Posterior propriety of an objective prior for generalized hierarchical normal linear models

Bayesian Hierarchical models has been widely used in modern statistical application. To deal with the data having complex structures, we propose a generalized hierarchical normal linear (GHNL) model which accommodates arbitrarily many levels, usual design matrices and ‘vanilla’ covariance matrices. Objective hyperpriors can be employed for the GHNL model to express ignorance or match frequentist properties, yet the common objective Bayesian approaches are infeasible or fraught with danger in hierarchical modelling. To tackle this issue, [Berger, J., Sun, D., & Song, C. (2020b). An objective prior for hyperparameters in normal hierarchical models. Journal of Multivariate Analysis, 178, 104606. https://doi.org/10.1016/j.jmva.2020.104606] proposed a particular objective prior and investigated its properties comprehensively. Posterior propriety is important for the choice of priors to guarantee the convergence of MCMC samplers. James Berger conjectured that the resulting posterior is proper for a hierarchical normal model with arbitrarily many levels, a rigorous proof of which was not given, however. In this paper, we complete this story and provide an user-friendly guidance. One main contribution of this paper is to propose a new technique for deriving an elaborate upper bound on the integrated likelihood, but also one unified approach to checking the posterior propriety for linear models. An efficient Gibbs sampling method is also introduced and outperforms other sampling approaches considerably

Reverse spatial visual top-k query

With the wide application of mobile Internet techniques an location-based services (LBS), massive multimedia data with geo-tags has been generated and collected. In this paper, we investigate a novel type of spatial query problem, named reverse spatial visual top- $k$ query (RSVQ k ) that aims to retrieve a set of geo-images that have the query as one of the most relevant geo-images in both geographical proximity and visual similarity. Existing approaches for reverse top- $k$ queries are not suitable to address this problem because they cannot effectively process unstructured data, such as image. To this end, firstly we propose the definition of RSVQ k problem and introduce the similarity measurement. A novel hybrid index, named VR 2 -Tree is designed, which is a combination of visual representation of geo-image and R-Tree. Besides, an extension of VR 2 -Tree, called CVR 2 -Tree is introduced and then we discuss the calculation of lower/upper bound, and then propose the optimization technique via CVR 2 -Tree for further pruning. In addition, a search algorithm named RSVQ k algorithm is developed to support the efficient RSVQ k query. Comprehensive experiments are conducted on four geo-image datasets, and the results illustrate that our approach can address the RSVQ k problem effectively and efficiently

Bimodal coupling of ripples and slower oscillations during sleep in patients with focal epilepsy.

OBJECTIVE: Differentiating pathologic and physiologic high-frequency oscillations (HFOs) is challenging. In patients with focal epilepsy, HFOs occur during the transitional periods between the up and down state of slow waves. The preferred phase angles of this form of phase-event amplitude coupling are bimodally distributed, and the ripples (80-150 Hz) that occur during the up-down transition more often occur in the seizure-onset zone (SOZ). We investigated if bimodal ripple coupling was also evident for faster sleep oscillations, and could identify the SOZ. METHODS: Using an automated ripple detector, we identified ripple events in 40-60 min intracranial electroencephalography (iEEG) recordings from 23 patients with medically refractory mesial temporal lobe or neocortical epilepsy. The detector quantified epochs of sleep oscillations and computed instantaneous phase. We utilized a ripple phasor transform, ripple-triggered averaging, and circular statistics to investigate phase event-amplitude coupling. RESULTS: We found that at some individual recording sites, ripple event amplitude was coupled with the sleep oscillatory phase and the preferred phase angles exhibited two distinct clusters (p \u3c 0.05). The distribution of the pooled mean preferred phase angle, defined by combining the means from each cluster at each individual recording site, also exhibited two distinct clusters (p \u3c 0.05). Based on the range of preferred phase angles defined by these two clusters, we partitioned each ripple event at each recording site into two groups: depth iEEG peak-trough and trough-peak. The mean ripple rates of the two groups in the SOZ and non-SOZ (NSOZ) were compared. We found that in the frontal (spindle, p = 0.009; theta, p = 0.006, slow, p = 0.004) and parietal lobe (theta, p = 0.007, delta, p = 0.002, slow, p = 0.001) the SOZ incidence rate for the ripples occurring during the trough-peak transition was significantly increased. SIGNIFICANCE: Phase-event amplitude coupling between ripples and sleep oscillations may be useful to distinguish pathologic and physiologic events in patients with frontal and parietal SOZ

Ripples Have Distinct Spectral Properties and Phase-Amplitude Coupling With Slow Waves, but Indistinct Unit Firing, in Human Epileptogenic Hippocampus

