*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
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.
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.
An instructor of the highest caliber; clear explanations, projects a seemingly universal likeable and fair personality, low intensity approach. Good hire MIT!
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.
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.
Excellent presentation. Don't know why TH-cam 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.
+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.
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.
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.
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!
If all mathematic teachers taught like this in classes, I'm pretty sure the amount of those who grew up hating math would have been a lot less. Very clever way of teaching by giving scenarios, explaining them with mathematical concepts, without diving too quick to the expressions or formulas which not everyone is ready for.
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.
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 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.
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.
At 8:30 he misses implications of Bayes theorem - if you observe 52 heads from 100 flips, it is still much more likely that the coin is fair than biased. Because as he mentions, there are many many more fair coins and dice our there than weighted ones. The probably you have to assess is P(52 heads | coin is fair) * P(coin is fair) vs P(52 heads | coin is biased) * P(coin is biased). Far more likely that it is fair.
It's in Monaco, the casino, I was there twice, as a visitor, and I never thought I would see it in an academic lecture. Amazing. It has just brought my memory back nothing to do with it's good or not. of course, i took a picture with it. That's why you need to go Europe. Everything is amazing.
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.
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 had a difficult time understanding the _Gambler’s Fallacy_ , well I understood it but couldn’t fully believe it. So back in the day on a PC with a 386 processor I wrote a Basic program that flipped a coin continuously and kept track of the results. After 2 “heads” in a row I bet on tails. I won roughly 50% of the time. I then incremented the waiting period by one more flip, betting tails after only 3 heads in a row, then 4 in a row, and so forth. I came ahead after waiting 8 flips, so then I ran the 8 heads in a row routine many times to test it and of course I never came ahead again. I fully grasp that the coin has no memory but my feelings still tug at me saying _Tails is overdue!_
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.
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.
Brilliant lecture...brought me back memories of school. Just one mistake @45:46 (perhaps oversimplification - discrete random variable need not have "finite" number of possible values, it can also be "countably infinte" as in Poisson). Again, I'm not trying to be a smart-ass...but this is an important consideration
This man is really good at explaining the sense. There were no crazy sets of symbols though i got the essence of his explanation. The only downside of this is that it s NOT about monte carlo but more about some basic assumptions lying at the base of Monte Carlo
Kinda rushed at the end, but i'm very fortunate to have studied probability and random processes under prof SNS of our institute, he took his sweet time to ensure that we all (class strength is 22) understand the basics of stats before moving on to analysis of Random variables. Great lecture nonetheless, far better than the Data Science lectures we have Love from IIITDMJ, India
As already stated a great lecture by a great lecturer. Though I be!ieve he misspoke @23.33. when he regarding "regression to the mean" said that "two parents who are shorter than the average, likely would have a child that is taller than THE AVERAGE", which (I believe) is incorrect. What I think he meant to say is that "... They are likely to have ahold that is taller THAN THEM"... And thanks again for making this and so much other fantastic content freely available :} Brgds
The roulette and coin flip needs to input other variables: maybe the next turn of the roulette the dealer spins the wheel harder or slower, or the balls shoots out of the fingers faster or slower. When you flip a coin maybe the thumb throws the coin harder or slower or you raise the hard to high and the results change. So, despite the simulations, in real life the odds are different. But, who has infinite time to flip infinite coins to confirm the mean value of 50% in a coin flip :)
Great professor! A slight hiccup on 23:38; I believe he meant to say if the parents are both shorter than average it is likely that the child will be taller than their parents (not average).
What strikes me the most about this lecture is that the quality of the professors at Ivy League universities is tremendously better than at average universities. I was unfortunate enough to go to the University of Arizona. There, the professors either did not care in the slightest about the students (at best) or were actively hostile to the students (at worst). Not a single professor in the 4 years I was there actually cared whether the students understood anything they said. To them, a lecture was just a job to get over with ASAP, go through the motions, and get out of there. Today, decades later, I realize the mistake I made. Had I gone to a place like MIT my education would have been exponentially better. This is something fathers are supposed to tell their sons. But when your father is an idiot you have to learn these things on your own.
