The sign of a good teacher--I landed here by accident, stayed for the entire lecture, and understood all of it...

*My takeaways:* 1. History of Monte Carlo Simulation 0:56 2. Monte Carlo Simulation 3:23 - Example1: coins 6:03 - Variance 10:00 - Example2: Roulette 11:00 3. Law of large numbers 18:40 4. Misunderstanding on the law of large numbers: Gambler's fallacy 19:48 5. Regression to the mean 22:42 6. Quantifying variation in data: variance and standard deviation 30:14 - Always think about standard deviation in the context of mean 35:10 7. Confidence level and intervals 36:00 8. Empirical rule for computing confidence intervals 39:27 9. Assumptions underlying empirical rule 43:40 - mean estimation error is 0 - Normal distribution 10. Probability density function 46:25

This is a true teacher. He actually explains the concepts instead of just scribbling equations on the board.

I've never met him, but he taught me python years ago. we should be grateful for such giving human beings.

00:00 Monte Carlo simulation is a method of estimating unknown quantities using inferential statistics. 06:48 Variance affects confidence in probability predictions 13:09 Law of large numbers: Expected return of fair roulette wheel is 0 over infinite spins 19:23 Understanding the Gambler's Fallacy and Regression to the Mean 25:16 Regression to the mean is a statistical phenomenon where extreme events tend to move towards the average with more samples. 31:11 Understanding variance and standard deviation for computing confidence intervals. 37:37 Understanding confidence intervals and the empirical rule 44:04 Probability distributions can be discrete or continuous, and are described by probability density functions. Crafted by Merlin AI.

Some of the best explanations of statistics I’ve heard. Does a great job of breaking down concepts.

For those looking for some visuals of how a Monte Carlo simulation works, see the second half or so of lecture 7 on Confidence Intervals.

Watching Prof. Guttah teaching is a joy. A true inspiration for those of us who also like teaching and want to do better

This guy is such a fantastic teacher. I would love to have him in person, thanks again for uploading the video!

Not what I was looking for, but couldn't help but watch the entire video. Well done sir.

What a beautiful way to explain a concept. Starts with something so simple and gradually builds up to the more complex part, also delivers the lecture in a way that even a tiny bit of boredom can't creep in.

I came here for the Monte Carlo simulation but got unexpectedly thus far the best explanation for simple concepts like Variance or Standard Deviation

Brilliant lecture. I can binge watch Professor John Guttag's lectures. Amazing.

Isn't he the most adorable teacher ever? Great job walking your audience through the material!

this man right here is a true teacher, understands the subject topic deeply and speaks passionately

26:53 Great answer to make the difference between gambler's fallacy and regression to the mean clear!

Great teaching style. Small number of teachers can teach such concise and clarify. I learn a lot from the great educators.

For those that may be confused, he misspoke at 23:36 "taller than average" should have been "taller than the parents". In the case that parents are shorter than average, it is expected that their children will be taller than them, not taller than average.

Had this same lecture in PSYCH Stats class at CofC. Learned a lot and this was fun to watch again

An instructor of the highest caliber; clear explanations, projects a seemingly universal likeable and fair personality, low intensity approach. Good hire MIT!

Wonderful professor. So casual but I believe what the students learn will stick with them forever.

Thanks for addressing the apparent contradiction of the Gambler's Fallacy vs Regression to the Mean ~25:00 in. I'd always thought these 2 were in opposition, but guess I'd never heard (or thought of it) in the right frame of reference.

Excellent lecture. Prof. Guttag is a great teacher. Thank you. Every course or lecture I have watched in this MIT Open Courseware has been superb. Thank you to the teachers and to MIT for posting.

This is the best lecture I have ever seen on statistics. It wasn't even what I was looking for but couldn't take my eyes off it till the end. Thank you Professor! Thank you MIT!

Thank you for this great lecture. You explain it so well. I was looking for Monte Carlo Simulation but ended up watching the whole video.

Excellent presentation. Don't know why KZfaq presented the option of the video, but watched until the end. Very gifted professor. The only thing that I can think to improve it is to repeat the question from the audience so that the question is picked up on the recording.

I love the sense of humour of the instructor. A great lecture indeed!

Actually you are an amazing demonstrator

such respect for these fantastic teachers

Hayatımdaki en iyi üniversite dersiydi.Thanks Prof J. Guttag

I love professors who make mistakes and make corrections accepting help from students.

Unfortunately, during my studies at Bachelor and Master, I never had such great real professor. Thanks so much for sharing such great video.

Thank you for share this amazing video

Very interesting lecture, was planning on skimming it and watching small sections but I watched the whole thing without noticing the time passing!

great video, such a clean delivery of the concepts. well done

Wow... fantastic lecture by Prof. Guttag... Thank you and congratulations.

He is such a great teacher on multiple topics. After this course I plan to finally take Linear Allgebra.

he is so funny, i wish i had such professors

WANTED MORE ABOUT MONTE CARLO, but he is such an amazing teacher that I got stuck anyways!!!!

I love these old school professors. They are true masters.

I really love the teachers at MIT. I have watched a ton of lectures from them and all have been great

Extremely Based series of lectures. Top tier professor!

Thank you Prof. Guttag & MIT.

Finally understood what statistics is about after 10 years of endeavour! Thanks so much!

The explanation is clear, his lecture is great!

After watching this lecture, I wish I was smart enough to get into such elite schools and be taught by such passionate teachers. Respect!

