These introductory lessons are sorta like a dream come true. I'm uber-glad to know that sir Taleb is looking out for the needs of us readers who lack a proper understanding of the complexities of probability. I remember first starting off with Taleb's work with a curious interest to know what a Black Swan was, ending up reading the entire Incerto collection. Truth be told, I couldn't understand many of his teachings. But I understood the spirit of it all, his adamance... his pissedoffness, which in turn, convinced me to know more. I have a lot more to know and I'm sure that these lessons, shared by the hero himself, are going to ease out my learning process.
This guy is INCREDIBLE. I keep hearing about his book I need to read it. This is the second video I watched, now I'm starting to understand what "standard deviation" really means (and why it's not always that useful). He makes it so crystal clear.
Taleb, that was great! Thanks for making your knowledge closer to people who are not technical, in an intuitively way of understanding, so we don't fall into domain dependence. ;) As a teacher, your video made me remember the good old times I didn't wear black shirts to go to work ! :D
Nassim Nicholas Taleb is the best teacher,I never had. He's the reason I decided to switch from engineering to business and management. It's a privilege to learn from him and his books,and mark my word-Dr. Taleb is going to be the most quoted Philosopher of the 21st century.
Wonderful! Looking forward to this series! Have: three Antifragiles( to share with friends) PaperBack Incerto Set, Hardback Incerto Set, Skin In The Game, Dynamic Hedging, and Statistical Consequences of Fat Tails, All next to my Mandelbrots! Cheers!
Excellent. I tell this to everyone who is interested in tail hedging with options to expect the markets to be quieter than you think. Don't be Afraid to sell butterflies
It’s easier to remember that “fat tails” imply that remote events from the mean happen less often if you keep in mind the fact that “lepto” means light in Greek, from there you can remember that the tails are more lightly sprinkled with data points (even if they are further from the mean than a normally distribution would suggest)
Thanks for sharing this simple explanation of and the importance of fat tails. Now I am concerned. Specifically, I'm concerned to know when I'm dealing with a fat tail scenario because I need to know that some rules or concepts are inapplicable. Very interesting.
Wow. Thanks. I just got you Incerto collection after seeing your discussion with Stephen Wolfram. I’m just starting Fooled by Randomness, and I like it so far. This will be a good supplement.
Taleb is so wise - he is a Mathematician, a Historian, a Philosopher and above all he makes all the wise connections between these domains!. I am a Canadian- Romanian and I was surprised to see the historical connections Taleb made about the history of the Ottoman Empire and its influence in the Eastern Europe and Middle East... He is a "rara avis" - a rare bird in Latin - otherwise a super rare extraordinary thinker who is willing to share knowledge with us for free. Some comments I red were representing a lack of understanding of what Great Thinker of our Times is...
I think part of confusion is picking the approach for drawing the graph of distribution. Lets say we take money in bank account for example. If we divide people in pay brackets and then we draw their frequencies distribution would probably be normal or normal like and in such case fat tail would be more cases of extreme or very high earners. But if we for the example show not only number of people in bracket but also sum of money in their accounts, then you can say goodbye to normal distribution and few outliers would bend distribution heavily in one direction and we would get what mr. Taleb is talking about.
Bonjour Professeur Nassim Taleb ! Thank you very much for this introduction. Could you make a short video (not too technical) about how to measure the dependence between X and Y if X and Y are fat tails ? (given that standard regression is not valid in this case) Thank you very much in advance!
WRT LLMs you may be interested in the concept of "model collapse", where models that are trained on synthetic data (that other LLMs create) start to avoid the statistical properties of the tails.
4:51 - "The professionals who made these mistakes, what they share in common, is that their mind has a clarity of a New York sewer the day after thanksgiving, so you can imagine the clarity of mind of the professors, so they don't get it, they have so much junk in their head, that they don't get the essential, that if you accept the fat tail... then the regression... the fat tail is not informative." The sarcasm, ha
NNT will singlehandedly create a new class of statisticians. I love his "if you know" remarks. It's so common for people to arrogantly claim "I know" while their behavior maps to the complete opposite. If you "know" but do the opposite, you merely intellectually know. But that knowledge hasn't become a part of you.
Awesome video! I would be interested in how the fat tails on this example relate to the fat tails of the Student t-distribution, and if that can make up for some of the normal distribution’s shortcomings.