A base ballbatter is a complicated example. Not independently random, player could be injured, getting divorced, loosing his house, about to be sacked or close to making his bonus. Over a season there will be more factors at work, such as different pitchers and weather conditions, more random but still not perfectly independent random. It is likely that data here will be skewed since the worst batter can do no worse than zero. A great average (above average) is 0.4. A batting average of 1.0 is theoretically possible but I doubt that it has ever been achieved over a career or even several seasons. Maybe in a single game or a one season carreer (odd to quit with that record short of serious injury or jail). It is very hard to prove that data is truely random by sampling even if it is. There are many ways though to prove that it is not random. Note; 36 Fair, 37 Europe and 37 US spins, not 35 are required. If you win on every one you will be asked to leave.
Good lecture overall but there is a bug in the code at 14:32 and 15:25 -- playRoulette should instead print 100 * totPocket / (numSpins * bet). The output in his example only looks correct because `bet` is 1. If `bet` were 2 and `numSpins` were 1, it either prints "-200%" or "7200%" (obviously you can't lose more than 100% or win more than 3600%).
4 ปีที่แล้ว
same thought. Should have divided the bet amount to calculate the percentage
Thank you Professor John guttag. You're a great teacher and reading your book --"introduction to computation and programming with python" has been a great experience thus far. Please, if you don't mind could you clarify me on this: When is an event said to be truly random? Or better still do we have truly random events? Randomness implies causal nondeterminism and from my little knowledge that's almost nonexistent. Events that yield uncertain outcomes are better delineated as predictively nondeterministic which doesn't imply that they are random but in stead reveals the limitations of our probing instruments and/ or statistical technique in unsheathing the nature of such events and correctly predicting their future states. No event to me qualifies as random, the outcome of coin flips, die throws could sufficiently be predicted to very high degrees of accuracy if only we could be patient enough to understand the physics of the processes - the coin/ die initial position, throwing/ flipping force, air drag, et cetera. So what processes are random?
Momoh Mustapha your question is very interesting and very deep. The only truly random variables that I know of are those that describe a microscopic system in Quantum mechanics. If you measure the spin of an electron for example you have a 50% chance of getting spin up or down, there's nothing we can do to predict If we're getting spin up or down before we measure It and that's not a tecnological limitation that's a limit Nature itself imposes to us.
I had the same question, I had to somehow answer it myself as I never found simple and satisfactory answers online. I first imagined a fully deterministic universe, but we humans have limited observability. Therefore, our observations would be noisy hence can be described as random because of its non-explainable nature. The hard part is to come up with specific distributions (such as uniformity) from which we would like to sample whenever we want; however, as far as I know, we humans can never find exactly such technique because confirming that a found phenomenon conforms a certain distribution takes infinite samples. We have to settle on "close enough". For your information, computational statistics often use deterministic methods to calculate samples; no randomness here.
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
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!
Read Slow and fast thinking where Daniel Kahneman explains regression to mean beautifully.... Its hard concept to fathom the way John Guttag is explaining
Three things that are wrong with this: 1.- It's not "Von Noiman" *Von Neumann* is pronounced: "Fon Noiman". 2.- The ENIAC machine wasn't John Von Neumann's but John Presper Eckert's and John Mauchly's brainchild. 3.- The "stored program computer" is an invention being attributed to Von Neumann because after Eckert had bumped into him at a train station, he asked Neumann to provide some ideas for some functions to be added to his computer, but Eckert had already intended to have a stored program in the ENIAC since he envisioned it for ballistic table computation, and only wanted Neumann's contribution on added operational functions, Neumann as was his character told Eckert he'd write a paper to explain what he though would be convenient to add to the ENIAC, the result was a 100 or so pages essay that prior to give to Eckert he distributed among colleagues and everyone who read it believed the stored program paradigm he made reference in it was his original idea, then he didn't made any attempt to correct the confusion about it.
Nice. Can I just argue something, there is always an example with coins but I don't think I have ever heard someone just adding a disclaimer that tossing a coin is not a random process. In theory, if you could start the tossing under the same initial conditions you would get the same outcome. So it is possible to get an infinite number of heads if you just manage to toss the coin the same way an infinite number of times (i.e. with the same initial conditions). I don't think that would be too difficult to achieve either. An example of a true random process is nuclear decay of radioactive atoms.
