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# Bayesian Statistics

### Overview

##### Class Central Tips
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."

### 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!
• The Basics of Bayesian Statistics
• 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.

• Bayesian Inference
• In this week, we will discuss the continuous version of Bayes' rule and show you how to use it in a conjugate family, and discuss credible intervals. By the end of this week, you will be able to understand and define the concepts of prior, likelihood, and posterior probability and identify how they relate to one another.
• Decision Making
• In this module, we will discuss Bayesian decision making, hypothesis testing, and Bayesian testing. By the end of this week, you will be able to make optimal decisions based on Bayesian statistics and compare multiple hypotheses using Bayes Factors.
• Bayesian Regression
• This week, we will look at Bayesian linear regressions and model averaging, which allows you to make inferences and predictions using several models. By the end of this week, you will be able to implement Bayesian model averaging, interpret Bayesian multiple linear regression and understand its relationship to the frequentist linear regression approach.
• Perspectives on Bayesian Applications
• This week consists of interviews with statisticians on how they use Bayesian statistics in their work, as well as the final project in the course.
• Data Analysis Project
• In this module you will use the data set provided to complete and report on a data analysis question. Please read the background information, review the report template (downloaded from the link in Lesson Project Information), and then complete the peer review assignment.

### Taught by

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

## Reviews

2.7 rating, based on 12 Class Central reviews

3.8 rating at Coursera based on 778 ratings

Start your review of Bayesian Statistics

• Farsan Rashid is taking this course right now.

This is the last course of specialization "Statistics with R". The first three courses were excellent but surprisingly this last course is a complete disappointment. I dropped the course after failing the first quiz multiple times even i carefully followed the lecture videos. Quiz questions were too complex (at least for me) based on the lecture videos. Previous three course contained a reading section that was very helpful but this course does not have that reading section part. Course instructor mine cetinkaya rundel was good at delivering lectures as always but as i could not relate quiz questions with video lectures.
• Michael Hint is taking this course right now.

This is definitely a challenging course. However, I took in that spirit and am really enjoying it so far. As well as Bayesian statistics, you can learn R/markdown through the very well constructed labs and the advanced, but really helpful extra pdfs put...
• Anonymous

Anonymous is taking this course right now.

This looks like a half-cooked course. It has everything to be an excellent course, like the quality of the other courses from the same group, but fails to deliver a correct learning experience. As of November of 2016, it still needs some polishing.
• Glen Alexander Macdonald

Glen Alexander Macdonald is taking this course right now and found the course difficulty to be hard.

I'm currently taking the Specialization "Introduction to Statistics in R". I have completed and reasonably understood the first three courses which were very interesting, well presented with basic concepts and implications continuously re-enforced....
• Anonymous

Anonymous is taking this course right now.

Concepts are abruptly introduced with no apparent thread. The instructors present these as if they are obvious.

This leaves the student scratching their heads.

Steve Wainstead is taking this course right now, spending 7 hours a week on it and found the course difficulty to be hard.

This course is part of a five course specialty. The first three courses were very good; you had the benefit of the free textbook that comes with them. I got a lot out of them and the textbook.

I'll echo another reviewer here: this course falls way short. I too watched the videos multiple times and could not get past the first quiz. The material for this course is not in the textbook.

Where the whole series in general, and this course in particular, would benefit is by giving the students lots and lots of story problems to solve. Why? Because this is the format of the quizzes. It's unfair that little of the homework material is in the format that the quizzes are in: story problems.
• José Luis Estévez Navarro completed this course, spending 10 hours a week on it and found the course difficulty to be hard.

This course is a real challenge for those with no backgrounds in Statistics. The course is the fourth in the framework of a five-course specialisation (Statistics with R) and, the general impression, is that this course is not balanced with the remainder of the specialisation. The three first courses are easy to follow, and there is book in addition to further understanding. This fourth course, on the contrary, lacks the appropiate materials and the video lectures are noticeably harder. I would only encourage you to enroll it if you feel confident with Statistics, probability, set theory,...
• T Williams

T Williams completed this course, spending 4 hours a week on it and found the course difficulty to be medium.

I have a background in applied statistics and I thought this course was pretty challenging. I'm not sure how this course was deemed to be appropriate for a beginner because I think I would have been frustrated and confused if I did not have prior familiarity with the topic.
I thought the discussions comparing the frequentist approach and outcomes to Bayesian techniques was most useful. Using R to do Bayesian modeling was something I wanted to learn how to do but the modeling techniques, diagnostics, and plots are easily transferable to SAS programming.
• Luv Suneja

Luv Suneja completed this course.

This is a challenging course, not the same as previous ones. I think Bayesian Statistics itself is a very challenging topic. I've finished all weeks except the final project. I highly recommend people to read the accompanying book on Github as compulsory reading. Without reading that, it can be difficult to follow the material.
• Anonymous

Anonymous completed this course.

Well, I find the lectures to be good, but the quizes are at times confusing and especially the last course. Sometimes using confusion to filter our learners to classify them according to bell curve can be drastic if too much confusion existed.
• Stephane Mysona completed this course.

• Alex Ivanov

Alex Ivanov completed this course.

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