Real Datasets Research Articles

Classical and Bayesian Estimation of PCI 𝒞pc Using Power Generalized Weibull Distribution

Abstract This article focuses on estimating the process capacity index (PCI), 𝒞 pc \mathcal{C}_{\rm pc} , where the underlying distribution is a power generalized Weibull distribution, using maximum likelihood and Bayesian techniques. The 𝒞 pc \mathcal{C}_{\rm pc} index may be used to both normal and non-normal quality attributes. This article aims to accomplish three things: Using the maximum likelihood approach, we first determine the estimator of the PCI 𝒞 pc \mathcal{C}_{\rm pc} . Secondly, the Metropolis-Hastings Algorithm is used to study Bayesian estimation under four loss functions (symmetric and asymmetric). Third, the index 𝒞 pc \mathcal{C}_{\rm pc} ’s 95 confidence intervals are built using Bayesian and four bootstrap techniques. The point estimates of 𝒞 pc \mathcal{C}_{\rm pc} have been evaluated using Monte Carlo simulation in terms of mean square errors (MSEs), four bootstrap methods, and highest posterior density (HPD) credible intervals in relation to their average width (AW) and coverage probabilities (CPs). Using two real data sets – one pertaining to the size of electrical connections and the other to the amount of protein (in g) for adult patients at the Hospital Carlos Van Buren in Valparaiso, Chile – a comparable analysis to that employed in the simulations is conducted in order to illustrate the effectiveness of the suggested methods.

On the improved estimation of the normal mixture components for longitudinal data

When analyzing real data sets, statisticians often face the question that the data are heterogeneous and it may not necessarily be possible to model this heterogeneity directly. One natural option in this case is to use the methods based on finite mixtures. The key question in these techniques often is what is the best number of mixtures or, depending on the focus of the analysis, the best number of sub-populations when the model is otherwise fixed. Moreover, when the distribution of the response variable deviates from meeting the assumptions, it's common to employ an appropriate transformation to align the distribution with the model's requirements. To solve the problem in the mixture regression context we propose a technique based on the scaled Box-Cox transformation for normal mixtures. The specific focus here is on mixture regression for longitudinal data, the so-called trajectory analysis. We present interesting practical results as well as simulation experiments to demonstrate that our method yields reasonable results. Associated R-programs are also provided.

A realistic 2D multi-offset, multi-frequency synthetic GPR data set as a benchmark for testing new algorithms

We present a 2D multi-offset, multi-frequency synthetic GPR data set specifically designed to evaluate and test processing, analysis and inversion techniques. The data set replicates realistic subsurface conditions at four sections separated by 2 m. We modeled four multi-offset GPR profiles at 50, 100 and 200 MHz frequencies using realistic wavelets. The data set provides a robust framework for validating advanced GPR algorithms and techniques such as pre-stack depth migration, amplitude versus offset analysis and full waveform inversion. Extensive technical validation ensures data reproducibility and affordability. The standardized, realistic synthetic data set can be used as a reliable benchmark for developing and testing new algorithms and methods, thereby advancing the understanding of subsurface imaging and real-world data interpretation.

On use of adaptive cluster sampling for variance estimation

Adaptive cluster sampling is particularly helpful whenever the target population is unique, dispersed unevenly, concealed or difficult to find. In the current investigation, under an adaptive cluster sampling approach, we propose a ratio-product-logarithmic type estimator employing a single auxiliary variable for the estimation of finite population variance. The bias and mean square error of the proposed estimator are developed by using simulation as well as real data sets. The study results show that for estimating the finite population variance, the proposed estimator outperforms the competing estimators.