As roulette dealer I am interested in how smaller bankrolls and length of playing sessions affect these numbers. Hold percentage for Roulette is much higher than 3% in our Casino. Most likely 20%+
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.
Watching Prof. Guttah teaching is a joy. A true inspiration for those of us who also like teaching and want to do better
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.
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??
I came here for the Monte Carlo simulation but got unexpectedly thus far the best explanation for simple concepts like Variance or Standard Deviation
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****.
Unfortunately, during my studies at Bachelor and Master, I never had such great real professor. Thanks so much for sharing such great video.
this man right here is a true teacher, understands the subject topic deeply and speaks passionately
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
An instructor of the highest caliber; clear explanations, projects a seemingly universal likeable and fair personality, low intensity approach. Good hire MIT!
Some of the best explanations of statistics I’ve heard. Does a great job of breaking down concepts.
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
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.
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.
I love professors who make mistakes and make corrections accepting help from students.
Should of done better in highschool and went to MIT. This is great. A true teacher
Makes even high level material understandable to a neophyte. That's the mark of a skilled educator.
Excellent presentation. Don't know why TH-cam 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.
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.
Brilliant lecture. I can binge watch Professor John Guttag's lectures. Amazing.
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.
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
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.
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!
Isn't he the most adorable teacher ever?
Great job walking your audience through the material!
Wonderful professor. So casual but I believe what the students learn will stick with them forever.
I love these old school professors. They are true masters.
If all mathematic teachers taught like this in classes, I'm pretty sure the amount of those who grew up hating math would have been a lot less. Very clever way of teaching by giving scenarios, explaining them with mathematical concepts, without diving too quick to the expressions or formulas which not everyone is ready for.
if all mathematics teachers taught like this, nobody would know any maths
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”
Great teaching style. Small number of teachers can teach such concise and clarify. I learn a lot from the great educators.
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.
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.
He is such a great teacher on multiple topics. After this course I plan to finally take Linear Allgebra.
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
This is what is used to determine results of A/B testing folks, i had to learn this on the fly at my job
What a great introduction course that is simple to understand yet extremely powerful to student.
WANTED MORE ABOUT MONTE CARLO, but he is such an amazing teacher that I got stuck anyways!!!!
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 the sense of humour of the instructor. A great lecture indeed!
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.
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
Thank you Sire.
I hope you're okay wherever you are
Thank you Professor Guttag and thank you late Stanislaw Ulam.
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.
26:53 Great answer to make the difference between gambler's fallacy and regression to the mean clear!
Had this same lecture in PSYCH Stats class at CofC. Learned a lot and this was fun to watch again
At 8:30 he misses implications of Bayes theorem - if you observe 52 heads from 100 flips, it is still much more likely that the coin is fair than biased. Because as he mentions, there are many many more fair coins and dice our there than weighted ones. The probably you have to assess is P(52 heads | coin is fair) * P(coin is fair) vs P(52 heads | coin is biased) * P(coin is biased). Far more likely that it is fair.
My thoughts too
the frequentist approach would work too
12:47 "win some lose some, it's all the same to me"
Lemmy
It's in Monaco, the casino, I was there twice, as a visitor, and I never thought I would see it in an academic lecture. Amazing. It has just brought my memory back nothing to do with it's good or not. of course, i took a picture with it. That's why you need to go Europe. Everything is amazing.
I completely agree,But MIT is in US
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.
I wish every teacher is just like him. Then every child would get to enjoy studying. Thanks professor. Thanks for making the content available online.
Well said, agreed!!
thanks lord for these free lectures
Its a great lecture. Covering basics of statistics but doesn't really have anything to offer on Monte Carlo Simulation 😐
Ok, he is really good 33:45, how I hoped to have a prof. like him back in college.
Thank you Prof. Guttag & MIT.
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.
Extremely Based series of lectures. Top tier professor!
I had a difficult time understanding the _Gambler’s Fallacy_ , well I understood it but couldn’t fully believe it. So back in the day on a PC with a 386 processor I wrote a Basic program that flipped a coin continuously and kept track of the results. After 2 “heads” in a row I bet on tails. I won roughly 50% of the time. I then incremented the waiting period by one more flip, betting tails after only 3 heads in a row, then 4 in a row, and so forth. I came ahead after waiting 8 flips, so then I ran the 8 heads in a row routine many times to test it and of course I never came ahead again. I fully grasp that the coin has no memory but my feelings still tug at me saying _Tails is overdue!_
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.
