We develop Riemannian Stein Variational Gradient Descent (RSVGD), a Bayesian inference method that generalizes Stein Variational Gradient Descent (SVGD) to Riemann manifold. The benefits are two-folds: (i) for inference tasks in Euclidean spaces, RSVGD has the advantage over SVGD of utilizing information geometry, and (ii) for inference tasks on Riemann manifolds, RSVGD brings the unique advantages of SVGD to the Riemannian world. To appropriately transfer to Riemann manifolds, we conceive novel and non-trivial techniques for RSVGD, which are required by the intrinsically different characteristics of general Riemann manifolds from Euclidean spaces. We also discover Riemannian Stein's Identity and Riemannian Kernelized Stein Discrepancy. Experimental results show the advantages over SVGD of exploring distribution geometry and the advantages of particle-efficiency, iteration-effectiveness and approximation flexibility over other inference methods on Riemann manifolds.
A powerful technique for inference concerning spatial dependence in a random field is to use spectral methods based on frequency domain analysis. Here we develop a nonparametric Bayesian approach to statistical inference for the spectral density of a random field. We construct a multi-dimensional Bernstein polynomial prior for the spectral density and establish its theoretical validity as a nonparametric prior. We devise a Markov chain Monte Carlo algorithm to simulate from the posterior of the spectral density. The posterior sampling enables us to obtain a smoothed estimate of the spectral density as well as credible bands at desired levels. Simulation shows that our proposed method is more robust than a parametric approach and for illustration, we analyze a soil data example.
A sensitive and label-free analytical approach for the detection of porcine circovirus type 2 (PCV2) instead of PCV2 antibody in serum sample was systematically investigated in this research based on surface plasmon resonance (SPR) with an establishment of special molecular identification membrane. The experimental device for constructing the biosensing analyzer is composed of an integrated biosensor, a home-made microfluidic module, and an electrical control circuit incorporated with a photoelectric converter. In order to detect the PCV2 using the surface plasmon resonance immunoassay, the mercaptopropionic acid has been used to bind the Au film in advance through the known form of the strong S-Au covalent bonds formed by the chemical radical of the mercaptopropionic acid and the Au film. PCV2 antibodies were bonded with the mercaptopropionic acid by covalent -CO-NH- amide bonding. For the purpose of evaluating the performance of this approach, the known concentrations of PCV2 Cap protein of 10 µg/mL, 7.5 µg/mL, 5 µg/mL, 2.5 µg/mL, 1 µg/mL, and 0.5 µg/mL were prepared by diluting with PBS successively and then the delta response units (ΔRUs) were measured individually. Using the data collected from the linear CCD array, the ΔRUs gave a linear response over a wide concentration range of standard known concentrations of PCV2 Cap protein with the R-Squared value of 0.99625. The theoretical limit of detection was calculated to be 0.04 µg/mL for the surface plasmon resonance biosensing approach. Correspondingly, the recovery rate ranged from 81.0% to 89.3% was obtained. In contrast to the PCV2 detection kits, this surface plasmon resonance biosensing system was validated through linearity, precision and recovery, which demonstrated that the surface plasmon resonance immunoassay is reliable and robust. It was concluded that the detection method which is associated with biomembrane properties is expected to contribute much to determine the PCV2 in sample solutions instead of PCV2 antibody in serum samples quantitatively.
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