Real Data Analysis Research Articles

Skew-Symmetric Generalized Normal and Generalized t Distributions

In this paper, we introduce the skew-symmetric generalized normal and the skew-symmetric generalized t distributions, which are skewed extensions of symmetric special cases of generalized skew-normal and generalized skew-t distributions, respectively. We derive key distributional properties for these new distributions, including a recurrence relation and an explicit form for the cumulative distribution function (cdf) of the skew-symmetric generalized t distribution. Numerical examples including a simulation study and a real data analysis are presented to illustrate the practical applicability of these distributions.

Enhancing disease risk gene discovery by integrating transcription factor-linked trans-variants into transcriptome-wide association analyses.

Transcriptome-wide association studies (TWAS) have been successful in identifying disease susceptibility genes by integrating cis-variants predicted gene expression with genome-wide association studies (GWAS) data. However, trans-variants for predicting gene expression remain largely unexplored. Here, we introduce transTF-TWAS, which incorporates transcription factor (TF)-linked trans-variants to enhance model building for TF downstream target genes. Using data from the Genotype-Tissue Expression project, we predict gene expression and alternative splicing and applied these prediction models to large GWAS datasets for breast, prostate, lung cancers and other diseases. We demonstrate that transTF-TWAS outperforms other existing TWAS approaches in both constructing gene expression prediction models and identifying disease-associated genes, as shown by simulations and real data analysis. Our transTF-TWAS approach significantly contributes to the discovery of disease risk genes. Findings from this study shed new light on several genetically driven key TF regulators and their associated TF-gene regulatory networks underlying disease susceptibility.

Shape Mediation Analysis in Alzheimer's Disease Studies.

As a crucial tool in neuroscience, mediation analysis has been developed and widely adopted to elucidate the role of intermediary variables derived from neuroimaging data. Typically, structural equation models (SEMs) are employed to investigate the influences of exposures on outcomes, with model coefficients being interpreted as causal effects. While existing SEMs have proven to be effective tools for mediation analysis involving various neuroimaging-related mediators, limited research has explored scenarios where these mediators are derived from the shape space. In addition, the linear relationship assumption adopted in existing SEMs may lead to substantial efficiency losses and decreased predictive accuracy in real-world applications. To address these challenges, we introduce a novel framework for shape mediation analysis, designed to explore the causal relationships between genetic exposures and clinical outcomes, whether mediated or unmediated by shape-related factors while accounting for potential confounding variables. Within our framework, we apply the square-root velocity function to extract elastic shape representations, which reside within the linear Hilbert space of square-integrable functions. Subsequently, we introduce a two-layer shape regression model to characterize the relationships among neurocognitive outcomes, elastic shape mediators, genetic exposures, and clinical confounders. Both estimation and inference procedures are established for unknown parameters along with the corresponding causal estimands. The asymptotic properties of estimated quantities are investigated as well. Both simulated studies and real-data analyses demonstrate the superior performance of our proposed method in terms of estimation accuracy and robustness when compared to existing approaches for estimating causal estimands.

On Optimality of Mallows Model Averaging

In the past decades, model averaging (MA) has attracted much attention as it has emerged as an alternative tool to the model selection (MS) statistical approach. Hansen introduced a Mallows model averaging (MMA) method with model weights selected by minimizing a Mallows’ C p criterion. The main theoretical justification for MMA is an asymptotic optimality (AOP), which states that the risk/loss of the resulting MA estimator is asymptotically equivalent to that of the best but infeasible averaged model. MMA’s AOP is proved in the literature by either constraining weights in a special discrete weight set or limiting the number of candidate models. In this work, it is first shown that under these restrictions, however, the optimal risk of MA becomes an unreachable target, and MMA may converge more slowly than MS. In this background, a foundational issue that has not been addressed is: When a suitably large set of candidate models is considered, and the model weights are not harmfully constrained, can the MMA estimator perform asymptotically as well as the optimal convex combination of the candidate models? We answer this question in both nested and non-nested settings. In the nested setting, we provide finite sample inequalities for the risk of MMA and show that without unnatural restrictions on the candidate models, MMA’s AOP holds in a general continuous weight set under certain mild conditions. In the non-nested setting, a sufficient condition and a negative result are established for the achievability of the optimal MA risk. Implications on minimax adaptivity are given as well. The results from simulations and real data analysis back up our theoretical findings. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Change point detection in INAR(p) models via likelihood ratio scanning method

In this paper, we consider an integer-valued autoregressive (INAR) model. Based on the likelihood ratio scanning method (LRSM), the numbers and locations of the piecewise stationary INAR process change points are discussed. The minimum description length (MDL) function of the INAR model is given. Moreover, we also study the case when the sum of coefficients in each segment of the model tends to 1 and make adjustments to the MDL criterion in the LRSM. In this way, the accuracy of change point detection is improved. In the end, simulation experiments and real data analysis are conducted to illustrate the efficiency of the LRSM.

