LOCAL INFLUENCE ASSESSMENT IN A MULTIVARIATE t-MODEL WITH RAO'S SIMPLE STRUCTURE

The local influence analysis is an important problem in statistical inference and some models have been discussed in many literatures This paper deals with the problem of assessing local influences in a multivariate t-model with Rao's simple struc-ture(RSS). Based on Cook's likelihood displacement, the effects of some minor perturbation on the statistical inference is assessed. As an application, a common covariance-weighted perturbation is thoroughly discussed.

Multivariate analysis of oral mucosal ulcers during orthodontic treatment

BACKGROUND Orthodontic treatment can easily cause local soft tissue reactions in the oral cavity of patients under mechanical stress,leading to oral mucosal ulcers and affecting their quality of life.At present,only limited literature has explored the factors leading to oral ulcers in orthodontic treatment,and these research results are still controversial.AIM To investigate the current status and related factors of oral mucosal ulcers during orthodontic treatment,aiming to provide a valuable reference for preventing this disease in clinical practice.METHODS A total of 587 patients who underwent orthodontic treatment at the Peking University School of Stomatology and Hospital of Stomatology between 2020 and 2022 were selected and allocated to an observation or control group according to the incidence of oral mucosal ulcers during orthodontic therapy.A questionnaire survey was constructed to collect patient data,including basic information,lifestyle and eating habits,treatment details,mental factors,and trace element levels,and a comparative analysis of this data was performed between the two groups.RESULTS A logistic regression model with oral ulcers as the dependent variable was established.The regression results showed that age(≥60 years:odds ratio[OR]:6.820;95%confidence interval[CI]:2.226–20.893),smoking history(smoking:OR:4.434;95%CI:2.527–7.782),toothbrush hardness(hard:OR:2.804;95%CI:1.746–4.505),dietary temperature(hot diet:OR:1.399;95%CI:1.220–1.722),treatment course(>1 year:OR:3.830;95%CI:2.203–6.659),and tooth brushing frequency(>1 time per day:OR:0.228;95%CI:0.138–0.377)were independent factors for oral mucosal ulcers(P<0.05).Furthermore,Zn level(OR:0.945;95%CI:0.927–0.964)was a protective factor against oral ulcers,while the SAS(OR:1.284;95%CI:1.197–1.378)and SDS(OR:1.322;95%CI:1.231–1.419)scores were risk factors.CONCLUSION Age≥60 years,smoking history,hard toothbrush,hot diet,treatment course for>1 year,tooth brushing frequency of≤1 time per day,and mental anxiety are independent risk factors for oral mucosal ulcers.Therefore,these factors should receive clinical attention and be incorporated into the development and optimization of preventive strategies for reducing oral ulcer incidence.

Multivariate Analysis of Female Stress Urinary Incontinence and Establishment of a Prediction Model

Stress urinary incontinence(SUI)is a symptom of uncontrolled urine outflow that affects millions of women worldwide[1].SUI is a significant healthcare issue that affects the quality of life of women across numerous domains,including social activities,physical health,mental well-being,employment,and sexual life.

Multivariate Time Series Anomaly Detection Based on Spatial-Temporal Network and Transformer in Industrial Internet of Things

In the Industrial Internet of Things(IIoT),sensors generate time series data to reflect the working state.When the systems are attacked,timely identification of outliers in time series is critical to ensure security.Although many anomaly detection methods have been proposed,the temporal correlation of the time series over the same sensor and the state(spatial)correlation between different sensors are rarely considered simultaneously in these methods.Owing to the superior capability of Transformer in learning time series features.This paper proposes a time series anomaly detection method based on a spatial-temporal network and an improved Transformer.Additionally,the methods based on graph neural networks typically include a graph structure learning module and an anomaly detection module,which are interdependent.However,in the initial phase of training,since neither of the modules has reached an optimal state,their performance may influence each other.This scenario makes the end-to-end training approach hard to effectively direct the learning trajectory of each module.This interdependence between the modules,coupled with the initial instability,may cause the model to find it hard to find the optimal solution during the training process,resulting in unsatisfactory results.We introduce an adaptive graph structure learning method to obtain the optimal model parameters and graph structure.Experiments on two publicly available datasets demonstrate that the proposed method attains higher anomaly detection results than other methods.