Student t helps improve predictions when sampling Gaussian processes, like human height. Many processes cannot be described by Gaussians, like income. If you didn’t know Gates and Bezos existed your student t estimate of income would be way off unless you happen to get one of those high income people in your sample-a rare event!
Genius video, I discussed this recently, people argued that high IQs are more commom than you would think in a normal distribution because the normal distribution actually had a fat tail. This is a cyclical logic phallacy, you assume that intelligence is normally distributed in order to measure it with a test, therefore you can't use the measurement made on that premise to conclude that this distribution is not normal, because even if intelligence is not, the distribution of the test results would be normal. A non normal IQ distribution only means bad standardization. And if you assume fat tail you can't keep using standard deviation the way you use in normal distributions, you would need a new mathematical approacha.
I would be grateful if Prof. Taleb would answer a question that might be both naïve and technical. I understand that probabilities can represent frequency of occurrence (as in coin toss) or degree of belief (as in a horse race). In estimating probability distribution from observed data on a given variable and computing statistical measures like mean, standard deviation etc., all observations are equally weighted, which is tantamount to assuming that the probability with which each observation occurs is its frequency of occurrence. Would you conclude that computing statistical measures would not be valid for variables where the probability is more likely to represent a degree of belief than frequency of occurrence? Would you further say that market participants assign probabilities to possible realizations of various financial and economic variables based on degree of belief rather than frequency of occurrence? Does the idea of estimating probability distribution make sense when probabilities are degree of belief? If not, how would empirical work be done when probabilities are degree of belief?
Can't answer for Taleb but I know he's a fan of Keynes' Treatise on Probability in which Keynes suggest rules that can still apply for "non-numerical" probabilities as he calls it. They are still ordered, and that can be exploited. You can also use laws of probability such as Bayes rule to ensure your estimates a logically consistent when you have several estimates that relate to each other. You will have less precision but more rigor.
If the size of the area under the curve increases with fat tail for extreme events, doesn’t that mean the probability goes up? What am I missing? Or is the point that the area doesn’t change because we are talking about 1 standard deviation from the mean?
Yes, they are usually compared to the Gaussian or Exponential distribution's tails. I'm confused by his phrasing. He says that in a fat tailed distribution events do not occur more often in the tail, I think he means wrt to the bulk of the fat-tailed distribution (-sigma, sigma) rather than a Gaussian distribution's tails. IMO he should have definately explained the relation to Gaussian dist tails.
@@WillyCSchneider events in the tail are rare; seldom seen. But when you do see one, it has a huge effect on how you describe the distribution. Because it’s rarely seen, you get into trouble making predictions when you mistakenly use tools made for thin (Gaussian) tails on fat tailed processes. His classic example, “never cross a river that is on average 4 feet deep.” That description might lead you to think you could walk across until you realize there are many possibilities of depth that could have sections way over your head yet still average out to 4 feet.
@@peterevans202 I don't understand this "huge effect on the distribution". What I would expect is that if you compare the distribution with and without the rare event that you would see completely different moments.
@@peterevans202 Yes, I understand this. However, a distinction should be made between fat-tails and long-tails. Given Taleb's explanation I think he is mostly referring to long-tails, given that in a fat-tailed distribution extreme outcomes take place more often than extreme outcomes in a Gaussian distribution. In a long-tailed distribution the tails are relatively thin however theres a non-negligible probability of having a really extreme event (i.e. Taleb's black swans)
@@andraro87 The usual situation is that you don’t know what distribution you’re dealing with. You make an estimate based on what you observe. With fat tails, things can look Gaussian at first, but when the significant event occurs all of the moments shift as you stated. The underlying distribution didn’t change, but your understanding of it did.
Dear Professor firstly thank you so much for your kind explanation. May I very kindly clear a conundrum that I have ? Here in this video you indicated clearly that as we fatten the tails there will be MORE observations in the intermediate region and LESS in the extreme region. Why is it not vice-versa ?
@@nntalebproba Noted Professor. Thank you so much for your kind reply Professor Taleb. I always thought of it to be the opposite, so thanks for giving me this important insight. Appreciate it a lot.
Speaking about economists, is the GDP statistic fat tailed? It gives higher weights to good and services with higher prices and lower (or no) weights to good and services with lower (or no) prices. Is the most important statistic economists use statistically flawed?