Inverse power XLindley distribution with statistical inference and applications to engineering data

In this article, a new two-parameter distribution is constructed using the inverse transformation technique on the power XLindley distribution. It is called the inverse power XLindley distribution. As an attractive property, it can generate symmetric and asymmetric probability density functions, ideal for modeling lifetime phenomena. In addition, it is suitable for various real data since the corresponding hazard rate function has an increasing, decreasing, reverse J-shape or J-shape. Essential characteristics and features of our study include quantiles, moments, inverse moments, probability-weighted moments, incomplete moments, and inequality measures. The inferences from the distribution are explored. In particular, the parameters are determined using twelve efficient estimation methods. These methods are maximum likelihood, Anderson-Darling, right-tailed Anderson-Darling, left-tailed Anderson-Darling, Cramér-von Mises, least squares, weighted least squares, maximum product of spacing, minimum spacing absolute distance, minimum spacing absolute-log distance, percentiles, and Kolmogorov. The performance of the resulting estimates is analyzed using Monte Carlo simulation. The numerical results and graphical presentation indicate that the maximum product of spacing estimation approach has the highest accuracy and precision. Using three real data sets and comparisons with other distributions, the effectiveness of the proposed distribution is demonstrated and visually presented.

Large language models generating synthetic clinical datasets: a feasibility and comparative analysis with real-world perioperative data

BackgroundClinical data is instrumental to medical research, machine learning (ML) model development, and advancing surgical care, but access is often constrained by privacy regulations and missing data. Synthetic data offers a promising solution to preserve privacy while enabling broader data access. Recent advances in large language models (LLMs) provide an opportunity to generate synthetic data with reduced reliance on domain expertise, computational resources, and pre-training.ObjectiveThis study aims to assess the feasibility of generating realistic tabular clinical data with OpenAI’s GPT-4o using zero-shot prompting, and evaluate the fidelity of LLM-generated data by comparing its statistical properties to the Vital Signs DataBase (VitalDB), a real-world open-source perioperative dataset.MethodsIn Phase 1, GPT-4o was prompted to generate a dataset with qualitative descriptions of 13 clinical parameters. The resultant data was assessed for general errors, plausibility of outputs, and cross-verification of related parameters. In Phase 2, GPT-4o was prompted to generate a dataset using descriptive statistics of the VitalDB dataset. Fidelity was assessed using two-sample t-tests, two-sample proportion tests, and 95% confidence interval (CI) overlap.ResultsIn Phase 1, GPT-4o generated a complete and structured dataset comprising 6,166 case files. The dataset was plausible in range and correctly calculated body mass index for all case files based on respective heights and weights. Statistical comparison between the LLM-generated datasets and VitalDB revealed that Phase 2 data achieved significant fidelity. Phase 2 data demonstrated statistical similarity in 12/13 (92.31%) parameters, whereby no statistically significant differences were observed in 6/6 (100.0%) categorical/binary and 6/7 (85.71%) continuous parameters. Overlap of 95% CIs were observed in 6/7 (85.71%) continuous parameters.ConclusionZero-shot prompting with GPT-4o can generate realistic tabular synthetic datasets, which can replicate key statistical properties of real-world perioperative data. This study highlights the potential of LLMs as a novel and accessible modality for synthetic data generation, which may address critical barriers in clinical data access and eliminate the need for technical expertise, extensive computational resources, and pre-training. Further research is warranted to enhance fidelity and investigate the use of LLMs to amplify and augment datasets, preserve multivariate relationships, and train robust ML models.

Query Mix-Max Method for FDR Estimation Supported by Entrapment Queries.

Estimating the false discovery rate (FDR) is one of the key steps in ensuring appropriate error control in the analysis of shotgun proteomics data. Traditional estimation methods typically rely on decoy sequence databases or spectral libraries, which may not always provide satisfactory results due to limitations of decoy construction methods. This study introduces the query mix-max (QMM) method, a decoy-free alternative for FDR estimation in proteomics. The QMM framework builds upon the existing mix-max procedure but replaces decoy matches with entrapment queries to estimate the number of false positive discoveries. Through simulations and real data set analyses, the QMM method was demonstrated to provide reasonably accurate FDR estimation across various scenarios, particularly when smaller sample-to-entrapment spectra ratios were achieved. The QMM method tends to be conservatively biased, particularly at higher FDR values, which can ensure stringent FDR control. While flexible, the protocol's effectiveness may vary depending on the evolutionary distance between the sample and entrapment organisms. It also requires a sufficient number of entrapment queries to provide stable FDR estimates, especially for low FDR values. Despite these limitations, the QMM method is a promising alternative as one of the first query-based FDR estimation approaches in shotgun proteomics.

