Regression to the meme… muahaha can't handle that much memes. Thanks for the course, it was awesome. You just made a small mistake while talking about the kid/parents reductin to the mean, but I?ll let you check that out.

"when they look at a political poll and they see how many votes somebody is expected to get" well apparently none of the numbers on those polls mean anything anyway.

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.

A lot of people seam to be liking this presentation. It seams a lot of people have not heard about the concept as it seams so watered down it is painful. I was expecting more from MIT course.

His thinking is very organized. wow…crazy. no kidding, God doesn't play dice. the thing is there is no chance but there is accident. oh great, probability…nah, god wouldn't do that

one very big looser. In presentation he show examples that has no realtion with Monte Carlo! He had two coins, then USA and EU Rulets, then his object class. No sens.

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.

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

This guy made a lot of errors. One of the earliest ones is at 3:25 when he attempts to define Monte Carlo simulation. He mentions an unknown quantity but that is incorrect. Suppose for example I wanted to simulate a known quantity, perhaps just to confirm that my programming skills are still good. So I would have someone good in math compute the exact answer using the "paper and pencil" method, and I would use a computer to simulate it to get an approximation. According to his definition, I would NOT be doing Monte Carlo simulation because the value is known.

To take that concept even farther, suppose I try to simulate an "unknown" quantity but unbeknownst to me, someone else already has the correct exact answer. According to his definition, that is also NOT Monte Carlo simulation. He didn't specify who the quantity is unknown to in the definition, therefore it is not a good definition because it is ambiguous. If you Google Monte Carlo simulation, you will see MUCH better definitions of it then the crappy definition presented here in this lecture.

Another big problem with his definition is he states the random sample tends to exhibit the same behavior as the population from which it is drawn. That is NOT true if the population has some super rare occurrence we are looking for such as 1 out of 1 quintillion. Now suppose 2 people, each with a computer, can simulate 1 trillion random samples. Since they are still 6 orders of magnitude below the full population size, it is VERY likely that they will both come up with 0 "hits" and possibly falsely concluding that there are no good "hits" (cases they are looking to count). Even if they reran the simulation 10 times each, then would still be 5 orders of magnitude below the population size which is 2/100,000 sampling which is not enough to get accurate results. Someone might say well 0 is very close to the real expected value (and that is true), but my point is by getting 0 "hits", no information is given about if a "good" event (the ones we are trying to count up exactly) even exist.

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.

You will be surprised to see that the circumference's constant Pi empirically approaches more to 3.1446… than 3.1415… In fact, the real value of the first 1000 significant decimal places of Pi are as follows:

Where Phi is the golden number, or the golden ratio of creation.

This is the only value for Pi that harmonizes the area and the perimeter for spheres and cubes, making them equivalent to each other and fulfilling the universal law of conservation of mass and potential energy of an object during its geometric transformation!

Thanks for the very informative video! Question – Prof. Guttag seems to be using the z critical value of 1.96 while he only knows the variance of the sample derived from his simulation. Shouldn't he be using a T critical value with the appropriate number of degrees of freedom for the sample size? Is that correct, or does he somehow know the population standard deviation?

I think he should remind students, that these systems have no memory, that is, each spin is an independent sample. Plenty of real systems are a combination of both deterministic (think Newton's laws) mixed with a noise term that is probabilistic.

The only math class in college I failed to "ace" was Probability and Statistics. It was taught by a gay, civilian instructor at the Naval Academy. He often voided my correct answers on tests and said with a lisp, "I rejected your answers because you used your silly, high school methods." A trip to the department chair resulted in a final grade of "C" for the semester. Never knew what really made the professor hate me with such vigor.

the gamblers falacy still confuses me with what the proff said next on extreme event – like the questin asked by the student, same question i happen to have – aren't both independent event cases

I still don't get how regression to means is consistent with the independence of events. Isn't the fact that the first 10 spins resulted in red (extreme) affect the next 10 spins (make it less likely to be as extreme)? Can someone pls explain that?

Roulette is not about spins , roulette is about being somewhere . This professor has obviously never actually been anywhere , never experienced anything. sorry , imho !

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).

Great video, thanks MIT. Just a small observation: Mon-tea Carlow?

Why am I surprised, Americans can't pronounce anything foreign.

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

what code is in the roulette example… is that C?

Excellent lecture

Set playback speed to 1.25 or 1.5. You’re welcome.