Didn't understand any of it but I appreciate the teacher's methods. Well done.
very explanatory ways to teach ... Sir you should teach teachers ... What a teaching style!!!
I had so much more fun learning the subject with Dr. Guttag than my uni professor.
My big interest is Monte Carlo simulation and Markov chain!!!
I give this professor two thumbs up. I like his style. Good presentation also. A hardy bravo zulo to the man.
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.
such respect for these fantastic teachers
Brilliant lecture...brought me back memories of school. Just one mistake @45:46 (perhaps oversimplification - discrete random variable need not have "finite" number of possible values, it can also be "countably infinte" as in Poisson). Again, I'm not trying to be a smart-ass...but this is an important consideration
This man is really good at explaining the sense. There were no crazy sets of symbols though i got the essence of his explanation. The only downside of this is that it s NOT about monte carlo but more about some basic assumptions lying at the base of Monte Carlo
Actually you are an amazing demonstrator
Kinda rushed at the end, but i'm very fortunate to have studied probability and random processes under prof SNS of our institute, he took his sweet time to ensure that we all (class strength is 22) understand the basics of stats before moving on to analysis of Random variables.
Great lecture nonetheless, far better than the Data Science lectures we have
Love from IIITDMJ, India
Wow... fantastic lecture by Prof. Guttag... Thank you and congratulations.
As already stated a great lecture by a great lecturer. Though I be!ieve he misspoke @23.33. when he regarding "regression to the mean" said that "two parents who are shorter than the average, likely would have a child that is taller than THE AVERAGE", which (I believe) is incorrect. What I think he meant to say is that "... They are likely to have ahold that is taller THAN THEM"...
And thanks again for making this and so much other fantastic content freely available :}
Brgds
proper: denoting a subset or subgroup that does not constitute the entire set or group, especially one that has more than one element.
The roulette and coin flip needs to input other variables: maybe the next turn of the roulette the dealer spins the wheel harder or slower, or the balls shoots out of the fingers faster or slower. When you flip a coin maybe the thumb throws the coin harder or slower or you raise the hard to high and the results change. So, despite the simulations, in real life the odds are different. But, who has infinite time to flip infinite coins to confirm the mean value of 50% in a coin flip :)
Great lecture, awesome teacher. Concepts were explained really well.
it says monte carlo simulation, but it's talking about distribution, conf interval. nice teacher tho
Great professor! A slight hiccup on 23:38; I believe he meant to say if the parents are both shorter than average it is likely that the child will be taller than their parents (not average).
What strikes me the most about this lecture is that the quality of the professors at Ivy League universities is tremendously better than at average universities. I was unfortunate enough to go to the University of Arizona. There, the professors either did not care in the slightest about the students (at best) or were actively hostile to the students (at worst). Not a single professor in the 4 years I was there actually cared whether the students understood anything they said. To them, a lecture was just a job to get over with ASAP, go through the motions, and get out of there. Today, decades later, I realize the mistake I made. Had I gone to a place like MIT my education would have been exponentially better. This is something fathers are supposed to tell their sons. But when your father is an idiot you have to learn these things on your own.
he is so funny, i wish i had such professors
A good session, I'll search for the prof and watch more videos. 👍
A base ballbatter is a complicated example. Not independently random, player could be injured, getting divorced, loosing his house, about to be sacked or close to making his bonus. Over a season there will be more factors at work, such as different pitchers and weather conditions, more random but still not perfectly independent random. It is likely that data here will be skewed since the worst batter can do no worse than zero. A great average (above average) is 0.4. A batting average of 1.0 is theoretically possible but I doubt that it has ever been achieved over a career or even several seasons. Maybe in a single game or a one season carreer (odd to quit with that record short of serious injury or jail).
It is very hard to prove that data is truely random by sampling even if it is. There are many ways though to prove that it is not random.
Note; 36 Fair, 37 Europe and 37 US spins, not 35 are required. If you win on every one you will be asked to leave.
Love your Data Table hack at 2'. Thank you for that!