Weighted past and paired dynamic varentropy measures, their properties, usefulness and inferences

We introduce two uncertainty measures, say weighted past varentropy (WPVE) and weighted paired dynamic varentropy (WPDVE). Several properties of these proposed measures, including their effect under the monotone transformations are studied. An upper bound of the WPVE using the weighted past Shannon entropy and a lower bound of the WPVE are obtained. Further, the WPVE is studied for the proportional reversed hazard rate (PRHR) models. Upper and lower bounds of the WPDVE are derived. In addition, the non-parametric kernel estimates of the WPVE and WPDVE are proposed. Furthermore, the maximum likelihood estimation technique is employed to estimate WPVE and WPDVE for an exponential population. A numerical simulation is provided to observe the behaviour of the proposed estimates. A real data set is analysed, and then the estimated values of WPVE are obtained. Based on the bootstrap samples generated from the real data set, the performance of the non-parametric and parametric estimators of the WPVE and WPDVE is compared in terms of the absolute bias and mean squared error (MSE). Finally, we have reported an application of WPVE. Abbreviations RV: Random variable; PDF: Probability density function; IC: Information content; SE: Shannon entropy; VE: Varentropy; MSE: Mean squared error; RVE: Residual varentropy; CDF: Cumulative distribution function; PVE: Past varentropy; WVE: Weighted varentropy; WPSE: Weighted past Shannon entropy; WRVE: Weighted residual varentropy; WPVE: Weighted past varentropy; WPRE: Weighted past Rényi entropy; PRHR: Proportional reversed hazard rate; WPDE: Weighted paired dynamic entropy; WPDVE: Weighted paired dynamic varentropy entropy; AB: Absolute bias; CRHR: Cumulative reversed hazard rate; VPL: Variance past lifetime; MPL: Mean past lifetime; MRL: Mean residual lifetime; VRL: Variance residual lifetime; GMB-II: Gumbel-II; GXE: Generalised X-exponential; EXP: Exponential; lnL: Log-likelihood criterion; AIC: Akaikes information criterion; BIC: Bayesian information criterion; MLE: Maximum likelihood estimate

Resilience of human gut microbiomes in autism spectrum disorder: measured using stiffness network analysis.

Autism spectrum disorder (ASD) affects an estimated 1%-2% of children worldwide, but its specific etiology remains unclear. In recent years, the gut microbiome's role in ASD pathogenesis has garnered increasing attention. However, the exact relationship between microbiota and ASD-such as which microbial species significantly impact disease onset and progression-remains unresolved, and effective methods to measure microbial interactions are still lacking. In this study, we introduce an innovative stiffness network analysis (SNA) method to quantify changes in microbial network structure and identify disease-specific microbial bacteria theoretically. The SNA method was applied to reanalyze eight ASD gut microbiome data sets, encompassing 898 ASD samples and 467 healthy control (HC) samples from 16S-rRNA sequencing data. Key findings include the following: (i) an "allies" biomarker subgroup consisting of Bacteroides plebeius, Sutterella, Lachnospira, and Prevotella copri was identified; (ii) a profile monitoring score of 0.72 for the biomarker subgroup, indicating significant relationship changes between HC and ASD states, and (iii) a P/N ratio of biomarker subgroup in ASD-associated gut bacteria that was three times higher than that of HC microbiomes. Additionally, we discuss the non-monotonic relationship alterations within microbial sub-communities in the ASD gut microbiome.IMPORTANCEIt is crucial to assess alterations in network structure in different biological states in order to promote health. The stiffness network allows for the exploration of species interactions and the measurement of resilience in complex microbial networks. The objective of this study was to develop a stiffness network analysis (SNA) method for evaluating the contribution of microbial bacteria in differentiating disease samples from healthy control samples by examining changes in network stiffness parameters. Furthermore, the SNA method was employed on both simulated and real autism spectrum disorder gut microbiome data sets to identify potential microbial biomarker subgroups, with a particular focus on the relationship alterations within microbial networks.

A Power Comparison and Simulation Study of Tests of Fit for the Gumbel Distribution with Application to COVID-19 Data

In this article, we investigate goodness-of-fit tests based on the empirical distribution function for the composite Gumbel (extreme value) hypothesis. The parameters of the Gumbel distribution are estimated using numerical methods through the maximum likelihood approach. We employ a Monte Carlo method to obtain critical values and determine the actual sizes of the tests for different sample sizes. Furthermore, we conduct a comprehensive simulation study to compare the power values of the tests against various alternatives and different sample sizes. Finally, for illustrative purposes, we analyse a real data set. AMS Subject Classification: 62G10; 62P10

Best Subset Solution Path for Linear Dimension Reduction Models Using Continuous Optimization.

The selection of best variables is a challenging problem in supervised and unsupervised learning, especially in high-dimensional contexts where the number of variables is usually much larger than the number of observations. In this paper, we focus on two multivariate statistical methods: principal components analysis and partial least squares. Both approaches are popular linear dimension-reduction methods with numerous applications in several fields including in genomics, biology, environmental science, and engineering. In particular, these approaches build principal components, new variables that are combinations of all the original variables. A main drawback of principal components is the difficulty to interpret them when the number of variables is large. To define principal components from the most relevant variables, we propose to cast the best subset solution path method into principal component analysis and partial least square frameworks. We offer a new alternative by exploiting a continuous optimization algorithm for best subset solution path. Empirical studies show the efficacy of our approach for providing the best subset solution path. The usage of our algorithm is further exposed through the analysis of two real data sets. The first data set is analyzed using the principle component analysis while the analysis of the second data set is based on partial least squareframework.

Wind turbine fault prognosis using SCADA measurements, pre-fault labeling, and KNN classifiers robust against data imbalance

Wind turbine fault prognosis using SCADA measurements, pre-fault labeling, and KNN classifiers robust against data imbalance

On the cluster of the families of hybrid polynomial kernels in kernel density estimation

This study introduces a novel cluster of hybrid polynomial kernel families, designed to achieve significantly lower asymptotic mean integrated squared error compared to traditional kernels. These hybrid kernels are developed by heuristically combining classical polynomial kernels using probability axioms. An in-depth analysis of error propagation within these kernels is conducted, utilizing both simulation experiments and real-life datasets, including the Life Span of Batteries and COVID-19 datasets. The findings consistently demonstrate that the proposed hybrid kernels outperform their classical counterparts in various density estimation tasks across different distribution types and sample sizes. This research highlights the potential of hybrid polynomial kernels to enhance accuracy in density estimation, advocating for their adoption in statistical modelling and analysis.

Investigating a Domain Adaptation Approach for Integrating Different Measurement Instruments in a Longitudinal Clinical Registry.

In a longitudinal clinical registry, different measurement instruments might have been used for assessing individuals at different time points. To combine them, we investigate deep learning techniques for obtaining a joint latent representation, to which the items of different measurement instruments are mapped. This corresponds to domain adaptation, an established concept in computer science for image data. Using the proposed approach as an example, we evaluate the potential of domain adaptation in a longitudinal cohort setting with a rather small number of time points, motivated by an application with different motor function measurement instruments in a registry of spinal muscular atrophy (SMA) patients. There, we model trajectories in the latent representation by ordinary differential equations(ODEs), where person-specific ODE parameters are inferred from baseline characteristics. The goodness of fit and complexity of the ODE solutions then allow to judge the measurement instrument mappings. We subsequently explore how alignment can be improved by incorporating corresponding penalty terms into model fitting. To systematically investigate the effect of differences between measurement instruments, we consider several scenarios based on modified SMA data, including scenarios where a mapping should be feasible in principle and scenarios where no perfect mapping is available. While misalignment increases in more complex scenarios, some structure is still recovered, even if the availability of measurement instruments depends on patient state. A reasonable mapping is feasible also in the more complex real SMA data set. These results indicate that domain adaptation might be more generally useful in statistical modeling for longitudinal registrydata.

