Back to Bayesian Statistics: From Concept to Data Analysis

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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....

JH

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Great course. The content moves at a nice pace and the videos are really good to follow. The Quizzes are also set at a good level. You can't pass this course unless you have understood the material.

AH

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Great course in a difficult subject. Well structured. Requires some previous knowledge otherwise difficult to follow. Big thanks to professor Lee for bringing to us this content.

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By Nathaniel S

•Aug 2, 2020

Overall, an informative and useful introduction to Bayesian statistics. I would have preferred if the examples in the lessons in which prior and posterior were introduced went beyond the "coin flipping" binomial examples. I've taken a number of stats classes, and while coin flipping is to stats as "hello world" is to computer programming, I feel that students would grasp the importance of Bayesian inference much better if more realistic examples were used. Related to this, while the theory is important and understanding how to integrate the likelihoods is useful for grasping key concepts, nobody in practice really does this. You're going to use a programming language like R or some kind of stats package. More focus on these would be good.

By Eunylson L

•Dec 8, 2021

It's a great course. I definetely recommend it. It's a great course also for us to understand the mathematics of Bayesian statistics. I would say that this course is more appropriate for those who already have a proper intuition of Bayesian statistics, philosophicaly speaking. Then you should come here to formalize your understanding with math. I give 4 stars just because in some of the classes the teacher skips some important math explanations and foundations (so we can easily get lost). Also, we could have spent more time on the applications of Bayesian statistics.

By עשהאל ב

•Feb 28, 2019

a really good course!

though sometimes the questions in quizes aren't clear enough,or not explaind else where,and sometime you could miss the big picture.

could also be good if you could add some python scripts,and maybe more reading material about the topics.

By Leandro G G

•Oct 22, 2019

This course provides a good overview to Bayesian statistics, but a larger dose of explanations of would be very useful. Mr Lee discusses, in the beginning, the differences between frequentist and bayesian paradigm. I feel that this would be beneficial in the other parts of the course, too. I feel that many of the lectures simply go too fast. After lectures full of Math, it would be useful to present lectures analyzing what had just been taught, in order to better grasp the content. And in general, this happens through the whole course - most lectures are basically math, without much time for grasping the intuition and underlying logic. For example: in the final part, under linear regression, it might be be difficult to grasp what a bayesian predictive interval means. All in all, I recommend this MOOC, but you might find hard to fully grasp it.

By Philip M

•May 29, 2020

Found the pace of the course to be a little uneven - sometimes jumps from basic introductions (good) to somewhat advanced concepts rather quickly. The sound quality was also a bit uneven, but improved with the later videos. Please wear dark clothing so that writing on the see-through board is readable - again, this improved with later videos.

Biggest suggestion for improvement is to provide downloadable lecture notes - having to take notes while the lecture is in process is distracting, and takes us back to the bad old days of "talk and chalk".

All of that said, the class was a very useful introduction, even though the application I have in mind requires discrete Bayes rather than continuous. I will be taking a look at the second course in this series.

By Marshall

•Jun 17, 2021

A pretty standard "college-like" course with many definitions and derivations that do not help with conceptual understanding of the material. There are better tutorial/explanation videos on YouTube.

By Siddhant R

•Jun 20, 2020

The course is more of remembering rather than understanding. Many of the formulas and distributions are used without proper derivations. I was determined to complete the second course of this series, but now I don't think I would.

By Kambiz “ T

•Apr 21, 2023

A monotonous barrage of content from what appear to be lecture notes known only to the instructor or otherwise pulled straight from Wikipedia delivered in a blind leading the blind manner.

By cuguilke

•Oct 30, 2019

I was hoping to get more intuition on bayesian statistics, but I couldn't. Hence, I think I am gonna forget what I have learned in a very very short time.

By Lukman A S

•Jan 4, 2020

The course only gives a lot of equations and formulas without explaining why this process should be done

By Will S

•Sep 14, 2022

Feels just like a college mathematics course with speedy note-taking (with the benefit of being able to pause the video) and assignments that help you understand the material better than the lectures. No time is wasted deriving formulas or proving theorems, making it a great course for anyone interested purely in applications. Toward the end, examples and practice problems tend to focus only on a few distributions (which is probably due to time constraints), but by then, you already have a decent understanding of the types of problems you can solve, so it isn't very hard to Google examples with different starting points. Overall, it's a very manageable course (especially if you take notes), and it does a good job of introducing you to a new branch of statistics even if you aren't fresh out of your last calculus class.

By Alfredo M

•Oct 11, 2022

Every one of us who studies statistics has much to thank Prof. Herbert Lee for the effort in creating this course. He puts so much passion and attention to detail into this course that any student could gradually build up her abilities from a total novice to a genuine member of the Bayesian Society (Given that you attended this course is very probable that you will join ISBA, pun intended, sorry for that), where professor Herbert Lee is very active. The quizzes are strategically crafted to exercise practical tasks, from the algebraic deductions (that can easily scale up in complexity on models) to simulations in R or Excel. I personally suggest to the student to do each one of the quizzes, in R and in Excel, it is an excellent opportunity to learn.