The explanation is clear, his lecture is great!
this is a concept everyone in research has to know. Amazing teacher explains the history and concept in a nice way. Great teacher
Good lecture overall but there is a bug in the code at 14:32 and 15:25 -- playRoulette should instead print 100 * totPocket / (numSpins * bet).
The output in his example only looks correct because `bet` is 1. If `bet` were 2 and `numSpins` were 1, it either prints "-200%" or "7200%" (obviously you can't lose more than 100% or win more than 3600%).
same thought. Should have divided the bet amount to calculate the percentage
He is the best! Such a pleasure and luck to be able to access this lecture.
Thats the best lecture I have ever seen.
most gracious creature alive... this one is.
Thank you Professor John guttag. You're a great teacher and reading your book --"introduction to computation and programming with python" has been a great experience thus far. Please, if you don't mind could you clarify me on this: When is an event said to be truly random? Or better still do we have truly random events? Randomness implies causal nondeterminism and from my little knowledge that's almost nonexistent. Events that yield uncertain outcomes are better delineated as predictively nondeterministic which doesn't imply that they are random but in stead reveals the limitations of our probing instruments and/ or statistical technique in unsheathing the nature of such events and correctly predicting their future states. No event to me qualifies as random, the outcome of coin flips, die throws could sufficiently be predicted to very high degrees of accuracy if only we could be patient enough to understand the physics of the processes - the coin/ die initial position, throwing/ flipping force, air drag, et cetera. So what processes are random?
Momoh Mustapha your question is very interesting and very deep. The only truly random variables that I know of are those that describe a microscopic system in Quantum mechanics. If you measure the spin of an electron for example you have a 50% chance of getting spin up or down, there's nothing we can do to predict If we're getting spin up or down before we measure It and that's not a tecnological limitation that's a limit Nature itself imposes to us.
I had the same question, I had to somehow answer it myself as I never found simple and satisfactory answers online. I first imagined a fully deterministic universe, but we humans have limited observability. Therefore, our observations would be noisy hence can be described as random because of its non-explainable nature. The hard part is to come up with specific distributions (such as uniformity) from which we would like to sample whenever we want; however, as far as I know, we humans can never find exactly such technique because confirming that a found phenomenon conforms a certain distribution takes infinite samples. We have to settle on "close enough". For your information, computational statistics often use deterministic methods to calculate samples; no randomness here.
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...
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!
Read Slow and fast thinking where Daniel Kahneman explains regression to mean beautifully.... Its hard concept to fathom the way John Guttag is explaining
Three things that are wrong with this:
1.- It's not "Von Noiman" *Von Neumann* is pronounced: "Fon Noiman".
2.- The ENIAC machine wasn't John Von Neumann's but John Presper Eckert's and John Mauchly's brainchild.
3.- The "stored program computer" is an invention being attributed to Von Neumann because after Eckert had bumped into him at a train station, he asked Neumann to provide some ideas for some functions to be added to his computer, but Eckert had already intended to have a stored program in the ENIAC since he envisioned it for ballistic table computation, and only wanted Neumann's contribution on added operational functions, Neumann as was his character told Eckert he'd write a paper to explain what he though would be convenient to add to the ENIAC, the result was a 100 or so pages essay that prior to give to Eckert he distributed among colleagues and everyone who read it believed the stored program paradigm he made reference in it was his original idea, then he didn't made any attempt to correct the confusion about it.
23:32 If the parents are shorter than average then the child will likely be taller than the parents, but not taller than average.
He probably just misspoke.
yup. It would be gambler's fallacy to say that.
caught that too. just a slip of the tongue.
Yeah, slip of the tongue, one of those is not worth to correct at the momento because are understood right away
I think he meant the average of their height
Nice. Can I just argue something, there is always an example with coins but I don't think I have ever heard someone just adding a disclaimer that tossing a coin is not a random process. In theory, if you could start the tossing under the same initial conditions you would get the same outcome. So it is possible to get an infinite number of heads if you just manage to toss the coin the same way an infinite number of times (i.e. with the same initial conditions). I don't think that would be too difficult to achieve either. An example of a true random process is nuclear decay of radioactive atoms.
As roulette dealer I am interested in how smaller bankrolls and length of playing sessions affect these numbers. Hold percentage for Roulette is much higher than 3% in our Casino. Most likely 20%+