Timeline for For intuition, what are some real life examples of uncorrelated but dependent random variables?
Current License: CC BY-SA 4.0
9 events
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| Jun 27, 2022 at 13:38 | comment | added | mribeirodantas | I can add this comment to the answer if you think it'd be a good idea. | |
| Jun 25, 2022 at 15:21 | comment | added | BCLC | So why don't you have that as an answer? | |
| May 8, 2022 at 15:04 | comment | added | mribeirodantas | When one says two random variables are independent, I would expect them to mean that the two variables are statistically independent (no sort of relationship, be it linear or not). You will find some real-life examples of independent ("uncorrelated") random variables with some dependence being measured (due to collider bias) in this scientific article: nature.com/articles/s41467-020-19478-2 | |
| May 6, 2022 at 16:44 | comment | added | BCLC | Or hell biology like if there's like height vs weight and then height$^2$ vs weight$^2$ | |
| May 6, 2022 at 16:44 | comment | added | BCLC | (...) is those lame examples like $X$ and $X^2$. Like who cares about comparing $X$ and $X^2$ ? Even all the examples here are hard (or at least I'm not familiar with them). In Christoph Hanck's answer...ok fine I did learn GARCH in bachelor's or master's (I think master's) but never minding that I've got some real uncorrelated X and Y that when squared are not uncorrelated. So ok you can generalise but what's your example for this? Make an intuitive real life example please. You can use finance, economics, physics, etc. | |
| May 6, 2022 at 16:39 | comment | added | BCLC | 1 - OH yeah kendall tau spearman rho riiiiiiiiight. 'If the variables are independent, Pearson's correlation coefficient is 0, but the converse is not true because' aaaaahhhhh so when we say independent implies uncorrelated...what we mean is pearson-uncorrelated? (1.1 - but probably independent implies uncorrelated in every other sense ?) 2 - ok ok you said what I wanted to ask is like 'When are variables dependent, but independent when measured?' ummmm why? Also please dumb it down. This just for elem prob/stat where we think 'independent implies uncorrelated'. My point of this question (...) | |
| May 6, 2022 at 15:37 | comment | added | mribeirodantas | 1 - There are many correlation measures that are not Pearson's correlation. There is Kendall rank correlation or Spearman's rank-order correlation. With the broader definition of correlation, there are numerous other techniques such as mutual information, Matthew's correlation coefficient, Maximal information coefficient and so on. 2 - Even though you know that A and B are correlated in a population, you could sample this population in a way that A and B will not correlate in individuals in your sampling. Feel free to ask a new questions. Comments can be hard to go into much detail. | |
| May 6, 2022 at 2:51 | comment | added | BCLC | Thanks mribeirodantas 1 - What exactly is correlation that isn't Pearson correlation? Or... do you mean to generalise that there's some measure of independence higher than linear independence but lower than full independence? 2 - what do you mean by 'independent when measured' ? | |
| Dec 13, 2021 at 16:45 | history | answered | mribeirodantas | CC BY-SA 4.0 |