Back to Bayesian Statistics: From Concept to Data Analysis

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2,716 ratings

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707 reviews

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....

GS

Aug 31, 2017

Good intro to Bayesian Statistics. Covers the basic concepts. Workload is reasonable and quizzes/exercises are helpful. Could include more exercises and additional backgroung/future reading materials.

JB

Oct 16, 2020

An excellent course with some good hands on exercises in both R and excel. Not for the faint of heart mathematically speaking, assumes a competent understanding of statistics and probability going in

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By Yildirim K

•Jan 19, 2019

I would have given it 5 stars if some of the materials were covered more in depth (e.g. Jeffrey's prior). It seems like someone can dedicate a lot of time learning about how to apply it in different situations and in some instances I had to hunt for more in depth or simpler explanations for specific subjects (such as Jeffrey's prior) in other sources online. Overall the course is helpful and very useful and very well organized and gives a good amount of extra resources to read on but, I think it can become better if, the instructor did not rush through some of the subjects and spent more time explaining (especially towards the end of the course). The discussion forums help in these types of situations but, there will be a lot of searching dedicated to the specifics you are looking for. Overall an update to the course based on feedback of people that completed the course (from discussion forums) seems necessary. Adding an extra 5-10 minutes to some of the video contents can save the student from hours of research on the internet and confusion (sometimes due to the outside source). I'm not saying one should not spend time learning the material further from outside sources. Just saying the explanation might help avoid the confusion caused by looking into other sources.

By Dmytro K

•Aug 19, 2020

The course is great and through, however, it lacks intuitional explanations of many concepts. Thus it is hard to follow sometimes. Also, it requires very decent mathematical background while, in my opinion, most of the viewers are rather economists without strong enough base (luckily I'm with actual mathematics BA). One more point is that I find this course rather unfinished because there is so much more about basic Bayesian statistics to say. For example, one of the most important topics for me and reasons to take the course are BVARs. However, they were not even barely mentioned and the course was cut off with simple regressions (without any clear use of prior/posterior ideas described in the majority of the course). Thus, I think that course is an excellent starting point for those who are really good in Statistics and Theory of Probabilities but do not know anything about Bayesian things. And this course should be definitely followed by some other, more applied one.

By spencer r

•Oct 1, 2016

There are several things in the course that were able to clear up my understanding. The course instructor responds to more questions than I would have expected as well. The course uses a lot of mathematical notation and it helps to take some time with it but once you get the idea of conjugate priors down you can quickly employ them in your own problems. The course covers conjugate priors for several different likelihoods including the normal distribution and the binomial distribution. Although the derivation of the conjugate priors looks daunting as it is written down, the usage of the priors make Bayesian statistics much easier.

This course uses R and Excel but is not a course in either. Most of the computations that are performed for the quizzes are pretty simple and require little skill in R.

I am glad that I have taken the course and would take another if provided by this instructor. I plan to reference the materials provided in the future whenever I need a refresher.

By Viachaslau B

•Sep 23, 2016

The course is a great introduction into Bayesian statistic analysis. I particularly liked the detailed explanations of where the parameter formulas came from. Also a great thing, in my opinion, was to write the explanations on the glass instead of just displaying the final results. It kind of provided a sense of interactivity and made the material more digestible for a person with not such a strong background in math. It greatly smoothed the learning curve for me and kept interested and motivated to finish the course. In the end the pace accelerated a bit but was still manageable. Four weeks seems a great duration for such a course - not becoming boring and tiring. Honors tests were quite easy, I'd prefer to have a little more challenge. Overall I'd recommend the course for everyone who wants a quick introduction into Bayesian statistics. It provides a solid background for further studies.

By Denitsa S

•Nov 19, 2018

What I liked in the course is that it focuses on examples and solving actual problems. The quantity and the quality of the lectures is great, but what I really missed is written lectures where one can always lookup forgotten things or read details etc. Also, one thing that I think might be added easily is a reference to Mathematica and Maple's routines. I'm using Maple and it took some efforts to get on track. And finally, I think that 4 quizes per week is really too much for working people. It's true that the tests weren't that difficult, but it took me about an hour to do each, so I think 30 mins of lectures vs. 4 hours of quizzes is a bit unfair. Of course, my background in statistics is non-existent so it may be that it took me longer than average. But I think the course material could have been spread over say 6 weeks for lighter load on the students. All best to the team!

By Ivan S F

•Mar 2, 2020

The course is good as an introductory course to Bayesian statistics. However, there is no much context and no much explanation for many of the calculations. I think the course would greatly benefit from: before each existing video, make a 2 minute video of a real world situation why that approach is helpful (bus arriving every 10 minutes, etc.) so that all students can connect with the content, then the video as it is now, then a 1 minute video linking the formulas with the real world example. As the course stands now, it is difficult to really follow why the formulas have any application and this only appear in the quizzes (where you are being tested, not learning in a non-stressful situation). I think more context and more examples with the formulas would make this course perfect. As of now, it is way too disconnected from real world, although still worth it.

