37 ms·

> In a large, Gaussian distributed population Where do we get one of those? The central limit theorem doesn't give us one of those. Not even the Lindeberg-Fe

> In a large, Gaussian distributed population Where do we get one of those? The central limit theorem doesn't give us one of those. Not even the Lindeberg-Feller central limit theorem. Neither does the strong law of large numbers. Nor the weak law of large numbers. Nor the martingale convergence theorem. There is some old material, from about 100 years ago, in schools of education that given a performance measure and a large population the measure will be Gaussian distributed on that population, and the larger the population the closer to a Gaussian distribution. An example is supposed to be the size of the largest eigenvalue in a principle components decomposition. Uh, that largest eigenvalue was long called IQ (intelligence quotient). Nothing intelligent about it. Nonsense. 100% total crackpot nonsense. Brain-dead, cult nonsense. "Low performers" in need of a "performance improvement program" (PIP)? Start with the managers who believe in a Gaussian distribution. Then move to the managers who believe that the "bottom 20%" are always low performers. A lot is known about how to be a good manager, and the Gaussian probability density distribution is not part of that. I've seen a lot of bad managers. A pattern is that they are tyrants, have lots of rules and measures, are big on formality over reality, dot i's and cross t's with great reliability, and have everyone with their nose to the grindstone, ear to the ground, shoulder to the wheel and trying to work in that position. But the organization is stagnant, is not changing or keeping up with the market or technology. So, after a few years like that, it becomes obvious to everyone, customers, BoD, stockholders, employees, even nearly all of the managers that the organization is about ready to die, and often that's what happens, e.g., by firing 50% of the people and going downhill from there. Once I saw a failing organization where nearly all the managers except at the lowest level were part of a tight clique, cult enforcing failure. Finally the BoD installed a new CEO and fairly soon 80+% of the clique, cult were given "PIPs" and demoted out of management or retired. But there is also good evidence that even such a sick organization does not have to die and, instead, just needs some good management, starting at the CEO level. In particular, with a good CEO, suddenly, wonder of wonders, 90+% of the employees can be seen as great performers. So, net, as bad as the situation can be, it is fair to say that Darwin is on the case with improvement on the way! At one time Amazon was a small mail-order book and record shop run by Bezos from a small office. At least looking from 10,000 feet up, Bezos was a good manager, and, thus, I doubt that he was playing with the Gaussian distribution, firing his bottom 20%, stack ranking, etc. Instead he knew all the employees and the work of each. Sooooo, it sounds like now Bezos should leave outer space, return to Amazon, and fix the destructive nonsense that is ruining the company.

efitz 5y ago
> "Low performers" in need of a "performance improvement program" (PIP)? Start with the managers who believe in a Gaussian distribution. Then move to the managers who believe that the "bottom 20%" are always low performers. HAHAHA well said.
dekhn 5y ago
Maybe I missed your point, but qualitative phenotypes caused by interactions of many genes that are measureable, like height, are gaussian distributed.
- graycat 5y ago
  At best, only approximately Gaussian. Height cannot be Gaussian if only because height is never negative but every Gaussian density is positive for all real numbers, including negative real numbers. "interactions of many genes that are measureable" The interactions of many is commonly used to justify a Gaussian assumption, but there is no such theorem. The main theorem to get a Gaussian density is the central limit theorem which usually assumes an infinite sequence of independent identically distributed random variables (plus some), i.e., i.i.d. The i.i.d. is asking a LOT!!! Asking so much that in practice it is essentially unrealistic. What people often mean by Gaussian is just a central peak, some symmetry, and long tails, but an actual Gaussian distribution has a lot more, e.g., sufficient statistics (as in a classic paper by Halmos and Savage, with a derivation in M. Loeve's two volumes, from Springer, Probability) which, as I recall, E. Dynkin showed are quite sensitive to deviations from actual Gaussian. Gaussian is important in a lot of derivations -- a LOT is known. But in practice Gaussian has some utility but only as an approximation where don't need to be very careful about accuracy.
  - dekhn 5y ago
    I am not really disagreeing with you, but for a first order approximation, treating human height as a bunch of iids is the simplest approach. https://www.nature.com/articles/s41431-021-00836-7 https://www.nature.com/articles/s41431-021-00836-7. "At the same time, it is well-understood that additivity of effects and normal distribution of residuals is only an approximation to the distribution of height in human populations. .... However, up until now, no evidence for non-additive genetic interactions was found for height [6, 18]. Moreover, if non-additive effects were to exist for polygenic traits, very large sample sizes would be required to detect them [9]."

efitz 5y ago

> "Low performers" in need of a "performance improvement program" (PIP)? Start with the managers who believe in a Gaussian distribution. Then move to the managers who believe that the "bottom 20%" are always low performers. HAHAHA well said.

dekhn 5y ago

Maybe I missed your point, but qualitative phenotypes caused by interactions of many genes that are measureable, like height, are gaussian distributed.

graycat 5y ago
At best, only approximately Gaussian. Height cannot be Gaussian if only because height is never negative but every Gaussian density is positive for all real numbers, including negative real numbers. "interactions of many genes that are measureable" The interactions of many is commonly used to justify a Gaussian assumption, but there is no such theorem. The main theorem to get a Gaussian density is the central limit theorem which usually assumes an infinite sequence of independent identically distributed random variables (plus some), i.e., i.i.d. The i.i.d. is asking a LOT!!! Asking so much that in practice it is essentially unrealistic. What people often mean by Gaussian is just a central peak, some symmetry, and long tails, but an actual Gaussian distribution has a lot more, e.g., sufficient statistics (as in a classic paper by Halmos and Savage, with a derivation in M. Loeve's two volumes, from Springer, Probability) which, as I recall, E. Dynkin showed are quite sensitive to deviations from actual Gaussian. Gaussian is important in a lot of derivations -- a LOT is known. But in practice Gaussian has some utility but only as an approximation where don't need to be very careful about accuracy.
- dekhn 5y ago
  I am not really disagreeing with you, but for a first order approximation, treating human height as a bunch of iids is the simplest approach. https://www.nature.com/articles/s41431-021-00836-7 https://www.nature.com/articles/s41431-021-00836-7. "At the same time, it is well-understood that additivity of effects and normal distribution of residuals is only an approximation to the distribution of height in human populations. .... However, up until now, no evidence for non-additive genetic interactions was found for height [6, 18]. Moreover, if non-additive effects were to exist for polygenic traits, very large sample sizes would be required to detect them [9]."