15 problems

The prior-averaging obstruction to inconsistency in oscillatory density models
arXiv@arxiv
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…
Conjectureopenbayesian-statistics posterior-consistency statistical-models
1
The geometric-stopping characterization conjecture for statistically stable extensions
arXiv@arxiv
A geometric stopping characterization conjecture asserts that only geometric stopping models lead to statistically stable randomly stopped extreme extensions. The stopping model is…
Conjectureopenprobability randomly-stopped-extremes statistical-models
0
The knowns-and-unknowns sufficiency conjecture for multi-channel factor analysis
arXiv@arxiv
Knowns-and-unknowns sufficiency conjecture. Condition should be sufficient for identifiability in multi-channel factor analysis.
Conjectureopenfactor-analysis identifiability statistical-models
0
Shapiro's global identifiability conjecture for single-channel factor analysis
arXiv@arxiv
Shapiro's conjecture. The identifiability threshold that is generically sufficient for local identifiability should also be generically sufficient for global identifiability.
Conjectureopenfactor-analysis identifiability statistical-models
0
Antisymmetry from symmetric parametrization in transformation models
arXiv@arxiv
Let a transformation model have a parameter $\psi$ and suppose it admits a $\psi$ -symmetric parametrization, with antisymmetry defined as in Definition. Antisymmetry conjecture. An…
Conjectureopenstatistical-models symmetry transformation-models
0
Conjecture on maximum divergence from trapezoid models
arXiv@arxiv
Let $\T_{a,b,d}$ be the trapezoid model in the simplex described above, with parameters $a$ , $b$ , and $d$ , and let $D(\T_{a,b,d})$ denote its maximum divergence. Trapezoid-model di…
Conjectureopeninformation-theory statistical-models toric-models
0
Factorization conjecture for the determinant of the Lyapunov Jacobian
arXiv@arxiv
Factorization conjecture. The determinant of $A(\Sigma)_{\cdot,E}$ factorizes as
Conjectureopenidentifiability lyapunov-equations statistical-models
0
Conjecture that every complete marginal log-linear parameterization is smooth
arXiv@arxiv
Smoothness conjecture. Any complete marginal log-linear parameterization is smooth.
Conjectureopenmarginal-log-linear-models smoothness statistical-models
1
Negative-definiteness conjecture for the quasisymmetry log-likelihood Hessian
arXiv@arxiv
Negative-definiteness conjecture. The Hessian ${\bf H}({\bf a})$ is negative definite for all ${\bf a}\in\mathbb{R}^I$ satisfying those parameter conditions.
Conjectureopenmaximum-likelihood-estimation quasisymmetry statistical-models
0
Composite-variable conjecture for fiducial distributions
arXiv@arxiv
Let an FD model have RD's $F_r(x\mid\theta)$ . Let $g(x)\equiv y$ and/or $h(\theta)\equiv\phi$ be composite variables, meaning that the relevant function is not continuous and stric…
Conjectureopenfiducial-inference probability-distributions statistical-models
0
Parameter-count conjecture for nested Markov models on ADMGs
arXiv@arxiv
Let $\mathcal{G}$ be an acyclic directed mixed graph (ADMG). Consider the model of conditional independence associated with $\mathcal{G}$ and the nested Markov model associated wit…
Conjectureopenacyclic-directed-mixed-graphs nested-markov-models statistical-models
0
Disjoint-face conjecture for simplicial refinements
arXiv@arxiv
Disjoint-face conjecture. The minimal faces satisfy
Conjectureopenconvex-geometry simplicial-refinements statistical-models
0
No smaller simplicial refinement conjecture
arXiv@arxiv
No smaller simplicial refinement conjecture. No simplicial refinement $(\varDelta,\mathcal{P}_{\varDelta},F,G)$ exists with $\varDelta$ having fewer extreme points than…
Conjectureopenconvex-geometry simplicial-refinements statistical-models
0
Lowest-dimensional simplicial refinement conjecture
arXiv@arxiv
Lowest-dimensional simplicial refinement conjecture. All simplicial refinements of $(\mathcal{C},\mathcal{P}_{\mathcal{C}})$ have this form; equivalently, the refinement obtained b…
Conjectureopenconvex-geometry simplicial-refinements statistical-models
0
Avoidance of finiteness for approximating sequences via quantitative WCLI
arXiv@arxiv
Let an approximating sequence for a system be a sequence of nested systems whose induced probability laws converge weakly to the true probability law. Assume that finiteness of the…
Conjectureopencausal-inference dynamical-systems statistical-models
0