Identifiability of Normal and Normal Mixture Models With Nonignorable Missing Data

Missing data problems arise in many applied research studies. They may jeopardize statistical inference of the model of interest, if the missing mechanism is nonignorable, that is, the missing mechanism depends on the missing values themselves even conditional on the observed data. With a nonignorable missing mechanism, the model of interest is often not identifiable without imposing further assumptions. We find that even if the missing mechanism has a known parametric form, the model is not identifiable without specifying a parametric outcome distribution. Although it is fundamental for valid statistical inference, identifiability under nonignorable missing mechanisms is not established for many commonly-used models. In this paper, we first demonstrate identifiability of the normal distribution under monotone missing mechanisms. We then extend it to the normal mixture and $t$ mixture models with non-monotone missing mechanisms. We discover that models under the Logistic missing mechanism are less identifiable than those under the Probit missing mechanism. We give necessary and sufficient conditions for identifiability of models under the Logistic missing mechanism, which sometimes can be checked in real data analysis. We illustrate our methods using a series of simulations, and apply them to a real-life dataset

Towards Constraining Parity-Violations in Gravity with Satellite Gradiometry

Parity violation in gravity, if existed, could have important implications, and it is meaningful to search and test the possible observational effects. Chern-Simons modified gravity serves as a natural model for gravitational parity-violations. Especially, considering extensions to Einstein-Hilbert action up to second order curvature terms, it is known that theories of gravitational parity-violation will reduce to the dynamical Chern-Simons gravity. In this letter, we outline the theoretical principles of testing the dynamical Chern-Simons gravity with orbiting gravity gradiometers, which could be naturally incorporated into future satellite gravity missions. The secular gravity gradient signals, due to the Mashhoon-Theiss (anomaly) effect, in dynamical Chern-Simons gravity are worked out, which can improve the constraint of the corresponding Chern-Simons length scale $\xi^{\frac{1}{4}}_{cs}$ obtained from such measurement scheme. For orbiting superconducting gradiometers or gradiometers with optical readout, a bound $\xi^{\frac{1}{4}}_{cs}\leq 10^6 \ km$ (or even better) could in principle be obtained, which will be at least 2 orders of magnitude stronger than the current one based on the observations from the GP-B mission and the LAGEOS I, II satellites.Comment: 15 pages, 6 figures. arXiv admin note: text overlap with arXiv:1606.0818

Characterizing the Dynamic Response of a Chassis Frame in a Heavy-Duty Dump Vehicle based on an Improved Stochastic System Identification

This paper presents an online method for the assessment of the dynamic performance of the chassis frame in a heavy-duty dump truck based on a novel stochastic subspace identification (SSI) method. It introduces the use of an average correlation signal as the input data to conventional SSI methods in order to reduce the noisy and nonstationary contents in the vibration signals from the frame, allowing accurate modal properties to be attained for realistically assessing the dynamic behaviour of the frame when the vehicle travels on both bumped and unpaved roads under different operating conditions. The modal results show that the modal properties obtained online are significantly different from the offline ones in that the identifiable modes are less because of the integration of different vehicle systems onto the frame. Moreover, the modal shapes between 7Hz and 40Hz clearly indicate the weak section of the structure where earlier fatigues and unsafe operations may occur due to the high relative changes in the modal shapes. In addition, the loaded operations show more modes which cause high deformation on the weak section. These results have verified the performance of the proposed SSI method and provide reliable references for optimizing the construction of the frame

The relationship of electron Fermi energy with strong magnetic fields

In order to depict the quantization of Landau levels, we introduce Dirac $\delta$ function, and gain a concise expression for the electron Fermi energy, $E_{F}(e) \propto B^{1/4}$. The high soft X-ray luminosities of magnetars may be naturally explained by our theory.Comment: 3 pages, 1 figure, submitted to OMEG11 Proceeding (Tokyo, Japan. Nov.14-18, 2011

High-energy Neutrinos from Outflows Powered by Kicked Remnants of Binary Black Hole Mergers in AGN Accretion Disks

Merging of stellar-mass binary black holes (BBH) could take place within the accretion disk of active galactic nuclei (AGN). The resulting BH remnant is likely to accrete the disk gas at a super-Eddington rate, launching a fast, quasi-spherical outflow (wind). Particles will be accelerated by shocks driven by the wind, subsequently interacting with the shocked disk gas or radiation field through hadronic processes and resulting in the production of high-energy neutrinos and potential electromagnetic (EM) emissions. This study delves into the intricate evolution of the shock driven by the remnant BH wind within AGN disks. Subsequently, we calculated the production of neutrinos and the expected detection numbers for a single event, along with their contributions to the overall diffuse neutrino background. Our analysis, considering various scenarios, reveals considerable neutrino production and possible detection by IceCube for nearby events. The contribution of the remnant BH winds on the diffuse neutrino background is minor due to the low event rate density, but it can be improved to some extent for some optimistic parameters. We also propose that there could be two neutrino/EM bursts, one originating from the premerger BBH wind and the other from the remnant BH wind, with the latter typically having a time gap to the GW event of around tens of days. When combined with the anticipated gravitational waves (GW) emitted during the BBH merger, such a system emerges as a promising candidate for joint observations involving neutrinos, GWs, and EM signals.Comment: 12 pages, 6 figures, 1 table; submitte