6. Monte Carlo Simulation
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- čas přidán 18. 05. 2017
- MIT 6.0002 Introduction to Computational Thinking and Data Science, Fall 2016
View the complete course: ocw.mit.edu/6-0002F16
Instructor: John Guttag
Prof. Guttag discusses the Monte Carlo simulation, Roulette
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
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
thank you Mr. Lei
Dr. Mohamed Ait Nouh you’re welcome :)
Thanks Mr. Lel
Pajeet Singh you’re welcome
Thank you Mr. Lei
This is a true teacher. He actually explains the concepts instead of just scribbling equations on the board.
Couldn't agree more. I am hooked.
Why MIT is a top school. I love that MIT allows anyone to watch these for free.
COULD NOT AGREE MORE!!! He is truly amazing. 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 wonder how much time and effort was made to ensure every word was meaningful and carefully stated (just been through a course with a lecturer who knew his stuff but mostly winged it which was one of the biggest wastes of my time). I also noticed not a single 'um' or 'uh' which is amazing.
@@benphua Well, I noticed four "ums" or "uhs" in second 0:35 to 0:45 alone, but I agree the lecture is very clear.
I've never met him, but he taught me python years ago.
we should be grateful for such giving human beings.
Not what I was looking for, but couldn't help but watch the entire video. Well done sir.
same
The same!
I love random walks through youtube
wanted to know what a monte carlo simulation is but I guess ill revise some stats intuition ¯\_(ツ)_/¯
@@GaoyuanFanboy123 hahaah same xD
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.
MVP
Thanks a lot, that was what I was looking for!
Which playlist??
This guy is such a fantastic teacher. I would love to have him in person, thanks again for uploading the video!
Have him for ... breakfast?
@@zZE94 Ken really sounded weird ahahahha
He prolly would love have you in person too, for sure.
At the university where I studied all teachers were also fantastic teachers until the exam. Afterwards they were all a**h****.
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.
Watching Prof. Guttah teaching is a joy. A true inspiration for those of us who also like teaching and want to do better
I came here for the Monte Carlo simulation but got unexpectedly thus far the best explanation for simple concepts like Variance or Standard Deviation
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.
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
An instructor of the highest caliber; clear explanations, projects a seemingly universal likeable and fair personality, low intensity approach. Good hire MIT!
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
Wonderful professor. So casual but I believe what the students learn will stick with them forever.
Excellent presentation. Don't know why CZcams 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.
26:53 Great answer to make the difference between gambler's fallacy and regression to the mean clear!
I love the sense of humour of the instructor. A great lecture indeed!
Actually you are an amazing demonstrator
I love these old school professors. They are true masters.
such respect for these fantastic teachers
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 this great lecture. You explain it so well. I was looking for Monte Carlo Simulation but ended up watching the whole video.
I love professors who make mistakes and make corrections accepting help from students.
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.
Hayatımdaki en iyi üniversite dersiydi.Thanks Prof J. Guttag
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.
After watching this lecture, I wish I was smart enough to get into such elite schools and be taught by such passionate teachers.
Respect!
But you have access to MIT open courseware
Should of done better in highschool and went to MIT. This is great. A true teacher
WANTED MORE ABOUT MONTE CARLO, but he is such an amazing teacher that I got stuck anyways!!!!
12:47 "win some lose some, it's all the same to me"
Lemmy
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!
Hint: Playing on 1.25 speed is ideal for this video.
Thanks. :))
2x for engineering students in south asia
For an foreign student from germany like me - 1.0 speed is good. But for all native english speakers i think he speaks quite slow.
But 1.0 speed is too good.
pro-tip, mate. Thx for the time back.
Finally understood what statistics is about after 10 years of endeavour! Thanks so much!
Trying applying it to obtain Lebsegue Integral. See, you probably have understood nothing.
Kasra Keshavarz your face shows how stupid you are
Howard Lam. It is “Lebesgue”
Thank you Prof. Guttag & MIT.
