Posterior Probabilities of Effect Sizes and Heterogeneity in Meta-Analysis: An Intuitive Approach of Dealing with Publication Bias

Publication bias remains to be a great challenge when conducting a meta-analysis. It may result in overestimated effect sizes, increased frequency of false positives, and over- or underestimation of the effect size heterogeneity parameter. A new method is introduced, Bayesian Meta-Analytic Snapshot (BMAS), which evaluates both effect size and its heterogeneity and corrects for potential publication bias. It evaluates the probability of the true effect size being zero, small, medium or large, and the probability of true heterogeneity being zero, small, medium or large. This approach, which provides an intuitive evaluation of uncertainty in the evaluation of effect size and heterogeneity, is illustrated with a real-data example, a simulation study, and a Shiny web application of BMAS.

Large-offset P-wave traveltime in layered transversely isotropic media

Large-offset seismic data processing, imaging, and velocity estimation require an accurate traveltime approximation over a wide range of offsets. In layered transversely isotropic media with vertical symmetry axis (VTI), the accuracy of traditional traveltime approximations is limited to near offsets. Herein, we propose a new traveltime approximation that maintains the accuracy of the classical equations around zero offset, and exhibits the correct curvilinear asymptote at infinitely large offsets. Our approximation is based on the conventional acoustic assumption. Its equation incorporates six parameters. To define them, we use the Taylor series expansion of the exact traveltime around zero offset, and a new asymptotic series for infinite offset. Our asymptotic equation shows that the traveltime behavior at infinitely large offsets is dominated by the properties of the layer with the maximum horizontal velocity in the sequence. The parameters of our approximation depend on: the effective zero offset traveltime, the normal moveout velocity, the anellipticity, a new large-offset heterogeneity parameter, and the properties of the layer with the maximum horizontal velocity in the sequence. We apply our traveltime approximation: (1) to directly calculate traveltime and ray parameter at given offsets, as analytical forward modeling; and (2) to estimate the first four of the aforementioned parameters for the layers beneath a known high-velocity layer. Our large-offset heterogeneity parameter includes the layering effect on the reflections traveltime.

Shear wave propagation in magneto poroelastic medium sandwiched between self-reinforced poroelastic medium and poroelastic half space

Purpose The purpose of this paper is to investigate the effect of reinforcement, inhomogeneity and initial stress on the propagation of shear waves. The problem consists of magneto poroelastic medium sandwiched between self-reinforced medium and poroelastic half space. Using Biot’s theory of wave propagation, the frequency equation is obtained. Design/methodology/approach Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium and poroelastic half space is investigated. This particular setup is quite possible in the Earth crust. All the three media are assumed to be inhomogeneous under initial stress. The significant effects of initial stress and inhomogeneity parameters of individual media have been studied. Findings Phase velocity is computed against wavenumber for various values of self-reinforcement, heterogeneity parameter and initial stress. Classical elasticity results are deduced as a particular case of the present study. Also in the absence of inhomogeneity and initial stress, frequency equation is discussed. Graphical representation is made to exhibit the results. Originality/value Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium, and poroelastic half space are investigated in presence of initial stress, and inhomogeneity parameter. For heterogeneous poroelastic half space, the Whittaker’s solution is obtained. From the numerical results, it is observed that heterogeneity parameter, inhomogeneity parameter and reinforcement parameter have significant influences on the wave characteristics. In addition, frequency equation is discussed in absence of inhomogeneity and initial stress. For the validation purpose, numerical results are also computed for a particular case.

Dispersion of Rayleigh-Type Wave in an Exponentially Graded Incompressible Crustal Layer Resting on Yielding Foundation

The objective of this study is to develop a theory to study the propagation of Rayleigh-type waves in an inhomogeneous layer having yielding surface. A detailed study of a Rayleigh-type wave propagating in an exponentially graded incompressible layer resting on yielding surface is considered. The frequency equation being a function of phase velocity, wave number and heterogeneity parameter associated with the yielding parameter and density of inhomogeneous layer reveals the fact that Rayleigh-type wave propagation is greatly influenced by the above-stated parameters. In particular cases, the dispersion relation has been discussed for stress-free foundation by taking yielding parameter tending to zero. In numerical and graphical computation, the significant effects of distortional velocity have been carried out. Moreover, the obtained dispersion relation is found in well agreement to the classical case in homogeneous isotropic layer resting on a yielding foundation.

