Statistical Estimation Methods Research Articles

A bivariate dependent degradation model based on artificial neural network supported stochastic process and Copula function

AbstractIn order to use the high ability of the artificial neural network (ANN) in data fitting, this paper introduces an ANN in stochastic process to describe the mean function for degradation modeling. Due to the fact that the existing method cannot handle the bivariate dependent degradation conditions, a bivariate dependent degradation model based on Copula function and ANN‐supported stochastic processes is proposed. Considering the random effects caused by individual difference, it is assumed that the unknown parameters in the stochastic processes and Copula functions are randomly distributed. Based on the maximum likelihood and moment estimation methods, a related statistical inference method for ANN training and parameter estimation is developed to use the bivariate dependent degradation model. An actual fatigue crack dataset is used to demonstrate the validity of the proposed method. The obtained results show that the dependent relationship between two degradation indicators should not be neglected, and it can be efficiently handled by the proposed method. Furthermore, the proposed degradation model can provide reliability and degradation intervals with enough precision due to the fact that it considers the random effects caused by individual difference.

Joint weight optimization for partial domain adaptation via kernel statistical distance estimation

The goal of Partial Domain Adaptation (PDA) is to transfer a neural network from a source domain (joint source distribution) to a distinct target domain (joint target distribution), where the source label space subsumes the target label space. To address the PDA problem, existing works have proposed to learn the marginal source weights to match the weighted marginal source distribution to the marginal target distribution. However, this is sub-optimal, since the neural network’s target performance is concerned with the joint distribution disparity, not the marginal distribution disparity. In this paper, we propose a Joint Weight Optimization (JWO) approach that optimizes the joint source weights to match the weighted joint source distribution to the joint target distribution in the neural network’s feature space. To measure the joint distribution disparity, we exploit two statistical distances: the distribution-difference-based L2-distance and the distribution-ratio-based χ2-divergence. Since these two distances are unknown in practice, we propose a Kernel Statistical Distance Estimation (KSDE) method to estimate them from the weighted source data and the target data. Our KSDE method explicitly expresses the two estimated statistical distances as functions of the joint source weights. Therefore, we can optimize the joint weights to minimize the estimated distance functions and reduce the joint distribution disparity. Finally, we achieve the PDA goal by training the neural network on the weighted source data. Experiments on several popular datasets are conducted to demonstrate the effectiveness of our approach. Intro video and Pytorch code are available at https://github.com/sentaochen/Joint-Weight-Optimation. Interested readers can also visit https://github.com/sentaochen for more source codes of the related domain adaptation, multi-source domain adaptation, and domain generalization approaches.

Novel approach to estimate the water isotope diffusion length in deep ice cores with an application to Marine Isotope Stage 19 in the Dome C ice core

Abstract. Accurate estimates of water isotope diffusion lengths are crucial when reconstructing and interpreting water isotope records from ice cores. This is especially true in the deepest, oldest sections of deep ice cores, where thermally enhanced diffusive processes have acted over millennia on extremely thinned ice. Previous statistical estimation methods, used with great success in shallower, younger ice cores, falter when applied to these deep sections, as they fail to account for the statistics of the climate on millennial timescales. Here, we present a new method to estimate the diffusion length from water isotope data and apply it to the Marine Isotope Stage 19 (MIS 19) interglacial at the bottom of the EPICA Dome C (EDC, Dome Concordia) ice core. In contrast to the conventional estimator, our method uses other interglacial periods taken from further up in the ice core to estimate the structure of the variability before diffusion. Through use of a Bayesian framework, we are able to constrain our fit while propagating the uncertainty in our assumptions. We estimate a diffusion length of 31±5 cm for the MIS 19 period, which is significantly smaller than previously estimated (40–60 cm). Similar results were obtained for each interglacial used to represent the undiffused climate signal, demonstrating the robustness of our estimate. Our result suggests better preservation of the climate signal at the bottom of EDC and likely other deep ice cores, offering greater potentially recoverable temporal resolution and improved reconstructions through deconvolution.