Extremely Based series of lectures. Top tier professor!
I really love the teachers at MIT. I have watched a ton of lectures from them and all have been great
Lies again? Support Indonesia Malaysia
He is such a great teacher on multiple topics. After this course I plan to finally take Linear Allgebra.
Makes even high level material understandable to a neophyte. That's the mark of a skilled educator.
Wow... fantastic lecture by Prof. Guttag... Thank you and congratulations.
he is so funny, i wish i had such professors
great video, such a clean delivery of the concepts. well done
The explanation is clear, his lecture is great!
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.
Very interesting lecture, was planning on skimming it and watching small sections but I watched the whole thing without noticing the time passing!
Thank you Professor Guttag and thank you late Stanislaw Ulam.
Thank you for share this amazing video
What a great teacher. Absolutely loved it
What a treat to watch him teach! :) Hats off!!
The best way to explain variance formula!
Beautifully done.
I am so grateful of your explanation
Professor, your lecture was engaging. Thank you.
Thanks you for being a great teacher. I really needed some background on Montecarlo.
Great lecture. The concepts were explained clearly. I understood them very well. Thank you!
Is the camera automated? Or is it hand-operated by human?
Thank you professor Guttag. Fantastic lecture and explanations.
I give this professor two thumbs up. I like his style. Good presentation also. A hardy bravo zulo to the man.
Thanks for sharing this video. Concepts very well explained and accessible. Thank you.
Love your Data Table hack at 2'. Thank you for that!
He is the best! Such a pleasure and luck to be able to access this lecture.
Thank you Eric.
Fortunate to find his video !! A legend I was looking for !!❤️❤️❤️
I had so much more fun learning the subject with Dr. Guttag than my uni professor.
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.
the next toss is independent of the previous toss ;but there is a different question that can be asked :what is the probability of of x tail(heads) in a row=1/2^x .Two completely different betting strategies
That is what they call a gamblers fallacy.
Congratulations, you just fell for the Gambler's Fallacy...
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.
This professor is incredible!
I think if you add captions for the questions it will be awesome.
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.
39.07 That a result will lie within an interval with probability 95% doesn't mean it will be within that interval 95% of the time. Probability cannot be directly translated into percent of times.
Ok, he is really good 33:45, how I hoped to have a prof. like him back in college.
My big interest is Monte Carlo simulation and Markov chain!!!
Excellent lecture
Wow..... He truly explained what monte carlo simulation in 50 min. Thank you Prof.
+Isaac Park I've heard everything but a Monte Carlo here. Confidence intervals, regression to the mean, Gambler's Fallacy etc, but not much about Monte Karlo and its many alghorithms.
Thank you for the great lecture. One question....at 39:00 I see it saying "The return on betting a pocket 10k times in European roulette is -3.3%". Was that based on the Monte Carlo sim? I ask because there are 37 pockets on a European roulette wheel. If you win it returns 35 to 1, plus your original wager, for 36 units returned on a win. 1/37 = 0.0270, for an expected return of -2.7%, or 97.3% (depending how you look at it) on European roulette. Thanks again for the awesome info...
Regression to mean is not the same as Gambler's fallacy in that Regression to mean basically says after an extreme event you are unlikely to get a successive extreme event. Gambler's fallacy says it is definite to get successive extreme events. Gambler's fallacy falls into the trap of assuming the events are dependent/correlated (linearly +ve/-ve). That is not the case in Fair Roulette.
Adorei a aula, excelente!
Amazing explanation
Thanks for this video. Amazing explanation!
A good session, I'll search for the prof and watch more videos. 👍
Thats the best lecture I have ever seen.
i love you sir. you are a great teacher.
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 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.
Thank you , professors.
How is this related to monte carlo tree search?
very explanatory ways to teach ... Sir you should teach teachers ... What a teaching style!!!
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
I like this professor a lot
Fantastic lecture
Awesome lecture; thanks!
Great lecturer! Amazing!
Genius teacher! Just so intuitive!! Wowwwww