzes to learn and practice different Bayesian methods.
Use the interactive simulations to visualize and understand Bayesian concepts.

Read 'Thinking and Deciding' by Jonathan Baron

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Gain a foundational understanding of cognitive biases and heuristics that can impact statistical reasoning and decision-making.

View Thinking and Deciding on Amazon

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Read chapters 1-3 to understand the basics of Bayesian reasoning.
Work through the practice problems at the end of each chapter to reinforce your understanding.
Apply the concepts to real-world examples to enhance your critical thinking skills.

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Complete 'Bayesian Statistics with R' on Coursera

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Enhance your understanding of Bayesian methods and their practical application using R.

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Enroll in the Coursera course and work through the video lectures and interactive exercises.
Complete the practice quizzes to test your comprehension.
Implement the Bayesian methods covered in the course using R code.

Participate in a study group

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Engage with peers, discuss course concepts, and enhance your learning through collaborative problem-solving.

Browse courses on Bayesian Statistics

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Find a study group or form one with classmates.
Meet regularly to review course material, work on assignments together, and clarify doubts.
Take turns presenting concepts and leading discussions.

Attend a workshop on Bayesian methods

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Enhance your skills and gain insights from experts in the field.

Browse courses on Bayesian Statistics

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Identify and register for a suitable workshop on Bayesian methods.
Attend the workshop and actively participate in discussions and hands-on exercises.
Network with other participants and industry professionals.

Write a blog post on 'Bayesian Statistics in Practice'

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Deepen your understanding of Bayesian concepts by explaining them to others.

Browse courses on Bayesian Statistics

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Identify a specific application of Bayesian statistics.
Research and gather relevant information.
Write a clear and engaging blog post that conveys the key concepts and their significance.

Develop a Bayesian model for a real-world problem

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Apply your Bayesian knowledge to solve a practical problem and gain hands-on experience.

Browse courses on Bayesian Statistics

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Identify a suitable problem and collect relevant data.
Choose appropriate Bayesian methods and build the model.
Validate and interpret the model's results.

Career center

Learners who complete Bayesian Statistics will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists analyze data to identify patterns and trends, and use this information to solve business problems as well as to help companies make optimal decisions about everything from product development to marketing campaigns. They build models to predict future outcomes and trends, and often need to communicate their findings to non-technical stakeholders, such as executives and clients. The Bayesian Statistics course can be extremely helpful for Data Scientists since it teaches them how to use Bayes' rule to transform prior probabilities into posterior probabilities. This is a critical skill for Data Scientists, as it allows them to update their beliefs about the world as new evidence becomes available.

See salaries and explore the career path for Data Scientist

Statistician

Statisticians use mathematical and statistical methods to collect, analyze, interpret, and present data. They work in a variety of industries, including healthcare, finance, and government. The Bayesian Statistics course can be extremely helpful for Statisticians, as it teaches them the underlying theory and perspective of the Bayesian paradigm. This is a critical skill for Statisticians, as it allows them to use Bayesian methods to solve a wide range of problems.

See salaries and explore the career path for Statistician

Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data and make investment decisions. They work in a variety of financial institutions, including investment banks, hedge funds, and asset management companies. The Bayesian Statistics course can be extremely helpful for Quantitative Analysts, as it teaches them how to use Bayesian methods to make optimal decisions under uncertainty.

See salaries and explore the career path for Quantitative Analyst

Risk Analyst

Risk Analysts identify, assess, and manage risks for organizations. They work in a variety of industries, including finance, insurance, and healthcare. The Bayesian Statistics course can be extremely helpful for Risk Analysts, as it teaches them how to use Bayesian methods to quantify and manage risk.

See salaries and explore the career path for Risk Analyst

Data Analyst

Data Analysts collect, clean, and analyze data to identify patterns and trends. They work in a variety of industries, including healthcare, finance, and retail. The Bayesian Statistics course can be extremely helpful for Data Analysts, as it teaches them how to use Bayesian methods to draw inferences from data.

See salaries and explore the career path for Data Analyst

Machine Learning Engineer

Machine Learning Engineers design, develop, and deploy machine learning models. They work in a variety of industries, including technology, healthcare, and finance. The Bayesian Statistics course can be extremely helpful for Machine Learning Engineers, as it provides a strong foundation in the theory and practice of Bayesian statistics. This knowledge is essential for developing and deploying machine learning models that are accurate and reliable.

See salaries and explore the career path for Machine Learning Engineer

Actuary

Actuaries use mathematical and statistical methods to assess and manage risk in the insurance industry. They work for insurance companies, pension funds, and other financial institutions. The Bayesian Statistics course can be extremely helpful for Actuaries, as it teaches them how to use Bayesian methods to quantify and manage risk.

See salaries and explore the career path for Actuary

Biostatistician

Biostatisticians use statistical methods to design and analyze studies in the medical field. They work for universities, hospitals, and pharmaceutical companies. The Bayesian Statistics course can be extremely helpful for Biostatisticians, as it teaches them how to use Bayesian methods to design and analyze clinical trials.

See salaries and explore the career path for Biostatistician

Epidemiologist

Epidemiologists investigate the causes and spread of diseases. They work for universities, hospitals, and government agencies. The Bayesian Statistics course can be extremely helpful for Epidemiologists, as it teaches them how to use Bayesian methods to design and analyze epidemiological studies.

See salaries and explore the career path for Epidemiologist

Market Researcher

Market Researchers collect and analyze data to understand consumer behavior. They work for a variety of organizations, including marketing firms, advertising agencies, and product development companies. The Bayesian Statistics course can be extremely helpful for Market Researchers, as it teaches them how to use Bayesian methods to design and analyze market research studies.

See salaries and explore the career path for Market Researcher

Operations Research Analyst

Operations Research Analysts use mathematical and statistical methods to solve problems in a variety of industries, including manufacturing, logistics, and healthcare. The Bayesian Statistics course can be extremely helpful for Operations Research Analysts, as it teaches them how to use Bayesian methods to develop and evaluate solutions to complex problems.

See salaries and explore the career path for Operations Research Analyst

Economist

Economists study the production, distribution, and consumption of goods and services. They work for universities, government agencies, and research institutions. The Bayesian Statistics course may be helpful for Economists, as it teaches them how to use Bayesian methods to analyze economic data.

See salaries and explore the career path for Economist

Financial Analyst

Financial Analysts evaluate the financial performance of companies and make investment recommendations. They work for investment banks, hedge funds, and asset management companies. The Bayesian Statistics course may be helpful for Financial Analysts, as it teaches them how to use Bayesian methods to analyze financial data.

See salaries and explore the career path for Financial Analyst

Computer Scientist

Computer Scientists design, develop, and implement computer software and systems. They work in a variety of industries, including technology, healthcare, and finance. The Bayesian Statistics course may be helpful for Computer Scientists, as it teaches them how to use Bayesian methods to develop and evaluate software systems.

See salaries and explore the career path for Computer Scientist

Software Engineer

Software Engineers design, develop, and maintain software systems. They work in a variety of industries, including technology, healthcare, and finance. The Bayesian Statistics course may be helpful for Software Engineers, as it teaches them how to use Bayesian methods to develop and evaluate software systems.

See salaries and explore the career path for Software Engineer

Reading list

We've selected 31 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.

Bayesian Data Analysis, Third Edition

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This is one of the most widely used textbooks for Bayesian statistics, and very useful reference text. It is used in many university courses.

Bayesian Statistics

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What's inside

Syllabus

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Reviews summary

Challenging introduction to bayesian statistics

Activities

Career center

Reading list

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