Ripple oscillations (80–200 Hz) in the normal hippocampus are involved in memory consolidation during rest and sleep. In the epileptic brain, increased ripple and fast ripple (200–600 Hz) rates serve as a biomarker of epileptogenic brain. We report that both ripples and fast ripples exhibit a preferred phase angle of coupling with the trough-peak (or On-Off) state transition of the sleep slow wave in the hippocampal seizure onset zone (SOZ). Ripples on slow waves in the hippocampal SOZ also had a lower power, greater spectral frequency, and shorter duration than those in the non-SOZ. Slow waves in the mesial temporal lobe modulated the baseline firing rate of excitatory neurons, but did not significantly influence the increased firing rate associated with ripples. In summary, pathological ripples and fast ripples occur preferentially during the On-Off state transition of the slow wave in the epileptogenic hippocampus, and ripples do not require the increased recruitment of excitatory neurons.Fil: Weiss, Shennan A.. Thomas Jefferson University; Estados UnidosFil: Song, Inkyung. Thomas Jefferson University; Estados UnidosFil: Leng, Mei. University of California at Los Angeles; Estados UnidosFil: Pastore, Tomás. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Fernandez Slezak, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Waldman, Zachary. Thomas Jefferson University; Estados UnidosFil: Orosz, Iren. University of California at Los Angeles; Estados UnidosFil: Gorniak, Richard. Thomas Jefferson University; Estados UnidosFil: Donmez, Mustafa. Thomas Jefferson University; Estados UnidosFil: Sharan, Ashwini. Thomas Jefferson University; Estados UnidosFil: Wu, Chengyuan. Thomas Jefferson University; Estados UnidosFil: Fried, Itzhak. University of California at Los Angeles; Estados UnidosFil: Sperling, Michael R.. Thomas Jefferson University; Estados UnidosFil: Bragin, Anatol. University of California at Los Angeles; Estados UnidosFil: Engel, Jerome. University of California at Los Angeles; Estados UnidosFil: Nir, Yuval. Tel Aviv University; IsraelFil: Staba, Richard. University of California at Los Angeles; Estados Unido

Constructing a Tough Shield around the Wellbore by Stabilizing the Multi-Scale Structure of Granular Plugging Zone in Deep Fractured Reservoirs

Fracture plugging zone with low strength is one of the key reasons for plugging failure in deep fractured reservoirs. Forming a high-strength plugging zone is a key engineering problem to be solved in wellbore strengthening. In this chapter, wellbore strengthening mechanisms of plugging zone for wellbore strengthening in deep fractured reservoirs are revealed from a relationship between mechanical structure and strength standpoint. Physical granular bridging materials dislocation and crushing under pressure fluctuation induce the strong force chains network failure, which leads to macroscale friction or shear failure of plugging zone. The main methods to improve microscale materials stability are to increase friction resistance, exert embedding effect, and strengthen bonding effect. Factors, which strengthen the meso-structure stability, include increasing shear strength and proportion of strong force chains. Key measures to strengthen the macrostructure stability of plugging zone are by improving its compactness, controlling its length, and ensuring the stability timeliness

Beat vibration of hybrid boron nitride-carbon nanotubes – A new avenue to atomic-scale mass sensing

In this paper a beat phenomenon is reported in molecular dynamics simulations for vibrating boron nitride-carbon nanotubes (BN-CNTs) and then analysed based on a continuum mechanics theory. It was shown that the distinctive dynamic behaviour is a result of the superposition of two orthogonal transverse vibrations whose frequencies are slightly different due to the oval cross-section of the hybrid nanotubes. In particular, the interaction between the two vibrations in BN-CNTs will facilitate to resolve the fundamental issue in developing mass nanosensors for atomic-scale mass measuring. To reach this goal, efforts should be made to maintain high quality factor of the BN-CNT oscillating system by minimising the damping effect of its surrounding environment. This issue turns out to be essential for the beat mode-based nanosensors as large damping will reduce the hybrid nanotubes to conventional resonators with only one transverse vibration same as that reported for homogeneous nanotubes

The Distance Matrices of Some Graphs Related to Wheel Graphs

Let D denote the distance matrix of a connected graph G. The inertia of D is the triple of integers (n+(D), n0(D), n-(D)), where n+(D), n0(D), and n-(D) denote the number of positive, 0, and negative eigenvalues of D, respectively. In this paper, we mainly study the inertia of distance matrices of some graphs related to wheel graphs and give a construction for graphs whose distance matrices have exactly one positive eigenvalue

A class of admissible estimators of multiple regression coefficient with an unknown variance

Suppose that we observe ${\boldsymbol y} \mid {\boldsymbol \theta },\ \tau \sim N_p({\boldsymbol X}{\boldsymbol \theta },\tau ^{-1}{\boldsymbol I}_p)$, where ${\boldsymbol \theta }$ is an unknown vector with unknown precision τ. Estimating the regression coefficient ${\boldsymbol \theta }$ with known τ has been well studied. However, statistical properties such as admissibility in estimating ${\boldsymbol \theta }$ with unknown τ are not well studied. Han [(2009). Topics in shrinkage estimation and in causal inference (PhD thesis). Warton School, University of Pennsylvania] appears to be the first to consider the problem, developing sufficient conditions for the admissibility of estimating means of multivariate normal distributions with unknown variance. We generalise the sufficient conditions for admissibility and apply these results to the normal linear regression model. 2-level and 3-level hierarchical models with unknown precision τ are investigated when a standard class of hierarchical priors leads to admissible estimators of ${\boldsymbol \theta }$ under the normalised squared error loss. One reason to consider this problem is the importance of admissibility in the hierarchical prior selection, and we expect that our study could be helpful in providing some reference for choosing hierarchical priors

Posterior Propriety of an Objective Prior in a 4-Level Normal Hierarchical Model

The use of hierarchical Bayesian models in statistical practice is extensive, yet it is dangerous to implement the Gibbs sampler without checking that the posterior is proper. Formal approaches to objective Bayesian analysis, such as the Jeffreys-rule approach or reference prior approach, are only implementable in simple hierarchical settings. In this paper, we consider a 4-level multivariate normal hierarchical model. We demonstrate the posterior using our recommended prior which is proper in the 4-level normal hierarchical models. A primary advantage of the recommended prior over other proposed objective priors is that it can be used at any level of a hierarchical model