They use weighted indices to make the numbers look good,no doubt. But also if they were to weigh all sectors equally, It would make the figures more flawed than the current system In the eyes of the suits. In general Growth projections,budget allocation,governing policies,loan defaults as well as frequency of corruption charges are the more interesting figures ,for me personally. But what do I know.
Can anyone explain why with fat tails the extreme events are less likely? With conventional understanding, the area under the PDF curve for fat tailed distribution is larger given any x (compared with normal), meaning it's more likely to occur right? How does one then take into account the impact of the unlikely, would this be reflected in the PDF?
I may be wrong but,think of it this way: if the event is less likely its impact is gonna be more. And then draw the natural conclusions to your problem from there on.
The impact is not in the PDF since impact and probability are different things. You can model impact/pay-off as a function of a random variable (which is a new random variable).
You are correct. Taleb's explanation is incomplete, and ironically, a cause for confusion. He has broadened his definition of the "tails" to +/- 1 deviations in this video, which supports the point he's making. It's worth noting that his previous work (fooledbyrandomness.com/DarwinCollege.pdf ) defines the "tails" as +/- 2 deviations. As you move further out along either extreme on the graph (positive or negative), you eventually reach a point where extreme events for a fat tailed distribution become more likely (more frequent) relative to the normal distribution. This is what people mean when they talk about very extreme events being more common in fat tailed distributions. Taleb has said so himself in the paper I linked to above: "When we fatten the tails we have higher peaks, smaller shoulders, and *higher incidence* of very large deviation." Here's a great example, which compares the Gaussian and Laplace distributions: www.vosesoftware.com/riskwiki/images/image15_632.gif I hope this helps.
@@honest_math From a mathematical point of view you can construct distributions to show all kinds of behaviour. I suppose what Taleb is getting at is that when modelling common fat tailed phenomena you often have that property. For instance putting out small fires immediately in California results in more undergrowth and larger occasional fires. Similarly FED intervention on the stock market results in less volatility most of the time and enormous crashes occasionally.
@@DanielJanzon My point is that people are *not* wrong to say that fat-tailed distributions result in more frequent extreme events, as Taleb suggests. That's literally the etymology of the term: fat tails refers to thicker ends further along the distribution curve. This results in more area under the curve, and thus a higher frequency of occurrence. Taleb himself has said as much (see my previous citation).
He's a genius, because of him I left data science and statistics because they are absurd in prediction of future I was safety Engineer you know... there is no need for predicting future events this idea is insane! I was suspected but didn't go deep in math like him! All we need is more technology protect us and managing our society based on domain knowledge and intuition about that guiding by deterministic science (being antifragile), believe me I was working on industrial accidents in railway I was fighting with people and managers to convince them mathematics of uncertainty (statistics) does work...! I couldn't believe that I'm saying this: they're just playing symbols...
obviously and expert cos he can draw a perfect curve... Question I'd ask, intuitively one thinks the tail should have MORE observations when we say 'fat tail'. If I understand it correctly though, assuming the same 'curve', effectively we're saying a fat tail implies 1σ is 'wider' hence fewer observations in the tails
Hello everyone! I'm new to statistics and probability, in a mathematical sense, but I enjoy pondering things philosophically. My question is, when do fat tails come into play? Like, in a hurricane-prone area there are insurance calculations... do they take place there? In finance I see how the effects of them NOT being taken into consideration --- crashes, Bob Rubin trades, etc.. --- but when ARE they properly, if at, accounted for. Are they ever accounted for? Can they be conceptualized in the abstract? I didn't understand the practicality of the "take a bunch of people with no money + Bill Gates" example, because why would someone be measuring money with all these people who have no money. Please let me know if anyone understands my question. Thank you to all, and Taleb specifically for posting this.
For a layperson like myself, the nomenclature is counterintuitive. "Long tails" hold many observations while "fat tails" don't have many observations but some are a long distance from the median. It sounds backwards.
![Nassim Taleb - The Secret Rule That RUNS The WORLD [w/ Naval Ravikant]](/img/1.gif)
In university I learned only to remove "outliers". What I learned later is that sometimes the outlier is all that matters.
brilliant
Great way to summarize it
well said!
Learned the same thing. Real life isn’t like that though.
Depends. It works great for the problems without a fat tail.