Data-driven determination of plant growth stages for improved weather index insurance design

PurposeThis paper aims to improve the delimitation of plant growth stages in the context of weather index insurance design. We propose a data-driven phase division that minimizes estimation errors in the weather-yield relationship and investigate whether it can substitute an expert-based determination of plant growth phases. We combine this procedure with various statistical and machine learning estimation methods and compare their performance.Design/methodology/approachUsing the example of winter barley, we divide the complete growth cycle into four sub-phases based on phenology reports and expert instructions and evaluate all combinations of start and end points of the various growth stages by their estimation errors of the respective yield models. Some of the most commonly used statistical and machine learning methods are employed to model the weather-yield relationship with each selected method we applied.FindingsOur results confirm that the fit of crop-yield models can be improved by disaggregation of the vegetation period. Moreover, we find that the data-driven approach leads to similar division points as the expert-based approach. Regarding the statistical model, in terms of yield model prediction accuracy, Support Vector Machine ranks first and Polynomial Regression last; however, the performance across different methods exhibits only minor differences.Originality/valueThis research addresses the challenge of separating plant growth stages when phenology information is unavailable. Moreover, it evaluates the performance of statistical and machine learning methods in the context of crop yield prediction. The suggested phase-division in conjunction with advanced statistical methods offers promising avenues for improving weather index insurance design.

Calculating Premiums for Extreme-Tail Risks with Liability Claims and Nuclear Verdicts

Purpose: When insurance claims, particularly liability claims and nuclear verdicts, are governed by fat-tailed distributions, considerable uncertainty exists about the value of the tail index. Material and Methods: Using the theory of risk aversion, this paper establishes a new premium principle (the power principle – analogous to the exponential principle for thin-tailed claims) and investigates its properties. Findings: Applied to claims arising from generalized Pareto distributions, the resultant premium is shown to be the ratio of the two largest expected claims. This structure provides a natural model for incorporating tail-index uncertainty into premiums. The theory is illustrated through possible ‘premiums’ for liability claims and nuclear verdicts, utilizing the consistent pattern of observed extremes. Implications to Theory, Practice and Policy: By integrating statistical methods for tail index estimation and addressing the inherent uncertainty, the power principle offers a robust framework for determining premiums in high-risk environments. The paper concludes with practical implications for insurers, highlighting the need for advanced risk management strategies and regulatory considerations in dealing with extreme liability claims.

A point mapping strategy-based sparse grid integration method for statistical moments estimation and structural reliability analysis

The high-order moment-based method is an attractive non-intrusive approach for structural reliability analysis, while it remains a challenge to strike a balance between accuracy, efficiency, and versatility in estimating statistical moments of performance functions. In this paper, a point mapping strategy-based sparse grid integration (SGI) method is proposed for statistical moment estimation and structural reliability analysis, with improved efficiency while ensuring the accuracy. Firstly, a point mapping strategy (PMS) is developed based on the adaptive high dimensional model representation (HDMR), by which the traditional SGI is reconstructed as a sum of multiple integrations over the sparse grid point sets with different effective dimensions. With this new form of SGI, the estimation of statistical moments only requires the evaluation of the performance function at a small number of necessary reference points, once the effects of some interaction terms are negligible. The validity and feasibility of the proposed PMS-based SGI method for statistical moments estimation are verified by several numerical examples. Then, the proposed method is applied to structural reliability analysis with the aid of an improved maximum entropy method. Two engineering examples are investigated, including the strength failure problem of tubular tower K-shape connection joints and the fatigue failure problem of a marine riser resulting from the vortex-induced vibration (VIV). The results indicate that the proposed method provides a better trade-off between accuracy and efficiency in evaluating the first four order statistical moments and structural failure probability compared to conventional methods.

