Data Examples Research Articles

Constrained simultaneous recovery of the depth to basement and lateral susceptibility variation

AbstractThe basin environment is a widely studied subject in both geology and geophysics for its economic significance in energy and mineral explorations. However, the estimation of the basement depth is often a challenging task given the complexity of the basement relief and lateral physical property change. Previous works simplify the problem by only inverting for the depth to the basement, and more recent studies have suggested the need to incorporate the variation of physical properties to improve basement structure imaging. In this study, we develop an inversion method with the associated workflow to simultaneously recover both the depth to a magnetic basement and a laterally varying magnetic susceptibility in the basement rock. To achieve this, we employ a set of constraints on the inverse problem. Particularly, both the recovered susceptibility and basement depth models are bounded below a possible maximum value, and the depth model is guided by a few depth points obtained from the resistivity models that are obtained from the one‐dimensional blocky inversions of magnetotelluric (MT) data. In addition, we apply the fuzzy C‐means (FCM) clustering to the susceptibility model during the inversion and use the inverted cluster centers to differentiate for different geological units in the basement. To show the effectiveness of our work, we compare the existing approaches and our method using two test inversions on one synthetic model resembling the basin–basement environment before demonstrating our method on a field data example with magnetic data collected by the U.S. Geological Survey (USGS) over the Illinois Basin. Our results show improved recovery in both basement relief and susceptibility in the basement rock, and inversion with field data is able to identify three different susceptibility zones in basement rock below the Illinois Basin.

Spectral induced polarization tomography inversion: Hybridizing homotopic continuation with Bayesian inversion

Induced polarization tomography offers the potential to better characterize the subsurface structures by considering spectral content from data acquisition over a broad frequency range. Spectral induced polarization (SIP) tomography is generally defined as a nonlinear inverse problem commonly solved through deterministic gradient-based methods. To this end, the spectral parameters, i.e., direct current resistivity, chargeability, relaxation time, and frequency exponent, are resolved by individually or simultaneously inverting all frequency data, followed by fitting a generalized Cole-Cole model to the inverted complex resistivities. Due to the high correlation between the Cole-Cole model parameters and a lack of knowledge about the initial approximation of the spectral parameters, using the classical least-squares methods may lead to inaccurate solutions and impede reliable uncertainty analysis. To cope with these limitations, we introduce a new approach based on a hybrid application of a globally convergent homotopic continuation method and a Bayesian inference to reconstruct the distribution of the subsurface spectral parameters. The homotopic optimization, owing to its fast and global convergence, is first implemented to invert multifrequency SIP data sets aimed at retrieving the complex-valued resistivity. Then, Bayesian inversion based on a Markov chain Monte Carlo (MCMC) sampling method, along with a priori information including the lower and upper bounds of the prior distributions, is used to invert the complex resistivity for the Cole-Cole model parameters. By applying the MCMC inversion algorithm, a full nonlinear uncertainty appraisal can be provided. We numerically evaluate the performance of our method using synthetic and real data examples in the presence of topographical effects. Numerical results prove that the homotopic continuation method outperforms the classic, smooth inversion algorithm in the sense of approximation accuracy and computational efficiency. In addition, we determine that our hybrid inversion strategy provides reliable representations of the main features and structure of the earth’s subsurface in terms of the spectral parameters.

Continuous Norming Approaches: A Systematic Review and Real Data Example.

Norming of psychological tests is decisive for test score interpretation. However, conventional norming based on subgroups results either in biases or require very large samples to gather precise norms. Continuous norming methods, namely inferential, semi-parametric, and (simplified) parametric norming, propose to solve those issues. This article provides a systematic review of continuous norming. The review includes 121 publications with overall 189 studies. The main findings indicate that most studies used simplified parametric norming, not all studies considered essential distributional assumptions, and the evidence comparing different norming methods is inconclusive. In a real data example, using the standardization sample of the Need for Cognition-KIDS scale, we compared the precision of conventional, semi-parametric, and parametric norms. A hierarchy in terms of precision emerged with conventional norms being least precise, followed by semi-parametric norms, and parametric norms being most precise. We discuss these findings by comparing our findings and methods to previous studies.

