Introduction to Bayesian data analysis - part 1: What is Bayes? 

There must be something magic going on here. I have been trying to learn Bayesian methods for countless times. This is the first time I all of the sudden understand every word the speaker says. And the learning curve? Flat!

You are great!!! For years I have been trying to understand Bayesian data analysis and you made so easy to understand!!! Thank you very much!!!

Genuinely one of the best and most straight forward tutorials I've found for Bayesian statistics, bless you

Nice. It's hard to find explanations of Bayesian data analysis on RU-vid that are clear and correct, and don't use Bayes rule as a rhetorical tool to make dubious assertions. This is excellent. I'll recommend this to students in my biostatistics class. Thank you!

This is an unreal explanation of Bayesian data analysis, thank you so much. This is the clearest and most intuitive introduction I've found, great job.

It's an outrage that you are the one thanking people by the end of the video. Thank YOU!

Thanks a lot. Finally, I got a glimpse of how Bayesian data analysis is working.

I too have tried to learn Bayesian analysis for a while and found you video to be the missing link I needed. Thank you Rasmus!

This explanation is amazing!!! I've been having a really hard time understanding the concepts and you just made it so easy to follow and understand! Thank you sooooo much! You have a great gift for teaching!

finally good video about bayessian models! man you're so great!! thank you for your work, the quality is great, and you're a great teacher! keep up good work, you've gained a subscriber!

In this clever guy’s video along with 3Blue1Brown ones I have found the best introductory explanation on the topic. Congratulations and thank you!

I am so happy to find a course of Bayesian method that is easy to understand. Excellent! 😀😀😀

God, this is the best channel of such DS and ML lecture! Thank you so much for the amazing lecture!

Why can’t professors give lectures like this? This helps so much with understanding.

Really really good video. Thank you for spending the time on creating this!

This was amazing. Thank you very much for making this accessible to us, mere mortals, in a fun way, easy to understand :)

These 3 videos are the best!! What great explanations you have given here. ty

great intro. Thanks Rasmus for these three videos!

Now I can picture the model in my head - super helpful! Thank you so much!

Thank you so much!!!... I have been listening to other videos on this topic, but I only got more confused. This has clarified everything for me. Thank you!

Oh my goodness! I finally understand this. Thank you so much. You are genius!

man you just blew my brain. wow that was an amazing lightbulb moment, thank you so much!

Excellent explanation...!!!! By far the best video on you tube explaining the concepts.

This is amazing teaching! Great work!

looking forward to it, really liked the first one!!

Good lecture. I've studied the Bayes theorem nowadays. It is another good lecture for me. I'm looking forward to next videos.

this is absolutely fantastic, enjoying this a lot

Thanks Rasmus, indeed you developed a great content and teaching method.

Greatest lecture on Bayesisn analysis

The almost religious divide there has been (and probably still is) between Frequentism and Bayesianism was most amusely described by Andy Field in his recent book "An Adventure in Statistics: The Reality Enigma". He refers to the "Secret Philanthropic Society" as a reserved bunch of innate believers in NHST and the "Doctrine of Chance" as an underground cult waiting outside the building of the NHST believers to bring salvation for their newest initiates. I highly recommend reading his book, if not only for the interesting take on a piece of statistics teaching material.

I enjoyed the brazilian music you "sang" while waiting we are acessing the exercise! Great!

Awesome voice structure.... fantastic....superb

loved this video, thank you for the wonderful explanation

You are an amazing teacher.

wow this was an insanely good video major props to you

Nice introduction! Hey, I recognized you humming Tom Jobin's song "Girl from Ipanema" during exercise break. Greetings from Brazil!!!

Thanks a lot. I think this one video says it all about Bayesian in core

3 parts of this series about Bayesian are the best videos i found, extremely helpful for beginner. However, this is my lesson after finishing 3 parts. You should highly focus on the reasons "Why NOT use Bayesian" at the end of part 2 and think about the pros and cons, cost-benefit related to your situation. I say this because i made a big mistake, i am NOT READY for this method at this very moment. I looked up for Bayesian because of the fancy and attractive outcome of this method and i wanted to apply it to my thesis in the SHORT TERM. It is obviously impossible! In short, please learn from my mistake, make sure you are ready for Bayes

Thanks a lot. Really clear explanation.

Excellent explanation from excellent country

Really nice introduction!

Thank you for a really good video and great explainations!

I am studying machine learning, and the term Bayesian analysis always appears in the papers that I read. I failed to understand it for quite a while, but you video explains everything I want to know. Thanks for all your effort, and the programming exercise is truly a gem for me.

Awesome work!

Excellent explanation. What material (books, courses) would you advice to deeper understand the Bayesian DA but with explination as clear as yours?

Awesome content! Thank you so much!

Awesome video, thanks!

brilliant explanation

Amazing, thank you!

This was super useful. I think it would've been helpful had you explained a bit more clearly why 55% was chosen as a prior given that the marketing manager had already completed a polling exercise and found a different %age. Anyways, nicely done. Heading over to DataCamp now. Thanks so much for what you are doing to help demystify Bayesian.

Great explanation...

Great video and I liked doing the exercises too. Oh and bonus points for "The Girl from Ipanema".

Crystal clear!

Thx so much! This was great!

Great work!

this is fantastic!

Amazing video!!!

This is great!