What a treat to watch him teach! :) Hats off!!

Makes even high level material understandable to a neophyte. That's the mark of a skilled educator.

What a great teacher. Absolutely loved it

Thanks you for being a great teacher. I really needed some background on Montecarlo.

Love your Data Table hack at 2'. Thank you for that!

Great lecture. The concepts were explained clearly. I understood them very well. Thank you!

Very good introduction of how the e-Pi-i conception of probabilistic Calculus by Pi circularity numberness/orbital is a dualistic +/- possible Infinite Sum, Normal/orthogonal self-defining "e", metastable +/- singularity convergence to zero difference, balance of frequency constants in Totality.

Thanks for sharing this video. Concepts very well explained and accessible. Thank you.

The best way to explain variance formula!

Should of done better in highschool and went to MIT. This is great. A true teacher

Professor, your lecture was engaging. Thank you.

Suddenly the Stats I did on a Data Science Coursera course start to make sense. A couple of more lectures by him and I will have everything sorted out in my mind... My God. Some lecturers just Got it and some just Don't.

I am so grateful of your explanation

Thank you Professor Guttag and thank you late Stanislaw Ulam.

Ok, he is really good 33:45, how I hoped to have a prof. like him back in college.

Beautifully done.

12:47 "win some lose some, it's all the same to me" Lemmy

I give this professor two thumbs up. I like his style. Good presentation also. A hardy bravo zulo to the man.

Thank you professor Guttag. Fantastic lecture and explanations.

He is the best! Such a pleasure and luck to be able to access this lecture.

Thank you Eric.

I feel like I with no prior knowledge just intuitively already understand all of this and use it in daily life. Cool to hear it's basis though and a more technical presentation

Thanks for this video. Amazing explanation!

My big interest is Monte Carlo simulation and Markov chain!!!

Fortunate to find his video !! A legend I was looking for !!❤️❤️❤️

Adorei a aula, excelente!

Amazing explanation

I am the Great Canadian Gambler and can attest that my biggest two 6.2 Standard Deviation swings ever were back to back. Same in my early years when I played Craps to get the free junket to the casinos. Biggest win followed by biggest loss. I note that because I heard poker champ Daniel Negreanu mention the same back-to-back phenomenon. Always believed in the odds but back-to-back streaks leave an eerie feeling.

i love you sir. you are a great teacher.

I think if you add captions for the questions it will be awesome.

Hint: Playing on 1.25 speed is ideal for this video.

This professor is incredible!

I had so much more fun learning the subject with Dr. Guttag than my uni professor.

Excellent lecture

A good session, I'll search for the prof and watch more videos. 👍

Thats the best lecture I have ever seen.

I was excited for this one

proper: denoting a subset or subgroup that does not constitute the entire set or group, especially one that has more than one element.

Thank you! Amazing teacher.

Great lecturer! Amazing!

take care professor and thank you for lecture

very explanatory ways to teach ... Sir you should teach teachers ... What a teaching style!!!

Genius teacher! Just so intuitive!! Wowwwww

In the slide "Gambler's Fallacy" it reads at the bottom: "Probability of 26 consecutive reds when the previous 25 rolls were red is:" The wording is poor in my opinion. Does it mean: "What is the probability of the next roll being red?" Or Does it mean: "What is the probability of the next 26 rolls being red?" Or maybe : "What is the probability of 26 consecutive reds occurring in the next roll if the previous 25 rolls were red?" Based on his answer I think that the question should have read: "What is the Probability of the next outcome being red when the last 25 outcomes where red?" And then he goes on to talk about it being independent after this question. He didn't establish at the beginning that the outcomes were independent.

Thanks for this video, very easy to understand

There are some problems with Monte Carlo simulation. For example, suppose the "winning" combinations we are looking to count are very small (unlike in coin flipping), and the # of possible outcomes is huge (such as 1 trillion squared). A computer may not be able to simulate all 10^24 possible outcomes because of time constraints but instead simulates only 10^12 (1 trillion of them). Since the "winners" are so rare, it is possible the simulation will show 0 "winners", basically giving us no information if a winner even exists. Another problem is if the # of possible outcomes is huge, our confidence level in the results of the simulation being representative of the entire sample space is low. That is, we cannot draw accurate conclusions from a very small subset of the "population". So this persons statement that a random sample tends to exhibit the same properties as the population from which it is drawn is NOT true if the sample is "too small". For example, suppose a population of 100 million people contains a very rare disease that only affects 100 of the people. Suppose 1000 of the 100 million people are selected at random and tested for the very rare disease. It is VERY likely that none of them will test true positive for the disease and one may falsely conclude that nobody in the population has the disease.

Thank you , professors.

This is what is used to determine results of A/B testing folks, i had to learn this on the fly at my job

Fantastic lecture

One observation, the code returns totPocket/numSpins, which is in fact return per spin, not the expected return in %. In the exemple in particular since the bet is 1, numSpins equals the total value payed to play, hence the expected return in %. If you change the value of the bet, the output is not right.

I like this professor a lot

Oh my God, I've got it now in detail. I took a semester course in Bayesian theory and treated this topic, I had to write a report at the end of the semester on it. It was a hell :-), I'm glad to refresh my memory about this topic here again. Thanks a lot, Sir!

Excellent class

I love a professional, whether he be a doctor or a scientist, who has the confidence and grace to admit that he makes an honest mistake.