4 ms·
What kinds of gaps should one expect if each day's temperature at each location was sampled identically and independently of past years? I don't know the exact
by CaptainNegative 5y ago
What kinds of gaps should one expect if each day's temperature at each location was sampled identically and independently of past years?
I don't know the exact parameters here, but mental math says that if we have data over 80 years, and we brashly pretend city temperatures are independent of each other, then the probability that any of the 400 cities exceeds its historical max on any given day is approximately 400/(80*365) ≈ 90 days, with arrivals following a Poisson train.
This expected gap can only grow if we correctly add in the positive correlation between nearby temperatures, but that will require working directly with the data. It would be nice if the website more obviously contrasted what we would see in toy models with no heating versus what we actually see in the real world.
- wave_function 5y agoYour mental math is correct. If each temperature was sampled identically and independently, each place’s “time since hottest” should be flatly distributed between now and however long the recording goes back to.
- deleted 5y ago[deleted]
- titzer 5y agoThis math is not correct, because a city can exceed its historical max more than once, and each time that happens, it becomes the new historical max.
- adhesive_wombat 5y agoOn the other hand, there's a strong indicator that there is substantial non-independence: lots of cities down the West coast set a record at about the same time, about 33-35 days ago. Also, what the visualisation doesn't show is the longest per-state time since a record. If they're all also on the order of a year, that's a strong signal that records are increasing. If that time varies randomly between now and decades ago, it's a sign the results are more random than trending.