Factors affecting farmers'choice to adopt risk management strategies:The application of multivariate and multinomial probit models

This study investigates the factors that impact farmers'adoption of risk management strategies(RMS)in Pakistan during times of uncertainty.The study examines farmers'adoption of RMS using both multinomial probit(MNP)and multivariate probit(MVP).Data were collected from 382 farmers sampled from four districts in KhyberPakhtunkhwa(KP)province of Pakistan via a multistage sampling technique.This study utilizes the MNP model,considering the assumption of Independence of Irrelevant Alternatives(IIA)and incorporating correlated error terms.The objective is to understand farmers'behavior in risky situations and determine if there is heterogeneity.Results are compared with the MVP model to assess robustness and gain deeper understanding of farmers'decisionmaking processes.The research findings reveal that our results are robust,and farmers behave homogeneously in various RMS scenarios.Farmers adopt RMS individually or in combination to mitigate the adverse effects of natural calamities on their livelihood.The risk-averse farmers,who perceive weather-related risks as a threat,access credits and information,and have farms close to a river are more likely to adopt RMS,irrespective of the format of the strategies available.Moreover,the predicted probabilities and correlation of the RMS and RM categories have strengthened our model estimation.These findings provide insights into the behavior of farmers in adopting RMS which are helpful for policymakers and stakeholders in developing strategies to mitigate the impacts of natural calamities on farmers.

AFSTGCN:Prediction for multivariate time series using an adaptive fused spatial-temporal graph convolutional network

The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries and other fields.Furthermore,it is important to construct a digital twin system.However,existing methods do not take full advantage of the potential properties of variables,which results in poor predicted accuracy.In this paper,we propose the Adaptive Fused Spatial-Temporal Graph Convolutional Network(AFSTGCN).First,to address the problem of the unknown spatial-temporal structure,we construct the Adaptive Fused Spatial-Temporal Graph(AFSTG)layer.Specifically,we fuse the spatial-temporal graph based on the interrelationship of spatial graphs.Simultaneously,we construct the adaptive adjacency matrix of the spatial-temporal graph using node embedding methods.Subsequently,to overcome the insufficient extraction of disordered correlation features,we construct the Adaptive Fused Spatial-Temporal Graph Convolutional(AFSTGC)module.The module forces the reordering of disordered temporal,spatial and spatial-temporal dependencies into rule-like data.AFSTGCN dynamically and synchronously acquires potential temporal,spatial and spatial-temporal correlations,thereby fully extracting rich hierarchical feature information to enhance the predicted accuracy.Experiments on different types of MTS datasets demonstrate that the model achieves state-of-the-art single-step and multi-step performance compared with eight other deep learning models.

A prediction comparison between univariate and multivariate chaotic time series

The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic time series including local mean prediction, local linear prediction and BP neural networks prediction are considered. The simulation results obtained by the Lorenz system show that no matter what nonlinear prediction method is used, the prediction error of multivariate chaotic time series is much smaller than the prediction error of univariate time series, even if half of the data of univariate time series are used in multivariate time series. The results also verify that methods to determine the time delays and the embedding dimensions are correct from the view of minimizing the prediction error.

