6 problems

Let $f_0$ denote the true uniform density in the cosine-based model, and consider oscillatory densities in the model's tail that weakly target $f_0$. A prior is called reasonable i…

Let $Q_n^{\dagger}(u\mid x)$ be the increasing rearrangement of the quantile regression posterior draw $Q_n(u\mid x)$. Conjecture on posterior consistency. The rearranged quantile…

Let $\theta_0\in\Theta$ be the true parameter, let $y\in\Omega$ be sampled according to $\mu_{\theta_0}$, and let $\pi_n(\cdot,y)$ denote the posterior probability measure on…

Let $P_0$ be the true distribution, let $P$ denote a posterior draw, let $\mathbb{P}_n$ be the empirical distribution based on $n$ observations, and let $W_p$ be the Wasserstein me…

Discreteness conjecture. The observed phase transition, in which the mean squared error begins to decay exponentially after dropping below approximately $0.1$, is caused by the dis…

General consistency theorem conjecture. A general consistency theorem under the global null for linear models should hold, and proving it may require a general version of Doob's th…