Guidance for practitioners on the choices of software implementation for frailty models: Simulations and an application in determining the birth interval dynamics

In clustered survival analysis applications, researchers frequently fit frailty models using parametric and nonparametric approaches to obtain the estimates for the parameters associated with the survival model covariates and heterogeneity (frailty). Availability of the off- the-shelve implementations and freely available R software packages makes it convenient for the practitioners to fit these complicated models easily. Even though there has been a couple of studies assessing the stability of the older packages (e.g., survival, coxme) under a variety of scenarios, some of the newer implementations (e.g., frailtySurv, JM and parfm) have not gone through similar rigorous assessment. It is worth evaluating these new software implementations, and comparing them with the older packages. In the current work, via simulations, we will examine the estimates from all of these popularly used software implementations under a variety of scenarios when the corresponding assumptions related to the baseline hazard and frailty distributions are misspecified. Additionally, true heterogeneity parameter, censoring patterns and number of clusters were varied in the simulations to assess respective impacts on the estimates. From these simulations, we observed that when there is a large number of clusters and mild censoring, Cox PH frailty models fitted using a newer semiparametric estimation technique (from the frailtySurv package) produced regression and heterogeneity parameter estimates that were associated with unusually large bias and variability. On the other hand, when the true heterogeneity parameter is substantially large, the Cox PH frailty models fitted using the coxme package were often producing highly variable estimates of the heterogeneity parameter. The simulation findings then guided our choice of appropriate frailty model in the context of determining the birth interval dynamics in Bangladesh.

Technical note: Saturated hydraulic conductivity and textural heterogeneity of soils

Saturated hydraulic conductivity (Ksat) is an important soil parameter that highly depends on soil's particle size distribution (PSD). The nature of this dependency is explored in this work in two ways, (1) by using the information entropy as a heterogeneity parameter of the PSD and (2) using descriptions of PSD in forms of textural triplets, different than the usual description in terms of the triplet of sand, silt, and clay contents. The power of this parameter, as a descriptor of ln⁡Ksat, was tested on a database larger than 19 000 soils. Bootstrap analysis yielded coefficients of determination of up to 0.977 for ln⁡Ksat using a triplet that combines very coarse, coarse, medium, and fine sand as coarse particles; very fine sand, and silt as intermediate particles; and clay as fine particles. The power of the correlation was analysed for different textural classes and different triplets using a bootstrap approach. Also, it is noteworthy that soils with finer textures had worse correlations, as their hydraulic properties are not solely dependent on soil PSD. This heterogeneity parameter can lead to new descriptions of soil PSD, other than the usual clay, silt, and sand, that can describe better different soil physical properties, that are texture-dependent.

Saturated Hydraulic Conductivity and Textural Heterogeneity of Soils

Saturated hydraulic conductivity Ksat is an important soil parameter that highly depends on soil's particle size distribution (PSD). The nature of this dependency is explored in this work in two ways, (1) by using the Information Entropy as a heterogeneity parameter of the PSD and (2) using descriptions of PSD in forms of textural triplets, different than the usual description in terms of the triplet of sand, silt and clay contents. The power of this parameter, as a descriptor of Ksat and log(Ksat) , was tested on a database of > 19 K soils. We found coefficients of determination of up to 0.977 for log(Ksat) using a triplet that combines very coarse, coarse, medium and fine sand as coarse particles, very fine sand as intermediate particles, and silt and clay as fines. The power of the correlation is analysed for different textural classes and different triplets. Overall, the use of textural triplets different than traditional, combined with IE, may provide a useful tool for predicting Ksat values.

Torsional Wave Propagation in a Pre-Stressed Structure with Corrugated and Loosely Bonded Surfaces

An analytical model is presented to study the behaviour of propagation of torsional surface waves in initially stressed porous layer, sandwiched between an orthotropic half-space with initial stress and pre-stressed inhomogeneous anisotropic half-space. The boundary surfaces of the layer and halfspaces are taken as corrugated, as well as loosely bonded. The heterogeneity of the lower half-space is due to trigonometric variation in elastic parameters of the pre-stressed inhomogeneous anisotropic medium. Expression for dispersion relation has been obtained in closed form for the present analytical model to observe the effect of undulation parameter, flatness parameter and porosity on the propagation of torsional surface waves. The obtained dispersion relation is found to be in well agreement with classical Love wave equation for a particular case. The cases of ideally smooth interface and welded interface have also been analysed. Numerical example and graphical illustrations are made to demonstrate notable effect of initial stress, wave number, heterogeneity parameter and initial stress on the phase velocity of torsional surface waves.