The importance of data preconditioning strategies for envelope full-waveform inversion methods: Demonstration on marine seismic data

Envelope full-waveform inversion (EI) of seismic data has been proposed to overcome the cycle-skipping issue and recover long-wavelength velocity components for over a decade. However, we are aware of few published successful applications of EI on real data examples (except for some correlation- or phase-based EI methods). We implement EI methods (EI with [Formula: see text], EI with p = 1, and improved EI) on 2D marine seismic data and find that the amplitude mismatching between the modeled and observed data is a critical factor that prevents the successful application of EI methods to real data. To match the amplitude better, we include a data weighting preconditioner in the objective function of the EI methods. The preconditioner term acts as a weighting factor to compensate for the amplitude mismatch between the observed and modeled data. We develop a method for calculating the preconditioner term using the amplitude of the head waves as a reference. Furthermore, we derive the adjoint source and gradient of the EI using the data preconditioning method. We illustrate the successful application of EI methods with the data preconditioning method using the 2D marine seismic data example. In comparison to the EI methods without the data preconditioning method, those using data preconditioning yield much more geophysically reasonable velocity models and Kirchhoff image sections and common-image gathers.

Introducing the Research Design of Phenomenography

This article introduces the lesser known qualitative research design of phenomenography to medical science and health professions education researchers. Phenomenography, as distinct from phenomenology, seeks to describe and organise the different ways people experience and understand a phenomenon. Here, the origins and philosophical underpinnings of phenomenography are briefly shared, and an outline of how a phenomenographic research study may be undertaken is presented. This includes data collection tools, analytic method, and examples from the field. Overall, phenomenography is valuable for better understanding the varied experiences of students, educators, practitioners, and patients, with implications for pedagogy, practice, and related outcomes.

Fast computation of local dips using the one-lag correlation method

We adapt the one-lag correlation (OLC) method to estimate the local dips of seismic events or velocity contrasts. The resulting local dips have extensive applications in exploration geophysics, including seismic inversion regularization, computation of seismic attributes like coherence-cube, and facilitating structural-oriented smoothing and extrapolation techniques. Compared to the widely adopted structure tensor (ST) method, the proposed OLC algorithm exhibits notable advantages. The OLC method is characterized by a recursive calculation process that yields significant computational efficiency, boasting an approximately 100 times faster performance for 3D scenarios. The fundamental principle of this novel approach lies in the computation of local dips by using the ratio of two inner products, i.e., OLC, performed on a 2D/3D array along the vertical and horizontal axes, respectively. Crucially, the elements of this array consist of complex numbers derived from the application of the Hilbert transform on the corresponding real-number inputs. Furthermore, the implementation of this algorithm is remarkably straightforward, as exemplified by the concise nature of the code, which comprises a mere ten lines of programming instructions. The OLC method excels in accuracy, surpassing the performance of the ST method, and exhibits superior resistance to random noise. Compelling demonstrations are provided herein to corroborate these desirable properties of the OLC approach, using both synthetic and field data examples.

A double sampling multivariate GLR control charting method for joint monitoring of process mean vector and covariance matrix under additive covariate model

A process is in its stable state when it has sufficient precision and accuracy. The accuracy is expressed as the deviation of the process mean from its target while the low dispersion indicates the high process precision. Therefore, joint monitoring of multivariate process mean and variability ensures a high rate of producing items. This study proposes a multivariate generalized likelihood ratio scheme called DS-MGLR with two features: (1) considering the effect of imprecise observations, and (2) enhancing the chart sensitivity in reacting to process disturbances. Since the shift magnitude in the distribution parameters is not known in advance, the expected average run length is also calculated for both the MGLR and DS-MGLR charts. To reduce the impact of measurement errors, an improved version of the DS-MGLR chart based on multiple measurement approach is developed. Three comparative studies are presented to indicate the importance of the properties of the developed charts. The first study confirms the efficiency of the double sampling strategy, while the second study indicates the error effect. The third one shows the effectiveness of the multiple measurement approach in compensating for the error contamination. Finally, the applicability of the proposed chart is highlighted using a real data example.