Tutored by Nassim Taleb himself..you gotta love the internet!!
yad ana gebt el gShock
@@JohnWick-xd5zu 💃💃
I want to contact nissam taleb for investment plz provide me his contact
He "hates" Gaussians but he draw them so quickly and precisely 😆😮✅
The clarity of the NYC sewer system the day after Thanksgiving. I laughed out loud.
These introductory lessons are sorta like a dream come true. I'm uber-glad to know that sir Taleb is looking out for the needs of us readers who lack a proper understanding of the complexities of probability. I remember first starting off with Taleb's work with a curious interest to know what a Black Swan was, ending up reading the entire Incerto collection. Truth be told, I couldn't understand many of his teachings. But I understood the spirit of it all, his adamance... his pissedoffness, which in turn, convinced me to know more. I have a lot more to know and I'm sure that these lessons, shared by the hero himself, are going to ease out my learning process.
Yesss more Nassim Talebs technical presentations.
Thank you Nassim, for all your work.
Gold. Keep going. Please, just empty my mind of statistics and let me start again with clarity.
How come I've found out about this channel just now, what a treasure!
Very nice introduction. Wish you an excellent whatever, weekend, too!
This guy is INCREDIBLE. I keep hearing about his book I need to read it. This is the second video I watched, now I'm starting to understand what "standard deviation" really means (and why it's not always that useful). He makes it so crystal clear.
This is the most practical and clear explanation I have ever heard of a thick/fat tail. Thank you!
nassim am from aleppo syria, stumbling on your books "saved my life" !
Taleb, that was great! Thanks for making your knowledge closer to people who are not technical, in an intuitively way of understanding, so we don't fall into domain dependence. ;) As a teacher, your video made me remember the good old times I didn't wear black shirts to go to work ! :D
Learning more useful information from your videos than my finance/econ degree and CFA has provided me. Please, keep going!!
Thank YOU for posting these 'basic' videos! It's SINCERELY appreciated and very educational.
I'm really enjoying these presentations. I can't wait to see how they progress.
Nassim Nicholas Taleb is the best teacher,I never had. He's the reason I decided to switch from engineering to business and management.
It's a privilege to learn from him and his books,and mark my word-Dr. Taleb is going to be the most quoted Philosopher of the 21st century.
Back at it again with the over the shoulders sweater!
Yea Nissan - just stumbled on this series of lectures - thank you. Very much fun. I have your set of books of course. Keep up the excellent work.
"Thank you very much and have an excellent whatever" :) Thanks for the introductory videos! Great content!
These are absolutely wonderful. So very thankful to be taught by you sir.
Looking forward for the rest of the series. شكراً
This perspective is so interesting. Please keep making these videos!
Thank you for producing this series.
Thank you. Really enjoying the short video format.
Really glad that you’re having this series!
Nassim, Thank you for starting the channel.
Chalk boards are deep Lindy.
Results over presentation.
Taleb.
Wonderful! Looking forward to this series! Have: three Antifragiles( to share with friends) PaperBack Incerto Set, Hardback Incerto Set, Skin In The Game, Dynamic Hedging, and Statistical Consequences of Fat Tails, All next to my Mandelbrots! Cheers!
شكرا جزيلا . ننتظر المزيد في مفاهيم الاحصاء والاحتمالات!
Thank you for the series!
Will be patiently waiting for more episodes!
Hey Nassim, thank you for offering your wisdom and knowledge to the world. I look forward to the content
Wow what a coincidence. I just got his book today and here I am watching him talk about it. The internet is so dam cool!
Taleb himself is the embodiment of the fat tail of living wisdom on this planet:)
Absolutely, Taleb never fails to impress.
Awesome begining, very didactic.
Absolutely loving these. So excited about what knowledge is about to be dropped on us.
Excellent. I tell this to everyone who is interested in tail hedging with options to expect the markets to be quieter than you think. Don't be Afraid to sell butterflies
Thank you for doing this course. I have benefited greatly by following your principles.
Your intellect is only matched by your sweater collection good sir.
It’s easier to remember that “fat tails” imply that remote events from the mean happen less often if you keep in mind the fact that “lepto” means light in Greek, from there you can remember that the tails are more lightly sprinkled with data points (even if they are further from the mean than a normally distribution would suggest)
Thanks for sharing this simple explanation of and the importance of fat tails. Now I am concerned. Specifically, I'm concerned to know when I'm dealing with a fat tail scenario because I need to know that some rules or concepts are inapplicable. Very interesting.
