17 problems

Nonnegativity conjecture for Riesz kernels. For $\alpha\gg 0$, the Riesz kernel $q_\alpha(\sigma)$ takes nonnegative values on $K$.

Let $1<p<\infty$, and let $U=\{u_k\}$ be an exponential-function family in $L^p(0,1)$, with the distance between normalized exponential-function families defined by the displayed q…

Minimax-rate conjecture. This sub-Exponential rate of convergence should be minimax optimal up to constants that may depend on the parameters of the mixture model.

Let the conditional distribution of the observed responses in a dependent mixture model belong to an exponential family, and suppose that its partition function is nontrivial and e…

Consider the maximizers of the variational-Laplace objective $I_j^{(n)}$ in the exponential-family setting described above, with the normalized objective converging in probability…

Let ${{S}_{\textsc{gro}({{\cal M}})}}$ be the e-variable based on the reverse information projection (RIPr) of a fixed simple alternative onto the null set…

The preceding discussion concerns a single-parameter family of densities and its multivariate exponential-family generalization. In settings where posterior asymptotics such as the…

The setup concerns the paper's post-machine-learning inference result for models whose original specification is based on a likelihood or an exponential family. Efficiency conjectu…

Normalizer-only reformulation conjecture. Our assumptions could be almost equivalently restated in terms of the normalizer $Z$ alone.

Generalization conjecture. The lower bound can also be generalized to all exponential families.

Uniqueness conjecture. The map

Let a statistical model be a smoothly parametrized family of distributions whose parameter space is finite-dimensional. Suppose that conditional MDL is a Bayesian prediction for th…

Let $P$ be a probability satisfying the tilted-law property (TLP), and let $P_t$ denote its associated exponential family. Define … A median of $P_t$ is a real number $a$ such that…

Riesz representation conjecture. Every hyperbolic polynomial should give rise to a statistical exponential family, namely one with an underlying measure.

The setting is a multidimensional exponential family, with MAP estimators of the form described in the preceding discussion and with KL divergence as the loss. Multidimensional suf…

Let $N$ be the size of the finite sample space and let $k$ be the dimension of an exponential family. For a class $\mathcal{H}$ of exponential families, define … In particular, let…

Milder-condition conjecture. Condition (2.4) in the cited reference is milder than the uan condition, although as stated it is applicable only to exponential families.