Parameter Identification of Maritime Vessel Rudder PMSM Based on Extended Kalman Particle Filter Algorithm

To address the issue of system parameter variations during the operation of a maritime light vessel rudder permanent magnet synchronous motor (PMSM), an extended Kalman particle filter (EKPF) algorithm that combines a particle filter (PF) with an extended Kalman filter (EKF) is proposed in this paper. This approach enables the online identification of motor resistance and inductance. For highly nonlinear problems that are challenging for traditional methods such as Kalman filtering, this algorithm is typically a statistical and effective estimation method that usually yields good results. Firstly, a standard linear discrete parameter identification model is established for a PMSM. Secondly, the PF algorithm based on Bayesian state estimation as a foundation for subsequent research is derived. Thirdly, the advantages and limitations of the PF algorithm are analyzed, addressing issues such as sample degeneracy, by integrating it with the Kalman filtering algorithm. Specifically, the EKPF algorithm for online parameter identification is employed. Finally, the identification model within MATLAB/Simulink is constructed and the simulation studies are executed to ascertain the viability of our suggested algorithm. The outcomes from these simulations indicate that the proposed EKPF algorithm identifies resistance and inductance values both swiftly and precisely, markedly boosting the robustness and enhancing the control efficacy of the PMSM.

EXCHANGE RATE VOLATILITY OF UKRAINE’S MAIN TRADING PARTNERS

Ukraine, as an open economy under conditions of Russian aggression, is highly vulnerable to the import of exogenous shocks. This is embodied in exchange rate volatility and the emergence of corresponding risks. Most studies are aimed at direct, explicit, or transactional risks. They reflect the negative impact of exchange rate fluctuations on economic entities' cash flows in foreign economic activities. However, changes in currency prices can also affect the subjects oriented to the local market and not carry out operations in foreign currencies by changing competitiveness. One speaks about the indirect, implicit, or economic currency risk in this case. The latter generally arises in the event of volatility in the exchange rates of currencies of importing countries or competitors. The study is devoted to the analysis of indirect currency risks, which reflect potential adaptations of competitiveness due to changes in exchange rates. For this purpose, the currencies of the countries that account for about 80% of Ukraine's trade turnover over the last 10 years, namely the euro, Japanese yen, British pound, Swiss franc, yuan, Indian rupee, Czech krona, Polish zloty, Hungarian forint, and Turkish lira were chosen. The article aims to assess the volatility of exchange rates of Ukraine's main trading partners as a stage of analyzing economic currency risks. The paper uses statistical methods for volatility estimation and distribution characteristics, namely standard deviation, skewness, and kurtosis. The obtained results show that some currencies have a high level of asymmetry and excess, indicating possible unpredictable rate changes. The calculated indicators' generalization allows identifying currencies with relatively high and low risk. The article complements the results of previous studies, as it covers both major reserve currencies and currencies of leading countries whose markets are developing globally and in Europe. Estimates of asymmetry and excess exchange rate distributions are essential for effective currency risk management.

Enhancing Broiler Weight Estimation through Gaussian Kernel Density Estimation Modeling

The management of individual weights in broiler farming is not only crucial for increasing farm income but also directly linked to the revenue growth of integrated broiler companies, necessitating prompt resolution. This paper proposes a model to estimate daily average broiler weights using time and weight data collected through scales. In the proposed model, a method of self-adjusting weights in the bandwidth calculation formula is employed, and the daily average weight representative value is estimated using KDE. The focus of this study is to contribute to the individual weight management of broilers by intensively researching daily fluctuations in average broiler weight. To address this, weight and time data are collected and preprocessed through scales. The Gaussian kernel density estimation model proposed in this paper aims to estimate the representative value of the daily average weight of a single broiler using statistical estimation methods, allowing for self-adjustment of bandwidth values. When applied to the dataset collected through scales, the proposed Gaussian kernel density estimation model with self-adjustable bandwidth values confirmed that the estimated daily weight did not deviate beyond the error range of ±50 g compared with the actual measured values. The next step of this study is to systematically understand the impact of the broiler environment on weight for sustainable management strategies for broiler demand, derive optimal rearing conditions for each farm by combining location and weight data, and develop a model for predicting daily average weight values. The ultimate goal is to develop an artificial intelligence model suitable for weight management systems by utilizing the estimated daily average weight of a single broiler even in the presence of error data collected from multiple weight measurements, enabling more efficient automatic measurement of broiler weight and supporting both farms and broiler demand.

What question are we trying to answer? Embracing causal inference.

This study summarizes a presentation at the symposium for the Calvin Schwabe Award for Lifetime Achievement in Veterinary Epidemiology and Preventive Medicine, which was awarded to the first author. As epidemiologists, we are taught that "correlation does not imply causation." While true, identifying causes is a key objective for much of the research that we conduct. There is empirical evidence that veterinary epidemiologists are conducting observational research with the intent to identify causes; many studies include control for confounding variables, and causal language is often used when interpreting study results. Frameworks for studying causes include the articulation of specific hypotheses to be tested, approaches for the selection of variables, methods for statistical estimation of the relationship between the exposure and the outcome, and interpretation of that relationship as causal. When comparing observational studies in veterinary populations to those conducted in human populations, the application of each of these steps differs substantially. The a priori identification of exposure-outcome pairs of interest are less common in observational studies in the veterinary literature compared to the human literature, and prior knowledge is used to select confounding variables in most observational studies in human populations, whereas data-driven approaches are the norm in veterinary populations. The consequences of not having a defined exposure-outcome hypotheses of interest and using data-driven analytical approaches include an increased probability of biased results and poor replicability of results. A discussion by the community of researchers on current approaches to studying causes in observational studies in veterinary populations is warranted.

Rhythm-adaptive statistical estimation methods of probabilistic characteristics of cyclic random processes

The paper is devoted to the rhythm-adaptive statistical estimation methods of cyclic random processes probabilistic characteristics. The main goal of the article is development and research of rhythm-adaptive methods of cyclic random processes statistical processing. Based on the fundamental fact of invariance of probabilistic characteristics of a cyclic random process to time shifts determined by its rhythm function, rhythm-adaptive statistical estimations of initial, central and mixed moment functions of cyclic random processes of discrete parameter were obtained. The article analytically proves the unbiasedness and consistency of rhythm-adaptive statistical estimates of the mathematical expectation and the initial moment functions of the higher order of cyclic random process. By conducting a series of computer simulation experiments, it has been demonstrated, that the absolute errors of rhythm-adaptive methods of statistical estimation are significantly smaller than the corresponding errors for classical non-rhythm adaptive methods of statistical estimation of cyclic stochastic signals probabilistic characteristics. The effectiveness of using rhythm-adaptive methods of statistical estimation of probabilistic characteristics of ECG signals has been demonstrated. The results obtained in the work clearly demonstrate the essential advantages of rhythm-adaptive methods of statistical processing of cyclic stochastic signals with a variable (irregular) rhythm in comparison with non-rhythm-adaptive analogues.

Corrigendum: A statistical learning method for simultaneous copy number estimation and subclone clustering with single-cell sequencing data.

Corrigendum: A statistical learning method for simultaneous copy number estimation and subclone clustering with single-cell sequencing data.

Birnbaum Saunders distribution for imprecise data: statistical properties, estimation methods, and real life applications

A neutrosophic statistic is a random variable and it has a neutrosophic probability distribution. So, in this paper, we introduce the new neutrosophic Birnbaum–Saunders distribution. Some statistical properties are derived, using Mathematica 13.1.1 and R-Studio Software. Two different estimation methods for parameters estimation are introduced for new distribution: maximum likelihood estimation method and Bayesian estimation method. A Monte-Carlo simulation study is used to investigate the behavior of parameters estimates of new distribution, compare the performance of different estimates, and compare between our distribution and the classical version of Birnbaum–Saunders. Finally, study the validity of our new distribution in real life.

Three-Dimensional Image Visualization under Photon-Starved Conditions Using N Observations and Statistical Estimation.

In this paper, we propose a method for the three-dimensional (3D) image visualization of objects under photon-starved conditions using multiple observations and statistical estimation. To visualize 3D objects under these conditions, photon counting integral imaging was used, which can extract photons from 3D objects using the Poisson random process. However, this process may not reconstruct 3D images under severely photon-starved conditions due to a lack of photons. Therefore, to solve this problem, in this paper, we propose N-observation photon-counting integral imaging with statistical estimation. Since photons are extracted randomly using the Poisson distribution, increasing the samples of photons can improve the accuracy of photon extraction. In addition, by using a statistical estimation method, such as maximum likelihood estimation, 3D images can be reconstructed. To prove our proposed method, we implemented the optical experiment and calculated its performance metrics, which included the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), peak-to-correlation energy (PCE), and the peak sidelobe ratio (PSR).