18:28 law of large numbers

Demonstrations made simple

Regression to the meme… muahaha can't handle that much memes. Thanks for the course, it was awesome. You just made a small mistake while talking about the kid/parents reductin to the mean, but I?ll let you check that out.

Is the camera automated? Or is it hand-operated by human?

Thanks, great lecture. Though he brought up Monte Carlo, he didn't talk about the simulation?

bookmark 12:46

Thanks for this video, very easy to understand

Great lecturer! Amazing!

He talks like Bill Gates. Very similar gestures. And I like it. 🙂 I want to listen him.

Why don't they show the screen the prof is pointing to. What's the point of this video?

"when they look at a political poll and they see how many votes somebody is expected to get"

well apparently none of the numbers on those polls mean anything anyway.

The true meaning of the teacher!

most gracious creature alive… this one is.

6:47 yeah gotta make sure those MIT students don't try to rob you of $20 bucks!

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.

dopey

How is this related to monte carlo tree search?

Amazing explanation

A lot of people seam to be liking this presentation. It seams a lot of people have not heard about the concept as it seams so watered down it is painful. I was expecting more from MIT course.

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

no number is close to infinite

i love you sir. you are a great teacher.

A Monte Carlo got pooped with $.and it brought suspicions. (they went on the tell the story)

His thinking is very organized. wow…crazy. no kidding, God doesn't play dice. the thing is there is no chance but there is accident. oh great, probability…nah, god wouldn't do that

Sounds best at 1.5x speed.

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

Great job! Bayesian FTW!

Thank you! Amazing teacher.

good content but best watched speeded up slighly

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

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

I wish my professor was like this guy over here.

one very big looser. In presentation he show examples that has no realtion with Monte Carlo! He had two coins, then USA and EU Rulets, then his object class. No sens.

16:17… "a positive 28 percent". Better check again. I see a negative 28 percent.

30:58. 35 times to get the exact right answer. Better think again. For fair roulette, you would not get even money with 35 simulations.

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.

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

What are the odds I would click an irrelevant video recommended by Youtube?

This guy made a lot of errors. One of the earliest ones is at 3:25 when he attempts to define Monte Carlo simulation. He mentions an unknown quantity but that is incorrect. Suppose for example I wanted to simulate a known quantity, perhaps just to confirm that my programming skills are still good. So I would have someone good in math compute the exact answer using the "paper and pencil" method, and I would use a computer to simulate it to get an approximation. According to his definition, I would NOT be doing Monte Carlo simulation because the value is known.

To take that concept even farther, suppose I try to simulate an "unknown" quantity but unbeknownst to me, someone else already has the correct exact answer. According to his definition, that is also NOT Monte Carlo simulation. He didn't specify who the quantity is unknown to in the definition, therefore it is not a good definition because it is ambiguous. If you Google Monte Carlo simulation, you will see MUCH better definitions of it then the crappy definition presented here in this lecture.

Another big problem with his definition is he states the random sample tends to exhibit the same behavior as the population from which it is drawn. That is NOT true if the population has some super rare occurrence we are looking for such as 1 out of 1 quintillion. Now suppose 2 people, each with a computer, can simulate 1 trillion random samples. Since they are still 6 orders of magnitude below the full population size, it is VERY likely that they will both come up with 0 "hits" and possibly falsely concluding that there are no good "hits" (cases they are looking to count). Even if they reran the simulation 10 times each, then would still be 5 orders of magnitude below the population size which is 2/100,000 sampling which is not enough to get accurate results. Someone might say well 0 is very close to the real expected value (and that is true), but my point is by getting 0 "hits", no information is given about if a "good" event (the ones we are trying to count up exactly) even exist.

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.

If I went to MIT and paid money and had this professor, I would ask for my money back.

He reminds me of Homer Simpson!

You will be surprised to see that the circumference's constant Pi empirically approaches more to 3.1446… than 3.1415… In fact, the real value of the first 1000 significant decimal places of Pi are as follows:

3.1446055110296931442782343433718357180924882313508929506596078804047281904892436548476515566340325422595160489765784452235018414818847721014580011238453531659969963123944614330895602447224013851373131501976513250168886718624703787313359434961827623424884419929696155384972370055738355223468907453641698014204369640943817463269453772663395414398903709747924249157889297802333906441767084172268827515380592173997026423023851194242244081992685573437499657987944611238911016107551387207358281657572181883283516336139159023992353694690024845170044516992781985453761660350519720800718970644071409668757828437246633219026822340025407725353821526637922670369853908547616452436921953232107331044735525949802311653660216067204763773809792592558234876801085351187469338952701406443781568048374310664077223404139952343917185562861066240175976669357645765480751311418697916950736513185281927426366978973484884146736468201663051035828968367940082442276210780785802770252790792921943126282608098219773061432750203769…

Pi = 4/sqrt((1+sqrt(5))/2) = 4/sqrt(Phi)

Where Phi is the golden number, or the golden ratio of creation.