Evaluating machine learning predicted subsurface properties via seismic data reconstruction

In recent years, machine learning (ML) approaches have gained significant attention in seismic-based subsurface property estimation problems. However, because of the purely data-driven nature, it is challenging to evaluate the quality of the estimated properties in regions without ground truth data. In this article, we discuss evaluating the quality of ML predicted subsurface properties through ML-based seismic data reconstruction. We use a deep learning workflow to reconstruct the poststack seismic data, then use the misfit between the measured data and the reconstructed data as a proxy for the quality of ML predicted subsurface properties. We also use self-supervised learning to improve the model generalization when training the deep learning model for reconstruction. This proposed method is particularly valuable for subsurface properties without direct physical relation to seismic data. We provide both synthetic and field data examples to demonstrate the consistency of the proposed method.

Two-sample test for high-dimensional covariance matrices: A normal-reference approach

Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required assumptions are not satisfied which attests that they are not always applicable in real data analysis. To overcome this difficulty, a normal-reference test is proposed and studied in this paper. It is shown that under some regularity conditions and the null hypothesis, the proposed test statistic and a chi-squared-type mixture have the same limiting distribution. It is then justified to approximate the null distribution of the proposed test statistic using that of the chi-squared-type mixture. The distribution of the chi-squared-type mixture can be well approximated using a three-cumulant matched chi-squared-approximation with its approximation parameters consistently estimated from the data. The asymptotic power of the proposed test under a local alternative is also established. Simulation studies and a real data example demonstrate that the proposed test works well in general scenarios and outperforms the existing competitors substantially in terms of size control.

Repeated Sieving for Prediction Model Building with High-Dimensional Data.

Background: The prediction of patients' outcomes is a key component in personalized medicine. Oftentimes, a prediction model is developed using a large number of candidate predictors, called high-dimensional data, including genomic data, lab tests, electronic health records, etc. Variable selection, also called dimension reduction, is a critical step in developing a prediction model using high-dimensional data. Methods: In this paper, we compare the variable selection and prediction performance of popular machine learning (ML) methods with our proposed method. LASSO is a popular ML method that selects variables by imposing an L1-norm penalty to the likelihood. By this approach, LASSO selects features based on the size of regression estimates, rather than their statistical significance. As a result, LASSO can miss significant features while it is known to over-select features. Elastic net (EN), another popular ML method, tends to select even more features than LASSO since it uses a combination of L1- and L2-norm penalties that is less strict than an L1-norm penalty. Insignificant features included in a fitted prediction model act like white noises, so that the fitted model will lose prediction accuracy. Furthermore, for the future use of a fitted prediction model, we have to collect the data of all the features included in the model, which will cost a lot and possibly lower the accuracy of the data if the number of features is too many. Therefore, we propose an ML method, called repeated sieving, extending the standard regression methods with stepwise variable selection. By selecting features based on their statistical significance, it resolves the over-selection issue with high-dimensional data. Results: Through extensive numerical studies and real data examples, our results show that the repeated sieving method selects far fewer features than LASSO and EN, but has higher prediction accuracy than the existing ML methods. Conclusions: We conclude that our repeated sieving method performs well in both variable selection and prediction, and it saves the cost of future investigation on the selected factors.

Versatile Descent Algorithms for Group Regularization and Variable Selection in Generalized Linear Models

This article proposes an adaptively bounded gradient descent (ABGD) algorithm for group elastic net penalized regression. Unlike previously proposed algorithms, the proposed algorithm adaptively bounds the Fisher information matrix, which results in a flexible and stable computational framework. In particular, the proposed algorithm (i) does not require orthogonalization of the predictors, and (ii) can be easily applied to any combination of exponential family response distribution and link function. The proposed algorithm is implemented in the grpnet R package (available from CRAN), which implements the approach for common response distributions (Gaussian, binomial, and Poisson), as well as several response distributions not previously considered in the group penalization literature (i.e., multinomial, negative binomial, gamma, and inverse Gaussian). Simulated and real data examples demonstrate that the proposed algorithm is as or more efficient than existing methods for Gaussian, binomial, and Poisson distributions. Furthermore, using two genomic examples, I demonstrate how the proposed algorithm can be applied to high-dimensional multinomial regression problems with grouped predictors. R code to reproduce the results is included as supplementary materials.

