3 ms·

> I said that if you had reason to believe in a linear relationship, then you could try to find it. That’s the huge catch to linear regression: no matter what d

by User23 6y ago

> I said that if you had reason to believe in a linear relationship, then you could try to find it. That’s the huge catch to linear regression: no matter what data you put in, you’ll always get a “best match” line out. This challenge generalizes to all model fitting. Incorrectly assuming a distribution is Gaussian is a big one.

xapata 6y ago
The variable of interest may not have a Gaussian distribution, but its expected value and variance generally are. Sure, there's some pathological cases, but the Cauchy distribution doesn't show up that often.
- solveit 6y ago
  Does the Cauchy distribution ever actually show up?
  - ooobit2 6y ago
    Less often than meetings start and end on time.
  - leephillips 6y ago
    Yes. Check the example section of: http://www.math.nagoya-u.ac.jp/~richard/teaching/s2019/Cauchy_Distribution.pdf http://www.math.nagoya-u.ac.jp/~richard/teaching/s2019/Cauch...
  - jointpdf 6y ago
    If X, Y ~ N(0,1), then X/Y ~ Cauchy(0,1) (Read: If X and Y are normally distributed random variables with mean 0 and standard deviation 1, then X/Y is equivalent to a Cauchy(0,1) distributed RV. This is a useful equivalence to know if working with standard normal RVs, which is often. E[X/Y] does not exist!) If X ~ Cauchy(0,1), then X ~ normalized student-t distribution. (student-t puts the “t” in t-SNE, where it acts as a weighting function on the Euclidean distance between points. UMAP uses a parameterized version of this weight function that is essentially a generalization of the Cauchy distribution: https://jlmelville.github.io/smallvis/umap.html https://jlmelville.github.io/smallvis/umap.html)
fractionalhare 6y ago
Another one is handwaving that a distribution is normal when n > 30 because "central limit theorem!" Amateur statistics is full of magical numbers and thresholds where everything "just works" :)
- ooobit2 6y ago
  When I applied to my MSDA program, I had to interview with the lady who would become my first year mentor. "Now, do it over again... on paper." That's what she'd say to anyone too confident in their outputs. She has a reputation for weeding out people who can pass the entrance testing and qualifications, but can't adapt. And what we do requires thick skin. You're wrong until you just happen to be right.
FridgeSeal 6y ago
This is what stresses me out about people doing "bootcamp" data science courses and then getting jobs where they're given the responsibility of making decisions based on analysis of data. Statistics is more involved than it appears, there are so many ways something can subtly violate underlying assumptions, or appear to be fine on the surface while being actually meaningless. It's really easy to fit a model, it's more involved and difficult to actually understand the complexities.

by User23 6y ago

xapata 6y ago

The variable of interest may not have a Gaussian distribution, but its expected value and variance generally are. Sure, there's some pathological cases, but the Cauchy distribution doesn't show up that often.

solveit 6y ago
Does the Cauchy distribution ever actually show up?
- ooobit2 6y ago
  Less often than meetings start and end on time.
- leephillips 6y ago
  Yes. Check the example section of: http://www.math.nagoya-u.ac.jp/~richard/teaching/s2019/Cauchy_Distribution.pdf http://www.math.nagoya-u.ac.jp/~richard/teaching/s2019/Cauch...
- jointpdf 6y ago
  If X, Y ~ N(0,1), then X/Y ~ Cauchy(0,1) (Read: If X and Y are normally distributed random variables with mean 0 and standard deviation 1, then X/Y is equivalent to a Cauchy(0,1) distributed RV. This is a useful equivalence to know if working with standard normal RVs, which is often. E[X/Y] does not exist!) If X ~ Cauchy(0,1), then X ~ normalized student-t distribution. (student-t puts the “t” in t-SNE, where it acts as a weighting function on the Euclidean distance between points. UMAP uses a parameterized version of this weight function that is essentially a generalization of the Cauchy distribution: https://jlmelville.github.io/smallvis/umap.html https://jlmelville.github.io/smallvis/umap.html)

fractionalhare 6y ago

Another one is handwaving that a distribution is normal when n > 30 because "central limit theorem!" Amateur statistics is full of magical numbers and thresholds where everything "just works" :)

ooobit2 6y ago
When I applied to my MSDA program, I had to interview with the lady who would become my first year mentor. "Now, do it over again... on paper." That's what she'd say to anyone too confident in their outputs. She has a reputation for weeding out people who can pass the entrance testing and qualifications, but can't adapt. And what we do requires thick skin. You're wrong until you just happen to be right.

FridgeSeal 6y ago

This is what stresses me out about people doing "bootcamp" data science courses and then getting jobs where they're given the responsibility of making decisions based on analysis of data. Statistics is more involved than it appears, there are so many ways something can subtly violate underlying assumptions, or appear to be fine on the surface while being actually meaningless. It's really easy to fit a model, it's more involved and difficult to actually understand the complexities.