Timeline for On bounding a certain discrepancy between probability distributions on the symmetric group
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 15, 2020 at 5:26 | comment | added | dohmatob | Thanks again for the input. Let me try to cut-off some dead branches from my problem. So, for $h \in [0, 1/2]$, let us say $P$ verifies the "low noise condition" $\mathbf N(h)$ if $\min_{i < j}|p_{ij}-1/2| \ge h$. Then, one might be interested in bounding $\Delta(P,Q)$ under the following scenarios: (A) $P$ verifies $\mathbf N(h)$; (B) Both $P$ and $Q$ verify $\mathbf N(h)$; (C) $P$ verifies $\mathbf N(h)$ and $Q=\hat{P}_N$ the empirical version of $P$ based on $N$ iid samples; etc. | |
| Mar 15, 2020 at 3:14 | comment | added | R W | It might still be quite interesting to decribe the collections of measures determined by presribed values of $p_{ij}$ and to look at the distances (in an appropriate sense) between these collections. | |
| Mar 15, 2020 at 2:36 | vote | accept | dohmatob | ||
| Mar 15, 2020 at 2:24 | comment | added | dohmatob | Thanks for the feedback; makes sense. As for the last comment, indeed $TV(P,Q) = \sup_A |P(A)-Q(A)|$ where sup is over measurables sets, and so my bound is loose enough (and not very informative, by the same token) to apply for even more general subsets $E_{ij}$. Unfortunately, someone thought it was the greatest idea to downvote the question... | |
| Mar 15, 2020 at 1:59 | history | answered | R W | CC BY-SA 4.0 |