This is the only value for Pi that harmonizes the area and the perimeter for spheres and cubes, making them equivalent to each other and fulfilling the universal law of conservation of mass and potential energy of an object during its geometric transformation!

he is so funny, i wish i had such professors <3

Thanks for the very informative video! Question – Prof. Guttag seems to be using the z critical value of 1.96 while he only knows the variance of the sample derived from his simulation. Shouldn't he be using a T critical value with the appropriate number of degrees of freedom for the sample size? Is that correct, or does he somehow know the population standard deviation?

Thanks for this video. Amazing explanation!

this proff. to funny

I think he should remind students, that these systems have no memory, that is, each spin is an independent sample. Plenty of real systems are a combination of both deterministic (think Newton's laws) mixed with a noise term that is probabilistic.

Sorry mate… Alan Turing was way ahead of Johnny von N.

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

Kjekken

i love this guy

The only math class in college I failed to "ace" was Probability and Statistics. It was taught by a gay, civilian instructor at the Naval Academy. He often voided my correct answers on tests and said with a lisp, "I rejected your answers because you used your silly, high school methods." A trip to the department chair resulted in a final grade of "C" for the semester. Never knew what really made the professor hate me with such vigor.

Watched this at 1.5 speed and I still was bored AF. To many stupid unfunny jokes.

TO the offline voice : such a shame, that now the MIT has to beg on the internet, to be able to finance its own courses…

I didnt c monte carlo methods….

14:32 Either his understanding of the FairRoulette script is not good, or he is misspeaking.

totPocket is the amount won, not the number you get right,

betPocket does not return 0, it returns the negative bet

playRoulette is missing the final parameter "toPrint" in the definition on the slide

playRoulette's expected return does not correctly calculate because it does not use bet size

40:45 code is incomplete and looks wrong, too. 🙁

38:40 Fuck you Eric!

Beautifully done.

Stanislaw Ulam the real father of the thermo nuclear device, not really Edward Teller who based the design on Ulam's X-ray trick to achieve fussion.

This professor reminds me of Bill Gates. Anybody?

Yo

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.

a lecture well given

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.

this guy is good!

at 23:37 shouldn't it be "taller than parents" instead of "taller than average"?

Very nice video, but watch it at 1.25x speed

the gamblers falacy still confuses me with what the proff said next on extreme event – like the questin asked by the student, same question i happen to have – aren't both independent event cases

do they get candy whenever they ask question? lol

Very good teacher..

great video on statistics but i thought this was going to teach monte carlo simulations

Check out my free advanced risk monte carlo simulator. Coded it by myself, would love to hear what you think: niclashummel.com/risk-simulator

Zoom out and quit trying to follow him as he paces. Thanks.

Not what I was looking for, however very interesting and useful video, I will see more, thanks

Truly a great professor.. we need more teachers and professors like him.

what a stupid video. It doesnt even use monte carlo.

I still don't get how regression to means is consistent with the independence of events. Isn't the fact that the first 10 spins resulted in red (extreme) affect the next 10 spins (make it less likely to be as extreme)? Can someone pls explain that?

lol! 33:50

THAT's how you teach intelligent but sleep-deprived teenagers!

Oh my god. In my country there are none of teacher like this

oh, bring me back to Dr S.C. Arora , faculty of Mathematics from HansRaj College, Univ of Delhi lectures from '78, '79 -:)

Roulette is not about spins , roulette is about being somewhere . This professor has obviously never actually been anywhere , never experienced anything. sorry , imho !

Good lecture, but I was expecting more Monte Carlo (Latin Hypercube, …) than elementary statistics.

"A million is getting close to infinite" 😂

Thank you, Prof. Guttag!

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).

20:20 if the baseball hitter hit with a probability > .5 then of course it is probable he will hit one per each attempt

49:00 likelihood not equal probability

awesome

The failed slingshot attempt made the prof 300% more likable that he already was to begin with.

Thanks. It did help!

The best way to explain variance formula! <3

1.25 speed