ADAPT: Analysis of Microbiome Differential Abundance by Pooling Tobit Models.

Microbiome differential abundance analysis remains a challenging problem despite multiple methods proposed in the literature. The excessive zeros and compositionality of metagenomics data are two main challenges for differential abundance analysis. We propose a novel method called "Analysis of Differential Abundance by Pooling Tobit Models" (ADAPT) to overcome these two challenges. ADAPT interprets zero counts as left-censored observations to avoid unfounded assumptions and complex models. ADAPT also encompasses a theoretically justified way of selecting non-differentially abundant microbiome taxa as a reference to reveal differentially abundant taxa while avoiding false discoveries. We generate synthetic data using independent simulation frameworks to show that ADAPT has more consistent false discovery rate control and higher statistical power than competitors. We use ADAPT to analyze 16S rRNA sequencing of saliva samples and shotgun metagenomics sequencing of plaque samples collected from infants in the COHRA2 study. The results provide novel insights into the association between the oral microbiome and early childhood dental caries. The R package ADAPT can be installed from Bioconductor at https://bioconductor.org/packages/release/bioc/html/ADAPT.html or from Github at https://github.com/mkbwang/ADAPT. The source codes for simulation studies and real data analysis are available at https://github.com/mkbwang/ADAPT_example. The supplementary notes and figures are compiled together in a PDF document. The supplementary tables are combined in an excel file. Both the PDF document and the excel file are available online.

Modal volatility function

We in this article propose a novel non‐parametric estimator for the volatility function within a broad context that encompasses nonlinear time series models as a special case. The new estimator, built on the mode value, is designed to complement existing mean volatility measures to reveal distinct data features. We demonstrate that the suggested modal volatility estimator can be obtained asymptotically as well as if the conditional mean regression function were known, assuming observations are from a strictly stationary and absolutely regular process. Under mild regularity conditions, we establish that the asymptotic distributions of the resulting estimator align with those derived from independent observations, albeit with a slower convergence rate compared to non‐parametric mean regression. The theory and practice of bandwidth selection are discussed. Moreover, we put forward a variance reduction technique for the modal volatility estimator to attain asymptotic relative efficiency while maintaining the asymptotic bias unchanged. We numerically solve the modal regression model with the use of a modified modal‐expectation‐maximization algorithm. Monte Carlo simulations are conducted to assess the finite sample performance of the developed estimation procedure. Two real data analyses are presented to further illustrate the newly proposed model in practical applications. To potentially enhance the accuracy of the bias term, we in the end discuss the extension of the method to local exponential modal estimation. We showcase that the suggested exponential modal volatility estimator shares the same asymptotic variance as the non‐parametric modal volatility estimator but may exhibit a smaller bias.

Robust estimation of the incubation period and the time of exposure using γ-divergence

Estimating the exposure time to single infectious pathogens and the associated incubation period, based on symptom onset data, is crucial for identifying infection sources and implementing public health interventions. However, data from rapid surveillance systems designed for early outbreak warning often come with outliers originated from individuals who were not directly exposed to the initial source of infection (i.e. tertiary and subsequent infection cases), making the estimation of exposure time challenging. To address this issue, this study uses a three-parameter lognormal distribution and proposes a new γ-divergence-based robust approach for estimating the parameter corresponding to exposure time with a tailored optimization procedure using the majorization-minimization algorithm, which ensures the monotonic decreasing property of the objective function. Comprehensive numerical experiments and real data analyses suggest that our method is superior to conventional methods in terms of bias, mean squared error, and coverage probability of 95% confidence intervals.