Very very helpful. Thank u

Great lecture

Excellent production of an excellent subject. Audio, video and slides did not get in the way of transference of the intended knowledge.

A great into to BAYES data analysis. Now, finally, the fog of confusion is clearing and I begin to think Bayesian.

You're a hero

Great stuff

You are the man!

video on Gaussian Process and Bayesian Optimization please 🙏🏻🙇🏻

breakthrough. thank you!

JUST AMAZING

When you simulate data, you need some kind of tolerance to compare the generated sample against the real sample, in your example it's a discrete stuff but if you have a distribution it gets tricky.

I have always been allergic to numbers and maths but now it is making sense.Thank you author

Thank you very much!

Thank you for 21:13 R Exercises. I did it somehow and it was great (a small point - a misspelling of the word signups in R script caused me a momentary confusion. :)

Thank you so much!

Thank you very much for these videos, Rasmus. I have really enjoyed them since I am actually trying to use Bayesian Data Analysis for a project within my company. Would it be possible to contact you in order to ask a few questions? Thank you very much in advance.

Pity the example links don't work anymore, But definitely the most down to earth explanation so far

This is so clear! Thank you for this !

@rasmusab - thank you very much

Thanks so much!

Did you sing "Girl from Ipanema"?

The fish thinking of the formula is Fire!.

for a shortcut: the rbinom function is vectorized so you can vastly improve on time by removing the loop. "sim_data

Very interesting. Is the "maximum likelihood estimate" the same thing as dividing 6/16 from the sample?

Thank a lot!

hello, please what microphone did you use ? sound quality is great ...

"... and it is targeted at you who isn't necessarily that well-versed in probability theory and statistics..." I think that it is everything that someone who comes to this kind of video hopes to listen.

Thank you

Great video🎉..... With a uniform distribution at start is this a beta distribution

Indeed very nice explanation of Bayes inference, still I have a problem to interpret the posterior, first what if we start with a prior being a binomial 50% (could we? it's could be our assumption why not?) then the posterior will probably show that the leaflet with 38% signing is a disaster business choice (it lowers the willgness to sign) , the prior choice isn't skewing too strongly the inferred result? May be the presented model is simplistic we lack of a "baseline" estimation (we should take this 16 peoples and ask them before seeing the leaflet what is their signing rates for example). The thing is that the leaflet "changes" only our "belief" in the reality not the reality.

I love ske doodles why he waits for me to finish the example.

Two very important decisions and assumptions first to start with the math model to assume for a generative model and the most likely PDF for the prior this will form the simulator. The second step is to perform the simulation and collect simulated data. Filter the results so that those results are picked based on the actual survey result. The way the problem was attacked and demonstrated is entirely unique from the so many people who tried to explain it as clear as mud. Now let me figure it out when there are like multivariate.

As every body else wrote... I am also was trying to understand it and how to use. You nail it man. Can I download the video please ... This gold for me... I can pair the idea of the video goes off line for some reason !!! can I ...

So we bruteforce all possible scenarios and see which instances give us the observed result. From the instances we keep we get a frequency distribution of the baselines for free. Got it!

holy shit this is so good!!!

I like the Fish as a Service (FaaS) example.

5:58 -- boom.

Notes for my future revision. 16:04 A parameter value that is more likely to generate the data we collected, is going to be proportionally more common in this blue distribution. A parameter value that is twice as likely (as some other parameter values) to generate the data we saw is roughly going to be twice as common in this blue distribution. Parameter value below 0.1 and above 0.8 almost never result in the data we observed. 18:33 The Posterior Distribution is really the end product of a Bayesian analysis. It contain both information from the model and from the data. It can be used to answer all sorts of questions (e.g. Maximum likelihood estimate of the mean sign up rate, the posterior mean, the probability of a range of rate, the shortest interval aka Credible Interval that cover 90% of the probability etc.) 17:05 Bayesian data analysis is all about representing uncertainties with probabilities. The sign up rate is still uncertain. But we can use the distribution to answer many questions e.g. Maximum likelihood estimate of the mean sign up rate, the poterior mean, the probability of a range of rate, the shortest interval aka Credible Interval that cover 90% of the probability etc. 17:52 Translating the histogram to probability, we end up with a probability distribution of the likely sign up rate. 19:09 As we used uniformly distributed Priors, this is also the parameter value that is the mostly to generate the data we observed. In classical statistic, this type of estimate is known as 'Maximum Likelihood Estimate'. This is why Bayesian data analysis is an extension of 'Maximum Likelihood Estimation'. If you used flat prior, you will always get maximum likelihood for free.

tres bien, tu a francais accent. merci! c'est très complet

Hi Rasmus, one question: IF you know your likelihood distribution to be binomial, shouldn't P(data | θ) = P(r=6, θ) for a given value of θ ? In theory, you wouldn't need sampling, just mathematical calculation using Bayes formula for each possible value of θ. For θ [0..1] P(θ | data) = P(r=6, θ) x P(θ) / P(data) Where P(data) = Σ P(θi) P(data|θi) which can be computed without simulation/sampling either. Am I mistaken? Please do correct me as I'm kind of new to this. Thanks!

OMG, so this is whats going on! ive tried readings few books on this, but it was never articulated clearly, the books did a lot of hand waving and i was always left extremely confused, and felt like the classical approach was superior. but i like this way of thinking, it has its advantages.

I am looking forward to ask for a help. May I get the slide for this tutorial? Thanks