By Benjamin J S

•Apr 27, 2024

Excellent course. Particularly the exercises are extremely useful with actual hints and explanations, rather than just telling one is right or wrong. Assignments vary in difficulty and there is one tough quiz whose answer one can only find in a side-note of the additional material, so that was somewhat frustrating. The Forum, unfortunately, as with most MOOC's is practically useless and its difficult to ask for qualified help, should one be stuck. Also, the lectures on Jeffrey's prior and the Fisher Information should be covered more extensively. The extra-material is very good, though and written in LaTeX. Overall, I enjoyed this course, and would rate it 4.5/5.

By Jay G

•Jan 11, 2018

I had a great experience. It was lot more in-depth than I originally anticipated. In the tech world, Machine Learning is a buzz word and Bayesian based algorithms / models are the key and this introduces one to the fundamentals of Bayesian statistics. I was totally hooked on to this and the quizzes with real world examples really helped understand and apply the concepts. This course definitely requires maths background to be able to complete. Course provides lot of helpful materials and a pace that can be adopted based on your time and ability. Really looking forward for another deep dive in the near future.

By Paolo P

•Feb 4, 2022

The course is well organized and quality. The topics are, for a number of distributions (bernoulli, binomial, normal), how to compute posterior from prior. All lectures are organized similarly to each other: to introduce a measure, the lecturer calculates it assuming starting distributions. Prerequisites are a minimal knowledge of how to calculate derivatives and integrals, so not advanced knowledge. The tests are simple but at the same time useful to consolidate the concepts introduced in the lectures. I recommend this course.

By Gary S

•Dec 19, 2016

Great intro to Bayesian Statistics. The math gets complex but the professor illustrates with examples to help with understanding. The exercises are generally similar to the examples in the lectures and honestly not as hard as they could've been. The course is only 4 weeks and moves pretty fast. Although I scored well, I may take the course again to help make sure all the details and concepts fully sank in.

I'm hungry for a deeper dive into the topic. I hope there is a follow up course in the future.

By Anupam K

•Mar 16, 2018

Extremely useful course. The way concepts are taught is amazing. However, if you are like me, you will have problems following the lectures at the speed at which the professor proceeds. It's a minor 'subjective' issue. The second issue is that sometimes, the equations in the quizzes may appear in the form of "cryptic codes", for the lack of better words, and you'll know it if you face it. A change of browser solves the problem, for me a shift from Chrome to Safari did the trick! Hope this helps.

By k. p b

•Feb 15, 2018

A good introduction to the concepts conveyed by revealing the equations and expressions on a whiteboard. Minimal work with data and programming - much less of this than other Coursera classes on the same topics. Also unlike other Coursera classes on the same topic, the quiz answers/hints are useful and contain the relevant equations or R commands - not merely "correct" or "you should not have chosen this answer." I found this very helpful for self learning and confirming solution approach.

By Francesco B

•Feb 18, 2020

Good introduction to the Bayesian approach to inference.

As an introduction, it doesn't go very deep on some interesting arguments and it leaves out Hierarchical Modeling and estimations through Monte Carlo Markov Chain, but it would have been unfeasible in such a short time.

Finally, I would like to point out that mathematical strictness doesn't mean that the course is too technical: you have just to go through some calculations and review some concepts in order to fully understand them.

By Melvyn B

•Jun 2, 2017

Professor Herbert Lee is world-class. The masterful and thoroughly outstanding presentation, organization and content of this activity are among the best of the best in any subject at any institution, whether on campus or otherwise -- more remarkably so for any senior undergraduate to graduate level mathematics activity, and most especially so in the broad field of Bayesian analysis. In summary: Extremely well-done and hats off to Professor Lee. I am thoroughly impressed.

By Jeff N

•Mar 30, 2017

As a long time frequentist, I occasionally run into problems that are very awkward to fit into the frequentist paradigm. I was aware at a high level that the Bayesian approach could be applied more naturally. Unfortunately, I was unable to "get it" simply be reading a book on the subject. This course made it very approachable. Professor Lee showed us the difficult math (tough integrals) behind it and how we can apply the results of that math in Excel or R

By Rob H

•Apr 17, 2020

Really enjoyed the course. Coming from an engineering background but little statistics study for 15 years, this course provided a great explanation of the concepts and terminology with really good quizzes and and an introduction to R. There are still some terms I have seen elsewhere that weren't covered, but it may well be that they aren't specifically related to Bayesian Statistics, or were more advanced. I look forward to taking the follow-on course.

By Johan D R P

•Dec 2, 2019

This course has been highly useful to understand how hypothesis testing works, starting from experimental design using prior distributions and assumptions to posterior statistics based on data. In my college courses it was always assumed that the parameters for the distribution were fixed, so, having a way to correct them through the information hidden in the data allows to overcome those assumptions and have a clearer perspective of the data behavior.

By Фирсанова В И

•Mar 25, 2021

The course is great! I am a computational linguist without strong math background, however, there were no problems in completing this course. The course is provided with supplementary materials that really helped me to fill my gaps in math. The course, however, is quite challenging (well, for me it was), and I had a great fun trying to complete some quizes several times. I hope that soon I will be able to implement my knowledge on real tasks.

By Georgy M

•Jan 10, 2019

I found the course very well made and beautifully presented. The material is systematic, the more advanced topics based on the previously learned information without gaps and any need to study additional sources. The examples and the tests provide additional insights. Thank you, prof. Herbert Lee, for this great course!

Was able to do the course with Python instead of R, though it got a bit complicated on the last topic (regression).