Wow. Thanks. I just got you Incerto collection after seeing your discussion with Stephen Wolfram. I’m just starting Fooled by Randomness, and I like it so far. This will be a good supplement.
Taleb is so wise - he is a Mathematician, a Historian, a Philosopher and above all he makes all the wise connections between these domains!. I am a Canadian- Romanian and I was surprised to see the historical connections Taleb made about the history of the Ottoman Empire and its influence in the Eastern Europe and Middle East... He is a "rara avis" - a rare bird in Latin - otherwise a super rare extraordinary thinker who is willing to share knowledge with us for free. Some comments I red were representing a lack of understanding of what Great Thinker of our Times is...
I think part of confusion is picking the approach for drawing the graph of distribution.
Lets say we take money in bank account for example. If we divide people in pay brackets and then we draw their frequencies distribution would probably be normal or normal like and in such case
fat tail would be more cases of extreme or very high earners. But if we for the example show not only number of people in bracket but also sum of money in their accounts, then you can say goodbye to normal distribution and few outliers would
bend distribution heavily in one direction and we would get what mr. Taleb is talking about.
Thanks for the videos. It will be nice if the camera can be looking down or same as eye level instead of looking up.
good video. did not know about that distinction between regular and fat tailed distributions
Bonjour Professeur Nassim Taleb ! Thank you very much for this introduction. Could you make a short video (not too technical) about how to measure the dependence between X and Y if X and Y are fat tails ? (given that standard regression is not valid in this case) Thank you very much in advance!
Coming.
WRT LLMs you may be interested in the concept of "model collapse", where models that are trained on synthetic data (that other LLMs create) start to avoid the statistical properties of the tails.
4:51 - "The professionals who made these mistakes, what they share in common, is that their mind has a clarity of a New York sewer the day after thanksgiving, so you can imagine the clarity of mind of the professors, so they don't get it, they have so much junk in their head, that they don't get the essential, that if you accept the fat tail... then the regression... the fat tail is not informative." The sarcasm, ha
Thank you for transcript this part ro me, im not english native.
haha i was thinking the same thing!!!!
funny! we have identical interests based on your youtube subscriptions :D
Thanks a lot. Very clear and useful information
Love these. Please make more.
At your service
Thank you for the quick, but valuable class.
Thanks Nassim for doing this, this is legendary !
Looking forward to the next lesson
NNT will singlehandedly create a new class of statisticians. I love his "if you know" remarks. It's so common for people to arrogantly claim "I know" while their behavior maps to the complete opposite. If you "know" but do the opposite, you merely intellectually know. But that knowledge hasn't become a part of you.
The best one he's made.
3:10 to 3:20 Could some one explain what fattening the tail means with an example?
I get so warm and fuzzy when he refers to us as friends
I also got warm and fuzzy when he said, have an excellent whatever
"clarity of a New York sewer after thanksgiving" NNT
Thank you for this series Nassim!
Very informative, first time I could fully understand the idea XD
The best! Thank you for this one.
Please continue doing those videos. I was to say this one just after 2 days after the previous
Great! I want to improve my knowledge about this topic. Thanks Nassim!
Wow~ Thank you for your introductory series.
Thank u Taleb.. practicing quant at bank and would like to translate this to my work
Wouldn't a better term be thin-long tails to describe few observations of gigantic magnitude? Love the clear videos! Thank you
Yeah, I think he has them mixed up
Awesome video! I would be interested in how the fat tails on this example relate to the fat tails of the Student t-distribution, and if that can make up for some of the normal distribution’s shortcomings.
Student t helps improve predictions when sampling Gaussian processes, like human height. Many processes cannot be described by Gaussians, like income. If you didn’t know Gates and Bezos existed your student t estimate of income would be way off unless you happen to get one of those high income people in your sample-a rare event!
Thanks for sharing your wisdom professor!
Genius video, I discussed this recently, people argued that high IQs are more commom than you would think in a normal distribution because the normal distribution actually had a fat tail. This is a cyclical logic phallacy, you assume that intelligence is normally distributed in order to measure it with a test, therefore you can't use the measurement made on that premise to conclude that this distribution is not normal, because even if intelligence is not, the distribution of the test results would be normal. A non normal IQ distribution only means bad standardization. And if you assume fat tail you can't keep using standard deviation the way you use in normal distributions, you would need a new mathematical approacha.