Benchmarking the non-flow contributions to the elliptic flow parameter (v2) in proton-proton collisions

Abstract This manuscript reports on the elliptic flow parameter, v 2 , in proton-proton (p–p) collisions using PYTHIA8 event generator simulations. The typical event plane (EP) method v 2 (EP) as the one used for the real data analysis has been adopted to measure the v 2 of particles composed of different quark flavors, and produced at mid-pseudorapidity ∣η∣≤1 at center-of-mass energy s = 200 GeV and s = 13 TeV. The event plane has been constructed using the soft-charged particles with transverse momentum ( p T < 2 GeV/c) produced in various η ranges. The pseudorapidity gap technique (Δη) between the particle of interest and the soft charged particles contributed to the event plane constructions has been utilized to benchmark the non-flow contributions. The v 2 π ± , π 0 , v 2 J ∕ ψ , ϒ , K , D , B , and the v 2 γ dir show similar pattern dependence on the transverse momentum for the same Δη, at both s = 200 GeV and s = 13 TeV. At each center-of-mass energy, the measured v 2 shows obvious dependence on the quark flavor contents where v 2 γ dir ≤ v 2 J ∕ ψ , ϒ , K , D , B ≤ v 2 π ± , π 0 for similar Δη gap. The measured v 2 shows slightly higher values at smaller s for particles of similar values of Δη gaps, particularly at small Δη gap. The measured v 2 for all particles shows systematic decreases with increasing the Δη gap as expected from the previous experimental results. Because PYTHIA8 simulations do not incorporate final state interactions, the v 2 ( EP ) values reported here primarily reflect the non-flow contributions and its dependence on the quark contents, pseudorapidity gap as a function on p T at each center of mass–energy. These contributions should be carefully subtracted from the signal in real data analysis that employs the same event plane determination algorithm.

Enhanced adaptive permutation test with negative binomial distribution in genome-wide omics datasets.

The permutation test has been widely used to provide the p-values of statistical tests when the standard test statistics do not follow parametric null distributions. However, the permutation test may require huge numbers of iterations, especially when the detection of very small p-values is required for multiple testing adjustments in the analysis of datasets with a large number of features. To overcome this computational burden, we suggest a novel enhanced adaptive permutation test that estimates p-values using the negative binomial (NB) distribution. By the method, the number of permutations are differently determined for individual features according to their potential significance. In detail, the permutation procedure stops, when test statistics from the permuted dataset exceed the observed statistics from the original dataset by a predefined number of times. We showed that this procedure reduced the number of permutations especially when there were many insignificant features. For significant features, we enhanced the reduction with Stouffer's method after splitting datasets. From the simulation study, we found that the enhanced adaptive permutation test dramatically reduced the number of permutations while keeping the precision of the permutation p-value within a small range, when compared to the ordinary permutation test. In real data analysis, we applied the enhanced adaptive permutation test to a genome-wide single nucleotide polymorphism (SNP) dataset of 327,872 features. We found the analysis with the enhanced adaptive permutation took a feasible time for genome-wide omics datasets, and successfully identified features of highly significant p-values with reasonable confidence intervals.

Scalable log-ratio lasso regression for enhanced microbial feature selection with FLORAL.

Identifying predictive biomarkers of patient outcomes from high-throughput microbiome data is of high interest, while existing computational methods do not satisfactorily account for complex survival endpoints, longitudinal samples, and taxa-specific sequencing biases. We present FLORAL, an open-source tool to perform scalable log-ratio lasso regression and microbial feature selection for continuous, binary, time-to-event, and competing risk outcomes, with compatibility for longitudinal microbiome data as time-dependent covariates. The proposed method adapts the augmented Lagrangian algorithm for a zero-sum constraint optimization problem while enabling a two-stage screening process for enhanced false-positive control. In extensive simulation and real-data analyses, FLORAL achieved consistently better false-positive control compared to other lasso-based approaches and better sensitivity over popular differential abundance testing methods for datasets with smaller sample sizes. In a survival analysis of allogeneic hematopoietic cell transplant recipients, FLORAL demonstrated considerable improvement in microbial feature selection by utilizing longitudinal microbiome data over solely using baseline microbiome data.

Large-scale dependent multiple testing via higher-order hidden Markov models

ABSTRACT Taking into account the local dependence structure in large-scale multiple testing is expected to improve both the efficiency of the testing procedure and the interpretability of scientific findings. The hidden Markov model (HMM), as an effective model to describe the sequential dependence, has been successfully applied to large-scale multiple testing with local correlations. However, in many applications, the first-order Markov chain is not flexible enough to capture the complexity of local correlations. To address this issue, this paper proposes a novel multiple testing procedure that uses a higher-order Markov chain to better characterize local correlations among tests. The proposed procedure is validated by theoretical results and simulation studies, which show that it outperforms its competitors in terms of power. Finally, a real data analysis is presented to demonstrate the favorable performance of the proposed procedure.