Multiple-Use Calibration for All Future Values and Exact Two-Sided Simultaneous Tolerance Intervals in Linear Regression

Multiple-use calibration using regression is an important statistical tool. Confidence sets for the x-values associated with all future y-values should guarantee a key property, which can be satisfied by simultaneous tolerance intervals (STI’s), and so multiple-use calibration requires the construction of STI’s. In this article, exact two-sided STI’s have been constructed for polynomial regression over any given covariate interval. There is a misconception that two-sided pointwise tolerance intervals (PTI’s) can be employed for multiple-use calibration. This article shows that the confidence sets based on the two-sided PTI’s do not satisfy the key property and so should not be used. Real-world data examples are given in this article for illustration. Supplementary materials for this article are available online.

Machine-learning-based particle identification with missing data

In this work, we introduce a novel method for Particle Identification (PID) within the scope of the ALICE experiment at the Large Hadron Collider at CERN. Identifying products of ultrarelativisitc collisions delivered by the LHC is one of the crucial objectives of ALICE. Typically employed PID methods rely on hand-crafted selections, which compare experimental data to theoretical simulations. To improve the performance of the baseline methods, novel approaches use machine learning models that learn the proper assignment in a classification task. However, because of the various detection techniques used by different subdetectors, as well as the limited detector efficiency and acceptance, produced particles do not always yield signals in all of the ALICE components. This results in data with missing values. Out of the box machine learning solutions cannot be trained with such examples without either modifying the training dataset or re-designing the model architecture. In this work, we propose the new method for PID that addresses these issues and can be trained with all of the available data examples, including incomplete ones. Our approach improves the PID purity and efficiency of the selected sample for all investigated particle species.

Instrumental Variable Method for Regularized Estimation in Generalized Linear Measurement Error Models

Regularized regression methods have attracted much attention in the literature, mainly due to its application in high-dimensional variable selection problems. Most existing regularization methods assume that the predictors are directly observed and precisely measured. It is well known that in a low-dimensional regression model if some covariates are measured with error, then the naive estimators that ignore the measurement error are biased and inconsistent. However, the impact of measurement error in regularized estimation procedures is not clear. For example, it is known that the ordinary least squares estimate of the regression coefficient in a linear model is attenuated towards zero and, on the other hand, the variance of the observed surrogate predictor is inflated. Therefore, it is unclear how the interaction of these two factors affects the selection outcome. To correct for the measurement error effects, some researchers assume that the measurement error covariance matrix is known or can be estimated using external data. In this paper, we propose the regularized instrumental variable method for generalized linear measurement error models. We show that the proposed approach yields a consistent variable selection procedure and root-n consistent parameter estimators. Extensive finite sample simulation studies show that the proposed method performs satisfactorily in both linear and generalized linear models. A real data example is provided to further demonstrate the usage of the method.

Graphical criteria for the identification of marginal causal effects in continuous-time survival and event-history analyses

Abstract We consider continuous-time survival and event-history settings, where our aim is to graphically represent causal structures allowing us to characterize when a causal parameter is identified from observational data. This causal parameter is formalized as the effect on an outcome event of a (possibly hypothetical) intervention on the intensity of a treatment process. To establish identifiability, we propose novel graphical rules indicating whether the observed information is sufficient to obtain the desired causal effect by suitable reweighting. This requires a different type of graph than in discrete time. We formally define causal semantics for the corresponding dynamic graphs that represent local independence models for multivariate counting processes. Importantly, our work highlights that causal inference from censored data relies on subtle structural assumptions on the censoring process beyond independent censoring; these can be verified graphically. Put together, our results are the first to establish graphical rules for nonparametric causal identifiability in event processes in this generality for the continuous-time case, not relying on particular parametric survival models. We conclude with a data example on Human papillomavirus (HPV) testing for cervical cancer screening, where the assumptions are illustrated graphically and the desired effect is estimated by reweighted cumulative incidence curves.

