5 problems

Interactive FDP lower-bound conjecture. The lower bound under the FDP constraint could be strengthened to allow some interaction while the result still holds.

Consider a change-point $\tau_k$ with associated scale $r_k$, effective height $\bar\Delta_k$, and critical height function $\rho^*_{r_k}(\cdot)$. Conjectured detection threshold.…

Fix an even range $r\geq 2$, and suppose that $n/(2r)$ is an integer. Let $\rho^*_{r}(\cdot)$ denote the critical height function, and let $({\bf NoSp})$ and $({\bf Detect})$ denot…

Rate-independence conjecture. In the regime $m\approx n/s$, the same scaling of $\mu$ is necessary for reliable detection, regardless of the value of $p$.

Sparse-signal lower-bound conjecture. When $p\geq 8/m$, if the risk of an adaptive sensing and test procedure is less or equal to $b5$, then necessarily