Hacker Newsnew | past | comments | ask | show | jobs | submitlogin

A special case of selection bias is sampling bias (as you said with "specifically"), and the inspection paradox is a special case of selection bias — it is specifically about whether you “inspect” a member of a population or the population as a whole. The article you linked on sampling bias has a list of “types” — https://en.wikipedia.org/w/index.php?title=Sampling_bias&old... — and most of them don't fall under the category of inspection bias/paradox (while the example with class sizes does).

So it's actually useful to have this article that collects many examples of this specific kind of sampling bias (and specific kind of selection bias). I especially like the one on relative speeds:

> when I overtook slower runners, they were usually much slower; and when faster runners passed me, they were usually much faster.



> the inspection paradox is a special case of selection bias

Nope. Turns out that there actually is such a thing as the "inspection paradox" but this ain't it.

https://en.wikipedia.org/wiki/Renewal_theory#Inspection_para...


The inspection paradox in renewal theory that you linked (for every t the interval containing t is on average larger than the average interval) is an instance of the inspection paradox described in the article (the mean seen by a random observer can be very different from the true mean). Bus/train waiting times are in fact the third example in the article.

It's a standard term in the literature (both in stochastic processes and probability more generally); look at the first dozen or so results in books search: https://www.google.com/search?q=%22inspection+paradox%22&udm...


> The inspection paradox in renewal theory that you linked ... is an instance of the inspection paradox described in the article

I think that's debatable. The standard definition of the IP is intimately bound to random processes, and there is nothing random about class sizes. So while I do see the similarity, I think that saying that the class-size example is an instance of the IP is at best misleading because it discards an essential feature of the actual IP, namely, randomness.

It might be useful as a pedagogical tool, i.e. "here is an analogous result in a deterministic system" but to say that they are the same is very misleading IMHO.

Here is the relevant quote from the Wikipedia article on renewal theory:

"The resolution of the paradox is that our sampled distribution at time t is size-biased (see sampling bias)"

So the resolution of both "paradoxes" is the same, i.e. they are both examples of sample bias. But that doesn't mean that the problems are the same, or that one is an instance of the other.




Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact

Search: