Timeline for How to estimate discrete probability distribution from a dataset of pairwise frequencies?
Current License: CC BY-SA 4.0
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| Jul 5, 2021 at 18:49 | comment | added | Lucas Prates | I imagine it is a complicated process. However, you might still be able to apply the analysis above. For instance, if you wished to include day of week and raining, you could suppose $N_t = Poisson(\lambda_{d(t), r(t)})$, where $d(t)$ would be the day of the week and $r(t)$ a rain boolean. The computations are almost the same, the only difference is that you would have to group the variables for estimation. The only strong hypothesis remaining is independence. In optimizing a "pseudo likelihood" that is decomposed as a product of observations, I think you are implicitly assuming independence. | |
| Jul 5, 2021 at 18:32 | comment | added | Ben | Nice writeup, but the assumption that $N_t$ does not vary with the day is false. The amount of cars on the road changes drastically from day to day depending on factors like weather, day of week, is it a holiday, etc. This is a fundamental part of the challenge. | |
| Jul 2, 2021 at 20:04 | history | edited | Lucas Prates | CC BY-SA 4.0 |
added 289 characters in body
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| Jul 2, 2021 at 19:37 | history | answered | Lucas Prates | CC BY-SA 4.0 |