9 problems

Sequential stopping detection-boundary conjecture. In the large-$K$ sense, stopping using an anytime-valid test should not be possible for $t<t^\star$, since then…

GPTA optimality conjecture. Among all nested testing procedures that preserve the order $u_1,u_2,\ldots,u_n$, the GPTA is an optimal nested procedure. It is not necessarily uniquel…

Let $W^{G,\epsilon}_{a,b}$ be the transportation cost used to measure distinguishability between arms $a$ and $b$ in the Gaussian private best-arm identification setting, and let i…

Let $V(n,\pi)$ be the value function defined in, where $n$ denotes the time index, $\pi$ is the relevant state variable, $\mu$ is a prior distribution, and $\nu$ is the parameter a…

Switching/stitching conjecture. At very small $b4$, the phenomenon observed in Figure(b) is a version of the switching/stitching phenomenon for a composite null; this effect occurs…

Let a sequence have equal zeroth- and first-order frequency limits. Powerlessness conjecture. Our test will be powerless on such a sequence. The conjecture concerns the behavior of…

Consider adaptive stopping procedures whose approximate type-I error guarantees are obtained from limit theorems, and alternative procedures using concentration inequalities to obt…

We consider Bernoulli bandit models with two arms, whose means satisfy $(\mu_1,\mu_2)\in(0,1)^2$ and $\mu_1\ne\mu_2$. In the fixed-confidence setting, a sampling strategy is non-un…

Let $(\tau,\delta)$ be a sequential test for a simple hypothesis against one-sided alternatives, and let $\beta_{\theta_0}(\tau,\delta)$, $\dot\beta_{\theta_0}(\tau,\delta)$, and…