12 papers · 1 filter
Posterior Convergence without Force Convergence: Resolution-Stable Sampling for Rough Bayesian Inverse Problems
Zhiliang Deng, Xiaomei Yang
Bayesian targets may converge under model refinement even when the exact sensitivities used by gradient-based samplers do not. We study this probability--sensitivity mismatch and i…
Contour Hankel dynamics and indicator fields for the Riemann -function
Zhiliang Deng, Xiaomei Yang, Huazhong Lü
We develop a moving-contour Hankel framework for encoding local zero configurations of the Riemann -function. Weighted contour integrals of the logarithmic derivative , ex…
Contour-count indicator fields for visible pole clusters in meromorphic continuation
Zhiliang Deng, Xiaomei Yang
We develop a contour-count indicator method for visible pole clusters in outward meromorphic continuation from circular boundary data. The method starts from determinant characteri…
Determinant Characteristics and Argument-Principle Certification for Visible Poles in Meromorphic Continuation
Xiaomei Yang, Zhiliang Deng
We study outward meromorphic continuation from circular boundary data in the unit disk. The unknown function is holomorphic in the unit disk and admits a meromorphic continuation t…
A persistent-homology-Gaussian prior for solving infinite-dimensional Bayesian inverse scattering problems
Zhiyuan Wang, Hang Qi, Xiaofei Guan +2
Bayesian inference methods have been developed to address inverse problems in function spaces where the unknown parameters are of infinite dimension. However, conventional Gaussian…
A Moment--Hankel Rank Method for Identifying the Number of Point Sources in the Heat Equation
Zhiliang Deng, Xiaomei Yang, Ailin Qian
We develop a low-frequency moment--Hankel rank method for identifying the number of time-independent point sources in the heat equation from boundary flux data. The method is formu…