Reflections on use of Monte Carlo methods

Monte Carlo methods have become ubiquitous in our society. Although statistical estimation methods date to earlier times, Monte Carlo (MC) methods were born in 1949 with publication of the paper by Metropolis and Ulam (1949). We address some of the many ways that MC methods have evolved over the years. Specifically, we consider electron transport calculations by MC, improvements in sampling efficiency afforded by the discrete alias sampling method, and solution of inverse problems by the Symbolic Monte Carlo (SMC) method. As a graduate student, one of us (WLD) used MC to estimate the improvement of cylindrical Geiger-Müller tube efficiency at low energies due to use of a thin coating of high atomic number material on the inside tube surface. Our methods were approximate but the results were reasonably good. We will discuss how discrete alias sampling—introduced in 1974—can improve the sampling efficiency significantly over simple table look-up. Finally, we consider an inverse problem in which the form of the governing probability density function is unknown but desired. We also briefly address matters of perspective on use of MC methods.N. Metropolis, S. Ulam, The Monte Carlo Method, 1949, J. Am. Stat. Assoc. 44, 335–341.

A statistical learning method for simultaneous copy number estimation and subclone clustering with single-cell sequencing data.

The availability of single-cell sequencing (SCS) enables us to assess intra-tumor heterogeneity and identify cellular subclones without the confounding effect of mixed cells. Copy number aberrations (CNAs) have been commonly used to identify subclones in SCS data using various clustering methods, as cells comprising a subpopulation are found to share a genetic profile. However, currently available methods may generate spurious results (e.g., falsely identified variants) in the procedure of CNA detection, thereby diminishing the accuracy of subclone identification within a large, complex cell population. In this study, we developed a subclone clustering method based on a fused lasso model, referred to as FLCNA, which can simultaneously detect CNAs in single-cell DNA sequencing (scDNA-seq) data. Spike-in simulations were conducted to evaluate the clustering and CNA detection performance of FLCNA, benchmarking it against existing copy number estimation methods (SCOPE, HMMcopy) in combination with commonly used clustering methods. Application of FLCNA to a scDNA-seq data set of breast cancer revealed different genomic variation patterns in neoadjuvant chemotherapy-treated samples and pretreated samples. We show that FLCNA is a practical and powerful method for subclone identification and CNA detection with scDNA-seq data.

A method for accurately extracting power lines and identifying potential intrusion risks from urban laser scanning data

Timely and accurate monitoring of power line safety is a key step in ensuring urban production and daily life. The rapid development of vehicle-borne mobile laser scanning (MLS) technology has provided an effective solution for intelligent maintenance of power grids. This paper proposes a comprehensive method for accurate extraction, missing completion, and intrusion risk detection of urban power lines. Firstly, local linear geometric features are described using principal component analysis (PCA) covariance matrix, and outliers are accurately separated using a joint Bezier curve distance threshold. Secondly, the statistical inference function estimation method is employed to accurately simulate the complete topology of power lines. Finally, a fast intrusion risk detection method based on the separating axis theorem (SAT) for boundary box neighboring objects is developed. Experimental results demonstrate that our method achieves a recall rate and precision rate of 98.28 % and 98.71 %, respectively, for power line extraction. The root mean square error (RMSE) accuracy and coordinate residual of catenary line fitting are both below 0.04 m, indicating strong noise resistance and robustness. Compared to mainstream geometric extraction methods, our approach exhibits superior performance.