By David N

•Jul 30, 2017

It was a really well taught class and I enjoyed watching it. Unfortunately I seem to lack some basic understanding, since I am not a statistician. Therefore I had problems following the course and had to do quite a bit of research to do on my own to get long. Still, I managed to get 100% correct on all quizzes and all honours quizzes. So it seems, that if you put in enough effort, you can get 100% on the course without understanding many things. This is not to say, that this course is easy, it took a LOT of effort, but it was possible. I will now investigate further to get all of the basics. Maybe I will come back and take this course as a refresher. Other than that I can whole-heartedly recommend this course. The presented material is very well organized and and presented and Professor Lee is a really good teacher.

By Megan R

•Sep 24, 2016

A great introduction. I feel like I know a lot more about bayesian statistics now. But I do mostly feel like there is quite a bit I don't know, and while I passed, I feel like there is quite a bit more I need to do to really 'get it'. The professor recommended some books in a discussion forum and I'll be going through some of those next I am sure. I also feel, looking back, I should have had some additional math preparation before starting. The calculus was vaguely familiar but with the pace of the lectures, I felt occasionally lost. I would have found it helpful if there was a quick primer on calculus to know and review at the beginning of the course. All in all great course. Loved the presentation method.

By Edward R

•Jul 9, 2017

This course provides a solid overview of simple Bayesian models and common distributions used in those models. It also provides an initial understanding of conjugate prior distributions and non-informative prior distributions. The R code used in this course is very simple; easy for a beginner, but perhaps a bit simple if you are already familiar with programming in R and doing commonplace frequentist statistical analyses (regressions, ANOVA, etc). Overall, this course is definitely worth taking if you are interested in Bayesian statistics and need a good place to start. There are quite a bit of videos and supplemental materials which allow for a broadened understanding of the materials. Thanks, Dr. Lee!!

By Aaron B

•Sep 14, 2017

This is a decent course that covers an important topic that I've had a trouble finding good resources for learning about.

Pros: comprehensive coverage of the topic at a high level.

Cons: not enough examples to understand what is talked about in the lectures (especially the continuous data and prior with normal distribution lectures) and to anchor the topic in its practical uses.

I recommend supplementing this course with the MIT OCW 18-05 statistics class (I actually put this on hold and did that then came back).

If this course had a lot more practice problems with fully worked out answers it would help tremendously. I understand a sequel to this class is in the works and I look forward to taking it.

By Jurriaan N

•Dec 17, 2016

This course provides the student a profound understanding of the statistics behind the bayesian approach. Also, it gives some intuition for the difference between the frequentist and the bayesian approach, although that part could have been more explicit in my opinion. It would be very helpful to have more examples on the differences in using freq vs bayesian approach, the gains from using bayesian approach, examples of where the freq approach is limiting / misleading in its 'objectiveness'. More 'real life' examples instead of coin flipping examples - although easy to follow - would be very helpful as well, maybe in a consecutive course with applied bayesian statistics?

By Jon I

•Jun 13, 2017

An interesting introduction to Bayesian statistics and inference. Not for people with no statistical background, as it does assume you are comfortable with various distributions, expectations, variances, etc. and the 'standard' frequentist worldview (including inferential procedures such as linear regression). The material was well explained, and generally well examined, with a mixture of multiple choice understanding questions, and numeric response tasks which also serve as a very basic introduction to R (or Excel if you are crazy). It was good to see the instructor realising that a light shirt was causing problems and switching to a darker one as the videos went on!

By Larry L E

•Oct 5, 2016

I enjoyed the course. My background is mathematics, but not specifically statistics, though I do have a basic understanding of elementary frequentist statistics. My goal was to understand the fundamentals and uses of Bayesian statistics, having attempted that via a couple of textbooks without much success; this time, I got it!

I do have some reservations about the course. Herbie Lee spent a huge amount of time deriving formulas and methods - a few gaps (either hand waving or 'leave it to the student to finish') would have been helpful, I think. This would leave more time for examples and applications. But the course was well worth my time and effort.

By Venkatesh U

•Dec 2, 2017

This course covers most of the basics in a very good manner. I personally feel, the last week chapters especially regression do not connect the dots between the foundation that was laid and the resources provided were also not very helpful to fill that gap. For e.g I wanted to understand regression from the bayesian context, the session mostly focused on how to do regression in R and the not the internals of how to understand the mechanics behind from the bayesian stand. I will be helpful to introduce some content that helps the user to move from univariate normal distribution to multivariate normal distribution and explains some intuition behind them.

By Lukas S

•Sep 11, 2017

The course itself is wonderful, and the contents are very thoughtfully selected. I'm not a particular fan of the mirror-technique they use to shoot the videos. Basically, Professor Lee stands in front of a mirror and writes onto the mirror with text markers. On the video you see both him, and the text he writes.