Joint multivariate statistical model and its applications to synthetic earthquake predic-tion

针对目前地震综合预报中的一些问题，利用近30年来迅速发展的多元统计分析中主成分分析、判别分析组成多元统计组合模型，在众多的地震预报指标(预报因子)中采用信息最大化方法，选择对中期预测信息累积贡献率大于90％地震预报指标，分别进行相关分析、预测、检验，最终应用马氏距离判别作外推综合预报；并以华北地区(30°～42°N，108°125°E)为例进行模型的应用检验，初步研究已取得了较好的效果．

多元质量特性预报：MULTIVARIATE回归分析的应用

对现象之间客观存在的因果关系建立回归分析模型,这是实际中较为普遍的做法.在这篇文章中,我们根据MULTIVARIATE回归分析的基本原理,利用从生产现场采集的观测数据,对产品两个质量特性及其五个关键影响因素之间的关系建立了多重多元回归分析方程,为说明MULTIVARIATE回归应用的可行性,我们还结合实例给出了因变量向量估计的两种形式,以及无条件预报的置信区间。

Multivariate Analysis of Community Structure Variation of Plankton and Zoobenthos in Municipal Polluted River

[Objective] The plankton and macrobenthos samples in municipal polluted river were analyzed by different methods, so as to explore the method suitable for biological data analysis in heavy polluted area. [Method] Shannon-Wiener diversity index, cluster analysis of multivariate statistical analysis and MDS （Non-matric Multi- dimentional Scaling）analysis were used to analyze biological data of phytoplankton, zooplankton and Zoobenthos collected from the representative municipal polluted river in Pearl River Delta. The sediment samples were also collected to determine. Pb, Cd, Hg, Cr, As, Cu, Ni, Zn, as well as CODe, and NH3-N of porewater. Hakanson potential ecological risk index method was used to evaluate the ecological risk. [Re- suit] Shannon-Wiener diversity index analysis results can not effectively reflect the difference of pollution status of various stations in heavy polluted area; despite the presence of some problems, multivariate analysis method is superior to the Shannon-Wiener diversity index method in biological monitoring of heavy polluted river in the city. [Conclusion] The paper provided theoretical basis for biological data analysis in heavy polluted area.

MULTIVARIATE ABSOLUTE DEGREE OF GREY INCIDENCE BASED ON DISTRIBUTION CHARACTERISTICS OF POINTS

The analysis result of absolute degree of grey incidence for multivariate time series is often inconsistent with the qualitative analysis. To overcome this shortage, a multivariate absolute degree of grey incidence based on distribution characteristics of points is proposed. Based on the geometric description of multivariate time se- ries, the neighborhood extrema are extracted in the different regions, and a characteristic point set is constructed. Then according to the distribution of the characteristic point set, a characteristic point sequence reflecting the ge- ometric features of multivariate time series is obtained. The incidence analysis between multivariate time series is transformed into the relational analysis between characteristic point sequences, and a grey incidence model is established. The model possesses the properties of translational invariance, transpose and rank transform invari- ance, and satisfies the grey incidence analysis axioms. Finally, two cases are studied and the results prove the ef- fectiveness of the model.

Monotonicity of the tail dependence for multivariate t-copula

This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.

Outcomes of treatment of male urethral stricture：a multivariate analysis

目的：分析外伤性和前列腺术后尿道狭窄各种治疗方法的优缺点及影响因素，为临床上合理选择治疗方式、减少狭窄复发提出有益建议。方法：对本科64例外伤性和59例前列腺术后的尿道狭窄初次治疗共123例进行回顾性多因素分析。结果：64例外伤性尿道狭窄患者中，尿扩22例，20例（90．9％）复发；尿道内切开21例，16例（76．2％）复发；尿道端端吻合21例，4例（19％）复发；59例前列腺术后尿道狭窄中，尿扩16例，15例（93．6％）复发；尿道内切开37例，5例（13．5％）复发；6例切开膀胱行膀胱颈疤痕切开切除膀胱颈整形术，3例（50％）复发。结论：①经尿道疤痕切开切除治疗外伤性尿道狭窄，其疗效与狭窄长度有关，狭窄长度〈2cm复发率低，〉2121／1则复发率高。②尿道疤痕切除端端吻合治疗外伤性尿道狭窄，其疗效与狭窄长度、狭窄部位、既往手术史无关，与手术本身有关，即术中如彻底切除狭窄疤痕及坏死组织、吻合无张力则复发率低，反之则高。⑧尿扩适用于尿道黏膜下狭窄，不适用于合并有尿道海绵体纤维化的尿道狭窄。④尿道内切开是治疗前列腺术后尿道狭窄的首选方法且疗效好。

Study on QSAR of Taxol and its Derivatives Based on Stepwise Multivariate Linear Regression Analysis

Abstract Using the method of stepwise multivariate linear regression (SMLR), the quantitative structure activity relationships (QSAR) of two isomeric series of taxol and its derivatives have been studied. It was found that the molar refractivity of the C3′substituent of the C13 side chain has significant correlation with its activity. We deduce that structural changes in the C3′substituents may be critical to the anticancer function. It would be useful to the design and synthesis of taxol like compounds with improved activities.