Об относительной точности оценки пола по черепу

Introduction. There are no fewer than two hundred algorithms for sex estimation based on cranial morphology, relying on statistical analysis of non-metric, linear, angular traits, and their combinations. Nevertheless, many physical anthropologists prefer to rely on visual observations. The objectives of this research encompass exploring potential reasons behind the preference for a visual approach and conducting an analysis of the comparative effectiveness of visual and statistical methods for sex estimation. Materials and methods. The study is grounded in an analysis of publications related to methods of sex estimation based on cranial traits, spanning the past 70 years. Comparison of accuracy estimates was conducted using non-parametric tests, considering differences in statistical methods, validation approaches (no validation, cross-validation, independent test), and variable types (non-metric traits, craniometry, geometric morphometrics). Results. General reasons for skepticism towards algorithms include unrealistic expectations regarding their capabilities, greater susceptibility to errors by models compared to humans, lack of control over classification. However, algorithms generally surpass experts in predicting the target variable. The average accuracy of visual sex estimations based on cranial traits is slightly lower than the estimates of statistical models and exhibits noticeable variability. The accuracy of estimations made by experienced anthropologists is comparable to the average performance of models. Nevertheless, the effectiveness of algorithms significantly diminishes when applied to datasets originating from sources other than the training set, particularly when dealing with craniometric traits. In a substantial portion of studies, the size of the training datasets is insufficient for a reliable assessment of model effectiveness, and the sex distribution is skewed towards male skulls, leading to some inflation of the accuracy of their estimates. Model effectiveness can also decline due to errors in the evaluation of non-metric traits, and the assessment of inter-researcher discrepancies does not allow for an evaluation of their impact on model accuracy. Conclusion. Despite an extensive bibliography, there remains a lack of data on both the accuracy of the visual approach to sex estimation and the reliability of models with claimed high effectiveness. The adoption of flexible methodologies enabling researchers to independently control both variable selection and the composition of the training set will help overcome algorithm aversion and enhance the quality of estimates. @ 2023. This work is licensed under a CC BY 4.0 license

Application of remote sensing methods for statistical estimation of organic matter in soils

The availability of reliable information on the physicochemical properties of soils is a necessary tool for maintaining and improving fertility and effective optimization of agricultural land management in many countries. However, ground-based research methods require significant financial and time resources. It has been established that methods based on remote sensing data are an efficient, accurate, and less costly solution for studying different types of soil cover parameters. This work aims to determine the predicted indicator of humus content in soils in selected regions of the Kyiv region (Ukraine) with the corresponding soil types. For this, the spectral properties of chernozem soils were investigated based on Landsat 8 OLI satellite images. A mosaic of the mean spectral reflectance values for the study period (2013-2015) was created using the Google Earth Engine. The vegetation indices NDSI, NDWI, NDBI, MSAVI, and NDVI were used to identify bare soils. Using multiple linear regression, an optimal F-Comparing Nested Model was created for predicting humus content in soils, including seven parameters. The model's accuracy was estimated with such indicators R=0.95, R2= 0.90, σy = 0.16 %. The approach based on the proposed model can be used to support the adoption of the necessary management decisions to improve soil fertility and maintain balanced land use.

Statistical properties and different estimation methods of Inverse Unit Gompertz Distribution with applications on health data sets

Continuous probability distributions are always helpful in lifetime data and health-related data sets. Various techniques exist to develop new probability distributions, adding new parameters and applying different transformations. Adding new parameters is not always good; rather, it can also have complex expressions for the function and properties. This research aimed to develop a model without adding new parameters, which will work more efficiently than the existing models. This study proposes a new probability density function by taking the inversion of a random variable whose probability density function is Unit Gompertz Distribution. The newly proposed distribution is called an Inverse Unit Gompertz Distribution (IUGD). Various properties include reliability/survivorship measures, odd function, elasticity, and Mills ratio. Different statistical properties such as moments, quantile function, and Lorenz and Bonferroni curves for IUGD are developed. Five estimation methods are discussed for unknown parameters of the IUGD, and simulations have been conducted. Finally, IUGD is applied to two real-life data sets, i.e., COVID-19 death rates in the Netherlands and the pain relief time of individuals who received analgesics experienced. IUGD is flexible compared to other competing densities. Moreover, the proposed density can be used for health-related data sets to take accurate precautions and treatments.