Carbon option pricing and carbon management under uncertain finance theory

Against the backdrop of increasingly severe global climate change issues, more and more countries and regions are adopting carbon emission trading, which is an effective market mechanism. As an important component of the carbon market, American carbon options provide more flexible trading tools to help companies avoid price risks. Therefore, the pricing research of American carbon options is of great significance for promoting the healthy development of the carbon market. Nonetheless, existing pricing methods are all based on probability theory, which need to satisfy the premise that the distribution function is close to the true frequency sufficiently. However, usually such premise is ill-suited in carbon market. To alleviate the predicament of the need for satisfying probability theory’s premise, this work investigates American carbon option pricing under the framework of uncertainty theory, which is another axiomatic mathematical system. For this purpose, uncertain differential equation is adopted to model the price of carbon future, and pricing formulae for American call and put carbon options are derived based on this model. Real data analyses illustrate the proposed method in details. Furthermore, it provides a detailed schema of applying the American carbon option for carbon asset management, which can optimize risk control for carbon consuming enterprises.

Maximum likelihood estimation of elliptical tail

This study is focused on the efficient estimation of the elliptical tail. Initially, we derive the density function of the spectral measure of an elliptical distribution concerning a dominating measure on the unit sphere, which consequently leads to the density function of the elliptical tail. Subsequently, we propose a maximum likelihood estimation based on the derived density function class. The resulting maximum likelihood estimator (MLE) is proven to be consistent and asymptotically normal. Moreover, it is demonstrated that the MLE is asymptotically efficient, with the added advantage that its asymptotic covariance matrix can be feasibly estimated at a low computational cost. A simulation study and real data analysis are conducted to illustrate the efficacy of the proposed method.

Local signal detection on irregular domains with generalized varying coefficient models

In spatial analysis, it is essential to understand and quantify spatial or temporal heterogeneity. This paper focuses on the generalized spatially varying coefficient model (GSVCM), a powerful framework to accommodate spatial heterogeneity by allowing regression coefficients to vary in a given spatial domain. We propose a penalized bivariate spline method for detecting local signals in GSVCM. The key idea is to use bivariate splines defined on triangulation to approximate nonparametric varying coefficient functions and impose a local penalty on L 2 norms of spline coefficients for each triangle to identify null regions of zero effects. Moreover, we develop model confidence regions as the inference tool to quantify the uncertainty of the estimated null regions. Our method partitions the region of interest using triangulation and efficiently approximates irregular domains. In addition, we propose an efficient algorithm to obtain the proposed estimator using the local quadratic approximation. We also establish the consistency of estimated nonparametric coefficient functions and the estimated null regions. The numerical performance of the proposed method is evaluated in both simulation cases and real data analysis.

Modelling motion energy in psychotherapy: A dynamical systems approach.

In this study we introduce an innovative mathematical and statistical framework for the analysis of motion energy dynamics in psychotherapy sessions. Our method combines motion energy dynamics with coupled linear ordinary differential equations and a measurement error model, contributing new clinical parameters to enhance psychotherapy research. Our approach transforms raw motion energy data into an interpretable account of therapist-patient interactions, providing novel insights into the dynamics of these interactions. A key aspect of our framework is the development of a new measure of synchrony between the motion energies of therapists and patients, which holds significant clinical and theoretical value in psychotherapy. The practical applicability and effectiveness of our modelling and estimation framework are demonstrated through the analysis of real session data. This work advances the quantitative analysis of motion dynamics in psychotherapy, offering important implications for future research and therapeutic practice.

Enhancing Prediction Stability and Performance in LIBS Analysis Using Custom CNN Architectures

LIBS-based analysis has experienced an ever-increasing interest in recent years as a well-suited technique for chemical analysis tasks relying on elemental fingerprinting. This method stands out for its ability to offer rapid, simultaneous multi-element analysis with the advantage of portability. In the context of this research, our aim is to bridge the gap between the analysis of simulated and real data to better account for variations in plasma temperature and electron density, which are typically not considered in LIBS analysis. To achieve this, we employ two distinct methodologies, PLS and CNNs, to construct predictive models for predicting the concentration of the 24 elements within each LIBS spectrum. The initial phase of our investigation concentrates on the training and testing of these models using simulated LIBS data, with results evaluated through RMSEP values. The IQR and median RMSEP values for all the elements demonstrate that CNNs consistently achieved values below 0.01, while PLS results ranged from 0.01 to 0.05, highlighting the superior stability and predictive accuracy of CNNs model. In the next phase, we applied the pre-trained models to analyze the real LIBS spectra, consistently identifying Aluminum (Al), Iron (Fe), and Silicon (Si) as having the highest predicted concentrations. The overall predicted values were approximately 0.5 for Al, 0.6 for Si, and 0.04 for Fe. In the third phase, deliberate adjustments are made to the training parameters and architecture of the proposed CNNs model to force the network to emphasize specific elements, prioritizing them over other components present in each real LIBS spectrum. The generation of the three modified versions of the initially proposed CNNs allows us to explore the impact of regularization, sample weighting, and a customized loss function on prediction outcomes. Some elements emerge during the prediction phase, with Calcium (Ca), Magnesium (Mg), Zinc (Zn), Titanium (Ti), and Gallium (Ga) exhibiting more pronounced patterns.