Joint Statistical Inference for the Area under the ROC Curve and Youden Index under a Density Ratio Model

The receiver operating characteristic (ROC) curve is a valuable statistical tool in medical research. It assesses a biomarker’s ability to distinguish between diseased and healthy individuals. The area under the ROC curve (AUC) and the Youden index (J) are common summary indices used to evaluate a biomarker’s diagnostic accuracy. Simultaneously examining AUC and J offers a more comprehensive understanding of the ROC curve’s characteristics. In this paper, we utilize a semiparametric density ratio model to link the distributions of a biomarker for healthy and diseased individuals. Under this model, we establish the joint asymptotic normality of the maximum empirical likelihood estimator of (AUC,J) and construct an asymptotically valid confidence region for (AUC,J). Furthermore, we propose a new test to determine whether a biomarker simultaneously exceeds prespecified target values of AUC0 and J0 with the null hypothesis H0:AUC≤AUC0 or J≤J0 against the alternative hypothesis Ha:AUC>AUC0 and J>J0. Simulation studies and a real data example on Duchenne Muscular Dystrophy are used to demonstrate the effectiveness of our proposed method and highlight its advantages over existing methods.

Discontinuous permafrost detection from neural network-ensemble learning based electrical resistivity tomography

Electrical resistivity tomography (ERT) is an effective method for detecting the distribution of permafrost. However, the general inversion method of ERT cannot satisfy the engineering designation demand, resulting in the foundation of thaw settlement in discontinuous permafrost regions. In this study, we proposed a neural network-ensemble learning inversion method to improve the detection accuracy of discontinuous permafrost. First, a series of different resistivity distributions was evaluated to establish forward models for the training of a backpropagation neural network (BPNN). The resistivity distributions of the forward models varied with the temperature gradient, similar to the resistivity distribution of real discontinuous permafrost. The bagging algorithm of ensemble learning was then used to optimize the BPNN inversion models. Finally, three discontinuous permafrost resistivity models and two field data examples are considered to demonstrate the feasibility of the proposed inversion model. The inversion results of synthetic and field examples show that the neural network-ensemble learning model achieved a greater inversion effect with better accuracy and less noisy points than a single BPNN model or the Res2Dinv method. The trained ensemble learning inversion method has good application in field permafrost exploration.

Nonparametric estimation of densities on the hypersphere using a parametric guide

AbstractHyperspherical kernel density estimators (KDE), which use a parametric distribution as a guide, are studied in this paper. The main benefit is that these estimators improve the bias of nonguided kernel density estimators when the parametric guiding distribution is not too far from the true density, while preserving the variance. When using a von Mises‐Fisher density as guide, the proposal performs as well as the classical KDE, even when the guiding model is incorrect, and far from the true distribution. This benefit is particular for the hyperspherical setting given its compact support, and is in contrast to similar methods for real valued data. Moreover, we deal with the important issue of data‐driven selection of the smoothing parameter. Simulations and real data examples illustrate the finite‐sample performance of the proposed method, also in comparison with other recently proposed estimation methods.

Integrating endogeneity in survey sampling using instrumental-variable calibration estimator

The endogeneity problem arises when the auxiliary variables correlate to the error terms. In such cases, appropriate instrumental variables ensure efficient estimation. Calibration has recognized itself as an important methodological tool at a large scale to estimate the population total in survey sampling. Which does not offer efficient estimation in the presence of endogeneity. When endogeneity is present in the auxiliary variables, the calibration using endogenous auxiliary variables may produce biasedness and increase variance due to inappropriate model assumptions. In this article, we propose instrumental-variable calibrated estimators by using the classical instrumental-variables approach for the case of exact identification that are more efficient than conventional calibration estimators when some auxiliary variables are endogenous. The necessary properties of the proposed estimators are presented. Our study is backed by both the simulation study and a real data example to check the performance of the proposed estimators.

Exact Bahadur Slope for combining independent tests in the case of the Pareto distribution

In this paper, we compared the Exact Bahadur Slope (EBS) and the asymptotic relative efficiency of four combination methods for testing a single hypothesis against a one-sided alternative in the case of Pareto distribution when the number of tests tends to infinity. These methods combine the p-value of the corresponding test into one overall test. Fisher's, logistic, the sum of p-values, and inverse normal procedures are the four techniques used in our study. To study the performance of the combination methods, we derived the EBS expressions and compared the limit ratios locally and for large values of the shape parameter of the Pareto distribution via EBS. We also computed the EBS numerically for when the parameter of interest starts moving from the null space and applied the four methods to real data examples. We found that Fisher's method uniformly dominates the other methods in terms of EBS.