The TAB-EOAO study: Trends in use and benefit of adjuvant chemotherapy between early onset and average onset locally advanced colon cancer.

105 Background: Despite the declining incidence rates (IR) in average onset colon cancer (AO-CC), IR for early onset colon cancer (EO-CC), defined as patients (pts) younger than 50-years-old at diagnosis, has been increasing. Treatment for high risk locally advanced colon cancer (CC) is surgical resection followed by adjuvant chemotherapy (AC). Data indicates a more permissive chemotherapy use in EO-CC. There is limited data about treatment and survival trends in EO-CC. Thus, we aimed to assess the use and benefit of AC between in EO vs AO CC in locally advanced disease. Methods: CC diagnosed between 2000-2020 were identified in the Surveillance, Epidemiology, and End Results Program (SEER) Database. Eligible pts were adults (≥18), Stage II or III at diagnosis. Stage II disease was further stratified as low risk (pT1-3) and high risk (pT4). Logistic regression methods were used to assess Odds Ratio (OR) of AC between EO-CC and AO-CC; Cox models were used to compare overall survival (OS) and Cancer-specific survival (CSS) between both groups during 2000-2010 and 2011-2020. Results: Our study included 136,676 pts (AO-CC= 121,606; EO-CC =15,070). The median age for EO-CC was 44 years versus 71 years for AO-CC population. The use of AC increased over time for both the EO-CC (63% vs 66%) and AO-CC (33% vs 40%). Moreover, pts with AO-CC received less AC than EO-CC in the entire study time (see table). In pts with AO-CC, AC improved CSS (HR=0.69 for 2000-2010, HR=0.50 2011-2020). However, among those with EO-CC, AC improved CSS in 2011-2020 (HR=0.76) but did not improve CSS in 2000-2010 (HR=1.02). Conclusions: Over the past 20 years EO-CC has been managed aggressively, especially for stage II low risk patients where current guidelines do not support the use of AC. In this real world data set we show that for EO-CC AC did not improve CSS in the decade 2000- 2010 but did improve CSS in the 2011- 2020 period. Further analysis may clarify stage specific benefits of AC. There clearly remains a need for better risk stratification, including the use of ctDNA, to identify the subpopulations of EO-CC patients that will best benefit from AC. Multivariable logistic regression model of chemotherapy by timeframe with interaction term: Age* stage. 2000-2010 2011-2020 AO-CC vs EO-CC OR 95% CI OR 95% CI Stage II low risk 0.23 (0.21, 0.26) 0.28 (0.24, 0.32) Stage II high risk 0.28 (0.22, 0.36) 0.28 (0.21, 0.36) Stage III 0.36 (0.32, 0.4) 0.30 (0.26, 0.34)

Learning Pose Controllable Human Reconstruction with Dynamic Implicit Fields from a Single Image.

Recovering a user-special and controllable human model from a single RGB image is a nontrivial challenge. Existing methods usually generate static results with an image consistent subject's pose. Our work aspires to achieve pose-controllable human reconstruction from a single image by learning a dynamic (multi-pose) implicit field. We first construct a feature-embedded human model (FEHM) as a bridge to propagate image features to different pose spaces. Based on FEHM, we then encode three pose-decoupled features. Global image features represent user-specific shapes in images and replace widely used pixel-aligned ways to avoid unwanted shape-pose entanglement. Spatial color features propagate FEHM-embedded image cues into 3D pose space to provide spatial high-frequency guidance. Spatial geometry features improve reconstruction robustness by using the surface shape of the FEHM as the prior. Finally, new implicit functions are designed to predict the dynamic human implicit fields. For effective supervision, a realistic human avatar dataset, SimuSCAN, with 1000+ models is constructed using a low-cost hierarchical mesh registration method. Extensive experiments demonstrate that our method achieves the state-of-the-art reconstruction level.