Convolutional sparse coding network for sparse seismic time-frequency representation

Seismic time-frequency (TF) transforms are essential tools in reservoir interpretation and signal processing, particularly for characterizing frequency variations in non-stationary seismic data. Recently, sparse TF transforms, which leverage sparse coding (SC), have gained significant attention in the geosciences due to their ability to achieve high TF resolution. However, the iterative approaches typically employed in sparse TF transforms are computationally intensive, making them impractical for real seismic data analysis. To address this issue, we propose an interpretable convolutional sparse coding (CSC) network to achieve high TF resolution. The proposed model is generated based on the traditional short-time Fourier transform (STFT) transform and a modified UNet, named ULISTANet. In this design, we replace the conventional convolutional layers of the UNet with learnable iterative shrinkage thresholding algorithm (LISTA) blocks, a specialized form of CSC. The LISTA block, which evolves from the traditional iterative shrinkage thresholding algorithm (ISTA), is optimized for extracting sparse features more effectively. Furthermore, we create a synthetic dataset featuring complex frequency-modulated signals to train ULISTANet. Finally, the proposed method's performance is subsequently validated using both synthetic and field data, demonstrating its potential for enhanced seismic data analysis.

Evaluation of Automated Object-Detection Algorithms for Koala Detection in Infrared Aerial Imagery.

Effective detection techniques are important for wildlife monitoring and conservation applications and are especially helpful for species that live in complex environments, such as arboreal animals like koalas (Phascolarctos cinereus). The implementation of infrared cameras and drones has demonstrated encouraging outcomes, regardless of whether the detection was performed by human observers or automated algorithms. In the case of koala detection in eucalyptus plantations, there is a risk to spotters during forestry operations. In addition, fatigue and tedium associated with the difficult and repetitive task of checking every tree means automated detection options are particularly desirable. However, obtaining high detection rates with minimal false alarms remains a challenging task, particularly when there is low contrast between the animals and their surroundings. Koalas are also small and often partially or fully occluded by canopy, tree stems, or branches, or the background is highly complex. Biologically inspired vision systems are known for their superior ability in suppressing clutter and enhancing the contrast of dim objects of interest against their surroundings. This paper introduces a biologically inspired detection algorithm to locate koalas in eucalyptus plantations and evaluates its performance against ten other detection techniques, including both image processing and neural-network-based approaches. The nature of koala occlusion by canopy cover in these plantations was also examined using a combination of simulated and real data. The results show that the biologically inspired approach significantly outperformed the competing neural-network- and computer-vision-based approaches by over 27%. The analysis of simulated and real data shows that koala occlusion by tree stems and canopy can have a significant impact on the potential detection of koalas, with koalas being fully occluded in up to 40% of images in which koalas were known to be present. Our analysis shows the koala's heat signature is more likely to be occluded when it is close to the centre of the image (i.e., it is directly under a drone) and less likely to be occluded off the zenith. This has implications for flight considerations. This paper also describes a new accurate ground-truth dataset of aerial high-dynamic-range infrared imagery containing instances of koala heat signatures. This dataset is made publicly available to support the research community.

Coefficient Shape Alignment in Multiple Functional Regression

In multivariate functional data analysis, different functional covariates often exhibit homogeneity. The covariates with pronounced homogeneity can be analyzed jointly within the same group, offering a parsimonious approach to modeling multivariate functional data. In this paper, a novel grouped multiple functional regression model with a new regularization approach termed “coefficient shape alignment” is developed to tackle functional covariates homogeneity. The modeling procedure includes two steps: first aggregate covariates into disjoint groups using the new regularization approach; then the grouped multiple functional regression model is established based on the detected grouping structure. In this grouped model, the coefficient functions of covariates in the same group share the same shape, invariant to scaling. The new regularization approach works by penalizing differences in the shape of the coefficients. We establish conditions under which the true grouping structure can be accurately identified and derive the asymptotic properties of the model estimates. Extensive simulation studies are conducted to assess the finite-sample performance of the proposed methods. The practical applicability of the model is demonstrated through real data analysis in the context of sugar quality evaluation. This work offers a novel framework for analyzing the homogeneity of functional covariates and constructing parsimonious models for multivariate functional data.