Thanks for the explanation, my understanding of fat-tails is now clearer. It feels like we should call them 'long tails', no?
This is stuff I wish I could conceptualise before. NNT, more please! 🙏
The clarity of a New York sewer
Damn I'm adding this to my repertoire
I would be grateful if Prof. Taleb would answer a question that might be both naïve and technical.
I understand that probabilities can represent frequency of occurrence (as in coin toss) or degree of belief (as in a horse race). In estimating probability distribution from observed data on a given variable and computing statistical measures like mean, standard deviation etc., all observations are equally weighted, which is tantamount to assuming that the probability with which each observation occurs is its frequency of occurrence. Would you conclude that computing statistical measures would not be valid for variables where the probability is more likely to represent a degree of belief than frequency of occurrence? Would you further say that market participants assign probabilities to possible realizations of various financial and economic variables based on degree of belief rather than frequency of occurrence? Does the idea of estimating probability distribution make sense when probabilities are degree of belief? If not, how would empirical work be done when probabilities are degree of belief?
Can't answer for Taleb but I know he's a fan of Keynes' Treatise on Probability in which Keynes suggest rules that can still apply for "non-numerical" probabilities as he calls it. They are still ordered, and that can be exploited. You can also use laws of probability such as Bayes rule to ensure your estimates a logically consistent when you have several estimates that relate to each other. You will have less precision but more rigor.
If the size of the area under the curve increases with fat tail for extreme events, doesn’t that mean the probability goes up? What am I missing?
Or is the point that the area doesn’t change because we are talking about 1 standard deviation from the mean?
Thank you for the lesson. If you use the natural log of income, can you do regression?
No, because it is not Lognormal.
when a disribution is "fat" tailed is it not always with respect to an other distribution?
Yes, they are usually compared to the Gaussian or Exponential distribution's tails. I'm confused by his phrasing. He says that in a fat tailed distribution events do not occur more often in the tail, I think he means wrt to the bulk of the fat-tailed distribution (-sigma, sigma) rather than a Gaussian distribution's tails. IMO he should have definately explained the relation to Gaussian dist tails.
@@WillyCSchneider events in the tail are rare; seldom seen. But when you do see one, it has a huge effect on how you describe the distribution. Because it’s rarely seen, you get into trouble making predictions when you mistakenly use tools made for thin (Gaussian) tails on fat tailed processes. His classic example, “never cross a river that is on average 4 feet deep.” That description might lead you to think you could walk across until you realize there are many possibilities of depth that could have sections way over your head yet still average out to 4 feet.
@@peterevans202 I don't understand this "huge effect on the distribution". What I would expect is that if you compare the distribution with and without the rare event that you would see completely different moments.
@@peterevans202 Yes, I understand this. However, a distinction should be made between fat-tails and long-tails. Given Taleb's explanation I think he is mostly referring to long-tails, given that in a fat-tailed distribution extreme outcomes take place more often than extreme outcomes in a Gaussian distribution. In a long-tailed distribution the tails are relatively thin however theres a non-negligible probability of having a really extreme event (i.e. Taleb's black swans)
@@andraro87 The usual situation is that you don’t know what distribution you’re dealing with. You make an estimate based on what you observe. With fat tails, things can look Gaussian at first, but when the significant event occurs all of the moments shift as you stated. The underlying distribution didn’t change, but your understanding of it did.
What can you do instead of regression to compensate? Anyone?
please publish more videos :)
Thank you kindly ✍️
Man i wish i lived next to NT, I could listen to master all day!
Thank you Nassim!
Thanks a lot, professor!
The man, the legend!
Keep them coming Taleb! These are pure gold and extremely enjoyable
Thank you Nassim.
Thanks for doing these.
Dear Professor firstly thank you so much for your kind explanation. May I very kindly clear a conundrum that I have ? Here in this video you indicated clearly that as we fatten the tails there will be MORE observations in the intermediate region and LESS in the extreme region. Why is it not vice-versa ?
No, more in the center and less in the intermediate region.
@@nntalebproba Noted Professor. Thank you so much for your kind reply Professor Taleb. I always thought of it to be the opposite, so thanks for giving me this important insight. Appreciate it a lot.
why are you giving a free download link to your book though??