His body often covers the text and generally, it is hard to read. Personally, I see no need to see the professor. Rather, I would prefer a note-taking app (white background). There, old formulas could also be replaced by LaTeX text making everything much more readable, plus there would be downloadable lecture slides automatically.

By Ramon R

•Mar 1, 2018

I liked that the teacher put things into perspective and showed the connections between the different concepts. I deduct 1 star, because the additional material in rare: Meaning, you have to take notes in the lectures to solve the quizzes and to have something for looking things up. Furthermore, in a few lectures it was difficult to read what the teacher was writing, because he was wearing a shirt with a too bright color. (Sounds funny, but I mean this serious ;-) ) In summary, a great lecture and perfect introduction into the concepts. The quizzes are constructed in a way, that they encourage learning rather than frustration.

By Andrea P

•Sep 23, 2016

The course is nice, the lectures are really clear. Professor Lee is brilliant and he often gives some excellent interpretations of Bayesian results. For example, the classic example of testing for rare diseases is explained in terms of ratio of true positives to all positives. Another example is the explanation of predictive mean for normal models, or the explanation of noninformative priors. They're all clearer than what usually found in many books. The only limit of the course is that it's strictly an introduction, thus very useful topics for applications such as hierarchical models or nonconjugate models are not covered.

By Lucas M

•Nov 18, 2019

It was a very nice course that got more practical towards the end. The only thing I found a little bit confusing is the regression part, without theory videos and with practical outcomes that are exactly the same as frequentist approaches.

Don't be discouraged if you come from a background where integers and derivatives are not usual! I come from psychology and I found it a little bit hard at the beginning, but if you put effort you will get to understand almost everything. As long as you get the idea of where things like formulas are coming from and why are they done that way I think it is enough.

By Carlos L

•Jun 16, 2020

I really liked this course. The material is great and the structure of the course is very well organised. A possible improvement, in my opinion, would be to include more explanatory material or take more time in the videos explaining some concepts or derivations. This is why I have to search for other resources in order to grasp some concepts and I took a lot of time in order to completely grasp all the concepts in this course (roughly 10hours for each week). The last week seems a bit rushed and lacks a bit of explanation in the linear regression, non informative priors and in the normal model.

By Maxence A

•Aug 30, 2020

Good curriculum overall, the course can be difficult for students that don't have a strong background of statistics. I found the video lectures lacking because it was mostly formulas and not much explaining. For intuition I had to consult external sources. Most of the quizzes were well designed and challenged our understanding of the subject. While I don't feel that confident in the subject i did gain a good understanding of the overall idea behing bayesian inference.

My advice would be to provide additional videos that give more insight and intuition behind thess concepts.

By Arkady S

•May 7, 2020

Really enjoyed weeks 1-3 of the course. It was well done and I felt like I had a good grasp of the materials, and the tests reflected that. The lecturer gave good intuition of what was going on with the math. Week 4 on the other hand was a bit hectic. I didn't feel like I had a good grasp of the material or the underlying math, and lots of it was rushed through. I also didn't feel like the quizzes in week 4 helped me understand the material more. I was able to complete them correctly just by using R, with little understanding of what's going on behind the scenes.

By Darjo

•Jul 9, 2019

Most of the stuff is explained quite well and I managed to understand it. I am quite satisfied overall and I am glad I completed the course. The exercises, however, were somewhat boring. I wish there were some optional exercises that are more challenging and require you to solve more realistic problems. I also wish there were more additional materials with more in depth theory and examples of how they use these concepts for solving problems that are actually of some use. I feel like these improvements would make the course much more interesting and engaging.

By Larry B

•May 13, 2021

I liked the course. It was a lot of work. It was probably beyond my skill levels. A few more plug in the value examples would have been a great benefit to me. I did not have an recent experience in Calculus and statistics, and I had never used R. However, I got through the course with the chance to retake the quizzes multiple times. That was a good learning experience for me because I could start to figure out how to fill in the blanks, so to speak. I think some more information on course prerequisites would have been helpful.

By Oleg

•Nov 9, 2018

It was my first Bayesian course. Good introduction! However more accent should be placed on intuitive understanding rather than mathematical formalism. To be fair that the issue not only with this course, that the issue with 90% of all stat courses/books. As for me, I find mathematical formalism is hard to digest, intuitive understanding should come first ... May be it's just because of my limited knowledge of stats. I'll update my belief once I get better understanding of stats:) Thank you very much Dr Lee!

By Matúš F

•Apr 26, 2020

I would highly recommend this course to everyone, who wishes to learn basics of Bayesian statistics. I very much appreciate quizzes, videos and reading material. Few things I recommend to improve: Provide reading material for the theory presented in videos, it would be helpful to have this when I will come back to material later. Also for some quizzes and questions in videos (W2 and W4) latex didn't interpret correctly, so I had to do it on my own by copying it to latex interpreter, which was irritating.

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