Multivariate adaptive regression splines and neural network models for prediction of pile drivability

Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and tension stresses in the piles. Hence, an important design consideration is to check that the strength of the pile is sufficient to resist the stresses caused by the impact of the pile hammer. Due to its complexity, pile drivability lacks a precise analytical solution with regard to the phenomena involved.In situations where measured data or numerical hypothetical results are available, neural networks stand out in mapping the nonlinear interactions and relationships between the system’s predictors and dependent responses. In addition, unlike most computational tools, no mathematical relationship assumption between the dependent and independent variables has to be made. Nevertheless, neural networks have been criticized for their long trial-and-error training process since the optimal configuration is not known a priori. This paper investigates the use of a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines（MARS）, as an alternative to neural networks, to approximate the relationship between the inputs and dependent response, and to mathematically interpret the relationship between the various parameters. In this paper, the Back propagation neural network（BPNN） and MARS models are developed for assessing pile drivability in relation to the prediction of the Maximum compressive stresses（MCS）, Maximum tensile stresses（MTS）, and Blow per foot（BPF）. A database of more than four thousand piles is utilized for model development and comparative performance between BPNN and MARS predictions.

GIS-based landslide susceptibility mapping using numerical risk factor bivariate model and its ensemble with linear multivariate regression and boosted regression tree algorithms

In this study, a novel approach of the landslide numerical risk factor(LNRF) bivariate model was used in ensemble with linear multivariate regression(LMR) and boosted regression tree(BRT) models, coupled with radar remote sensing data and geographic information system(GIS), for landslide susceptibility mapping(LSM) in the Gorganroud watershed, Iran. Fifteen topographic, hydrological, geological and environmental conditioning factors and a landslide inventory(70%, or 298 landslides) were used in mapping. Phased array-type L-band synthetic aperture radar data were used to extract topographic parameters. Coefficients of tolerance and variance inflation factor were used to determine the coherence among conditioning factors. Data for the landslide inventory map were obtained from various resources, such as Iranian Landslide Working Party(ILWP), Forestry, Rangeland and Watershed Organisation(FRWO), extensive field surveys, interpretation of aerial photos and satellite images, and radar data. Of the total data, 30% were used to validate LSMs, using area under the curve(AUC), frequency ratio(FR) and seed cell area index(SCAI).Normalised difference vegetation index, land use/land cover and slope degree in BRT model elevation, rainfall and distance from stream were found to be important factors and were given the highest weightage in modelling. Validation results using AUC showed that the ensemble LNRF-BRT and LNRFLMR models(AUC = 0.912(91.2%) and 0.907(90.7%), respectively) had high predictive accuracy than the LNRF model alone(AUC = 0.855(85.5%)). The FR and SCAI analyses showed that all models divided the parameter classes with high precision. Overall, our novel approach of combining multivariate and machine learning methods with bivariate models, radar remote sensing data and GIS proved to be a powerful tool for landslide susceptibility mapping.

Reliability analysis of structure with random parameters based on multivariate power polynomial expansion

A new method for calculating the failure probabilityof structures with random parameters is proposed based onmultivariate power polynomial expansion, in which te uncertain quantities include material properties, structuralgeometric characteristics and static loads. The structuralresponse is first expressed as a multivariable power polynomialexpansion, of which the coefficients ae then determined by utilizing the higher-order perturbation technique and Galerkinprojection scheme. Then, the final performance function ofthe structure is determined. Due to the explicitness of theperformance function, a multifold integral of the structuralfailure probability can be calculated directly by the Monte Carlo simulation, which only requires a smal amount ofcomputation time. Two numerical examples ae presented toillustate te accuracy ad efficiency of te proposed metiod. It is shown that compaed with the widely used first-orderreliability method （ FORM） and second-order reliabilitymethod （ SORM）, te results of the proposed method are closer to that of the direct Monte Carlo metiod,and it requires much less computational time.

Groundwater quality assessment using multivariate analysis,geostatistical modeling, and water quality index(WQI): a case of study in the Boumerzoug-El Khroub valley of Northeast Algeria

In this study,the analytical data set of 26 groundwater samples from the alluvial aquifer of Boumerzoug-E1 khroub valley has been processed simultaneously with Multivariate analysis,geostatistical modeling,WQI,and geochemical modeling.Cluster analysis identified three main water types based on the major ion contents,where mineralization increased from group 1 to group 3.These groups were confirmed by FA/PCA,which demonstrated that groundwater quality is influenced by geochemical processes(water-rock interaction)and human practice(irrigation).The exponential semivariogram model WQI.Groundwater chemistry has a strong spatial structure for Mg,Na,Cl,and NO3,and a moderate spatial structure for EC,Ca,K,HCO3,and SO4.Water quality maps generated using ordinary Kriging are consistent with the HCA and PCA results.All water groups are supersaturated with respect to carbonate minerals,and dissolution of kaolinite and Ca-smectite is one of the processes responsible for hydrochemical evolution in the area.

Comprehensive multivariate grey incidence degree based on principal component analysis

To overcome the too fine-grained granularity problem of multivariate grey incidence analysis and to explore the comprehensive incidence analysis model, three multivariate grey incidences degree models based on principal component analysis （PCA） are proposed. Firstly, the PCA method is introduced to extract the feature sequences of a behavioral matrix. Then, the grey incidence analysis between two behavioral matrices is transformed into the similarity and nearness measure between their feature sequences. Based on the classic grey incidence analysis theory, absolute and relative incidence degree models for feature sequences are constructed, and a comprehensive grey incidence model is proposed. Furthermore, the properties of models are researched. It proves that the proposed models satisfy the properties of translation invariance, multiple transformation invariance, and axioms of the grey incidence analysis, respectively. Finally, a case is studied. The results illustrate that the model is effective than other multivariate grey incidence analysis models.

Using Multivariate Statistical and Geostatistical Methods to Identify Spatial Variability of Trace Elements in Agricultural Soils in Dongguan City,Guangdong,China

Dongguan （东莞） City, located in the Pearl River Delta, South China, is famous for its rapid industrialization in the past 30 years. A total of 90 topsoil samples have been collected from agricultural fields, including vegetable and orchard soils in the city, and eight heavy metals （As, Cu, Cd, Cr, Hg, Ni, Pb, and Zn） and other items （pH values and organic matter） have been analyzed, to evaluate the influence of anthropic activities on the environmental quality of agricultural soils and to identify the spatial distribution of trace elements and possible sources of trace elements. The elements Hg, Pb, and Cd have accumulated remarkably here, incomparison with the soil background content of elements in Guangdong （广东） Province. Pollution is more serious in the western plain and the central region, which are heavily distributed with industries and rivers. Multivariate and geostatistical methods have been applied to differentiate the influences of natural processes and human activities on the pollution of heavy metals in topsoils in the study area. The results of cluster analysis （CA） and factor analysis （FA） show that Ni, Cr, Cu, Zn, and As are grouped in factor F1, Pb in F2, and Cd and Hg in F3, respectively. The spatial pattern of the three factors may be well demonstrated by geostatistical analysis. It is shown that the first factor could be considered as a natural source controlled by parent rocks. The second factor could be referred to as ＂industrial and traffic pollution sources＂. The source of the third factor is mainly controlled by long-term anthropic activities, as a consequence of agricultural activities, fossil fuel consumption, and atmospheric deposition.