Speaking about economists, is the GDP statistic fat tailed? It gives higher weights to good and services with higher prices and lower (or no) weights to good and services with lower (or no) prices. Is the most important statistic economists use statistically flawed?
They use weighted indices to make the numbers look good,no doubt. But also if they were to weigh all sectors equally, It would make the figures more flawed than the current system In the eyes of the suits.
In general Growth projections,budget allocation,governing policies,loan defaults as well as frequency of corruption charges are the more interesting figures ,for me personally. But what do I know.
Can anyone explain why with fat tails the extreme events are less likely? With conventional understanding, the area under the PDF curve for fat tailed distribution is larger given any x (compared with normal), meaning it's more likely to occur right? How does one then take into account the impact of the unlikely, would this be reflected in the PDF?
I may be wrong but,think of it this way: if the event is less likely its impact is gonna be more. And then draw the natural conclusions to your problem from there on.
The impact is not in the PDF since impact and probability are different things. You can model impact/pay-off as a function of a random variable (which is a new random variable).
You are correct. Taleb's explanation is incomplete, and ironically, a cause for confusion. He has broadened his definition of the "tails" to +/- 1 deviations in this video, which supports the point he's making. It's worth noting that his previous work (fooledbyrandomness.com/DarwinCollege.pdf ) defines the "tails" as +/- 2 deviations. As you move further out along either extreme on the graph (positive or negative), you eventually reach a point where extreme events for a fat tailed distribution become more likely (more frequent) relative to the normal distribution. This is what people mean when they talk about very extreme events being more common in fat tailed distributions. Taleb has said so himself in the paper I linked to above: "When we fatten the tails we have higher peaks, smaller shoulders, and *higher incidence* of very large deviation."
Here's a great example, which compares the Gaussian and Laplace distributions: www.vosesoftware.com/riskwiki/images/image15_632.gif
I hope this helps.
@@honest_math From a mathematical point of view you can construct distributions to show all kinds of behaviour. I suppose what Taleb is getting at is that when modelling common fat tailed phenomena you often have that property. For instance putting out small fires immediately in California results in more undergrowth and larger occasional fires. Similarly FED intervention on the stock market results in less volatility most of the time and enormous crashes occasionally.
@@DanielJanzon My point is that people are *not* wrong to say that fat-tailed distributions result in more frequent extreme events, as Taleb suggests. That's literally the etymology of the term: fat tails refers to thicker ends further along the distribution curve. This results in more area under the curve, and thus a higher frequency of occurrence. Taleb himself has said as much (see my previous citation).
Thank you Maestro
Legend!! Thanks for doing this
He's a genius, because of him I left data science and statistics because they are absurd in prediction of future I was safety Engineer you know... there is no need for predicting future events this idea is insane! I was suspected but didn't go deep in math like him! All we need is more technology protect us and managing our society based on domain knowledge and intuition about that guiding by deterministic science (being antifragile), believe me I was working on industrial accidents in railway I was fighting with people and managers to convince them mathematics of uncertainty (statistics) does work...! I couldn't believe that I'm saying this: they're just playing symbols...
🤣 I love how he rips on bill gates. “You know... one of the people on your hero list..” hahaha
obviously and expert cos he can draw a perfect curve...
Question I'd ask, intuitively one thinks the tail should have MORE observations when we say 'fat tail'. If I understand it correctly though, assuming the same 'curve', effectively we're saying a fat tail implies 1σ is 'wider' hence fewer observations in the tails
Hello everyone! I'm new to statistics and probability, in a mathematical sense, but I enjoy pondering things philosophically. My question is, when do fat tails come into play? Like, in a hurricane-prone area there are insurance calculations... do they take place there? In finance I see how the effects of them NOT being taken into consideration --- crashes, Bob Rubin trades, etc.. --- but when ARE they properly, if at, accounted for. Are they ever accounted for? Can they be conceptualized in the abstract? I didn't understand the practicality of the "take a bunch of people with no money + Bill Gates" example, because why would someone be measuring money with all these people who have no money. Please let me know if anyone understands my question. Thank you to all, and Taleb specifically for posting this.
For a layperson like myself, the nomenclature is counterintuitive. "Long tails" hold many observations while "fat tails" don't have many observations but some are a long distance from the median. It sounds backwards.
Hurray for Mr Taleb!