MODIFIED INVERTED KUMARASWAMY DISTRIBUTION USING INVERSE POWER FUNCTION: PROPERTIES AND APPLICATIONS

In the area of distribution theory, statisticians have proposed and developed new models for generalizing the existing ones to make them more flexible and to aid their application in a variety of fields. In this article, we present a new distribution called the Modified Inverted Kumaraswamy Distribution Using Inverse Power Function with three positive parameters, which extends the Inverted Kumaraswamy distribution with two parameters. Some statistical properties of the MIK distribution, such as explicit expressions for the quantile function, probability-weighted moments, moments, generating function, Reliability function, hazard function, and order statistics are discussed. A maximum likelihood estimation technique is employed to estimate the model parameters and the simulation study is presented. The superiority of the new distribution is illustrated with an application to a real data set. The results showed that the new distribution fits better in the real data set amongst the range of distributions considered.

REGRESSION ESTIMATION AND FEATURE SELECTION USING MODIFIED CORRELATION-ADJUSTED ELASTIC NET PENALTIES

Regularized regression techniques such as the least absolute shrinkage and selection operator (LASSO), elastic-net, and the type 1 and type 2 correlation adjusted elastic-net (CAEN1 and CAEN2 respectively) are used for simultaneously carrying out variable selection and estimation of coefficients in machine learning. Modified estimators based on the CAEN1 and CAEN2 are proposed in this study by rescaling the estimates to undo the double shrinkage incurred due to the application of two penalties. The scale factors are derived by decomposing the correlation matrix of the predictors. The derived scale factors, which depend on the magnitude of correlations among the predictors, ensure that the elastic-net is included as a special case. Estimation is carried out using a robust worst-case quadratic solver algorithm. Simulations show that the proposed estimators referred to as corrected correlation adjusted elastic-net (CCAEN1 and CCAEN2) perform competitively with the CAEN1, CAEN2, LASSO, and elastic-net in terms of variable selection, estimation and prediction accuracy with CCAEN1 yielding the best results when the number of predictors is more than the number of observations and CCAEN2 producing the best performance when there is grouping effect, where highly correlated predictors tend to be included in or excluded from the model together. Applications to two real-life datasets further demonstrate the advantage of the proposed methods for machine learning.

An Extension of Some Truncated Distributions Family With Application

This paper represents a suggested a combination of continuous distributions based on Truncated Gompertz-G (tgo-gd[0,1]) and Truncated Gompertz-Weibull (tgo-wd) distributions. Some of the main properties of the suggested combination such as the distribution function (cdf), the probability function (pdf), survival function (Sf), hazard function (Hrf), quintile function (Qf), moment generating function (mgf), skewness ,, kurtosis , entropy, and maximum likelihood estimator (MLE) for the proposed combination of tgo-wd[0,1] have been presented. As well, an experimentally estimation for the parameters of the distributions using MLE have been studied. After the application, the potentiality of the proposed family by means of one real data sets are shown more flexibility in compare with the other models.

Comparison of Different Bandwidth Determination Methods in Kernel Equating

The study aims to compare the presented methods for determining the bandwidth parameter in the kernel equating method on a real data set. A bandwidth parameter needs to be determined when kernel equating is used to equate two test forms. The bandwidth parameters determine the smoothness of the continuousized score distributions, so their effect on equating results is inevitable. Gaussian Kernel, Logistic Kernel and Uniform Kernel methods were used for bandwidth selection and the results were compared according to the Percentage Relative Error (PRE), the Standard Error and the Standard Error of Equating Difference (SEED). The findings of the study show that the three different approaches to minimizing the penalty function have similar results. Although the standard errors of the equated scores obtained with the uniform kernel method were slightly smaller, the results were almost the same as the other two approaches. When the three equating methods are compared according to the percent relative error, the distribution obtained from Gaussian kernel equating is more consistent with the population distribution.