Classical multivariate statistical methods concern models, distributions and inference based on the Gaussian distribution. These are the topics in the first textbook for mathematical statisticians by T.W. Anderson that was published in 1958 and that appeared as a slightly expanded 3rd edition in 2003. Matrix theory and notation is used there extensively to efficiently derive properties of the multivariate Gaussian or the Wishart distribution, of principal components, of canonical correlation and discriminant analysis and of the general multivariate linear model in which a Gaussian response vector variable Ya has linear least-squares regression on all components of an explanatory vector variable Yb. In contrast, many methods for analysing sets of observed variables have been developed first within special substantive fields and some or all of the models in a given class were justified in terms of probabilistic and statistical theory much later. Among them are factor analysis, path analysis, structural equation models, and models for which partial-least squares estimation have been proposed. Other multivariate techniques such as cluster analysis and multidimensional scaling have been often used, but the result of such an analysis cannot be formulated as a hypothesis to be tested in a new study and satisfactory theoretical justifications are still lacking. Factor analysis was proposed by psychologist C. Spearman (1904), (1926) and, at the time, thought of as a tool for measuring human intelligence. Such a model has one or several latent variables. These are hidden or unobserved and are to explain the observed correlations among a set of observed variables, called items in that context. The difficult task is to decide how many and which of a possibly large set of items to include into a model. But, given a set of latent variables, a classical factor analysis model specifies for a joint Gaussian distribution mutual independence of the observed variables given the latent variables. This can be recognized to be one special type of a graphical Markov model; see Cox and Wermuth (1996), Edwards (2000), Lauritzen (1996), Whittaker (1990).

Multivariate Statistical Analysis.

Bayesian Networks For Supply Chain Risk, Resilience, and Ripple Effect Analysis

Evaluating the quality risk level in the food supply chain can reduce quality information asymmetry and food quality incidents and promote nationally integrated regulations for food quality. In order to evaluate it, a quality risk evaluation indicator system for the food supply chain is constructed based on an extensive literature review in this paper. Furthermore, a mathematical model based on the fuzzy comprehensive evaluation model (FCEM) and failure mode, effects, and criticality analysis (FMECA) for evaluating the quality risk level in the food supply chain is developed. A computational experiment aimed at verifying the effectiveness and feasibility of this proposed model is conducted on the basis of a questionnaire survey. The results suggest that this model can be used as a general guideline to assess the quality risk level in the food supply chain and achieve the most important objective of providing a reference for the public and private sectors when making decisions on food quality management.

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Quality Risk Evaluation of the Food Supply Chain Using a Fuzzy Comprehensive Evaluation Model and Failure Mode, Effects, and Criticality Analysis

An accurate and stable prediction of the corrosion rate of natural gas pipelines has a major impact on pipeline material selection, inhibitor filling process, and maintenance schedules. At present, corrosion data are impacted by non-linearity and noise interference. The traditional corrosion rate prediction methods often ignore noise data, and only a small number of researchers have carried out in-depth research on non-linear data processing. Therefore, an innovative hybrid prediction model has been proposed with four processes: data preprocessing, optimization, prediction, and evaluation. In the proposed model, a decomposing algorithm is applied to eliminate redundant noise and to extract the primary characteristics of the corrosion data. Stratified sampling is applied to separate the training set and the test set to avoid deviation due to the sampling randomness of small samples. An improved particle swarm optimization algorithm is applied to optimize the parameters of support vector regression. A comprehensive evaluation of this framework is also conducted. For natural gas pipelines in southwest China, the coefficient of determination and mean absolute percentage error of the proposed hybrid model are 0.925 and 5.73%, respectively, with better prediction performance compared to state-of-the-art models. The results demonstrate the best approach for improving the prediction accuracy of the proposed hybrid model. This can be applied to improve the corrosion control effect and to support the digital transformation of the corrosion industry.

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Research and Application for Corrosion Rate Prediction of Natural Gas Pipelines Based on a Novel Hybrid Machine Learning Approach

To find the risks in food supply chain and to take appropriate measures to guard against risks and increase capacity of food supply chain to resist risks. The paper established Logistic regression early-warning model to recognise magnitude of risks based on principal component analysis and Logistic regression analysis. An empirical analysis is carried out to test the model by take out some food enterprises randomly as analytic samples and calculate their risk indices in supply chain. The result shows this method is applicable to food supply chain risk early-warning.

Research on Early-Warning Model for Food Supply Chain Risk Based on Logistic Regression

The Research progress and prospect of data mining methods on corrosion prediction of oil and gas pipelines

To solve the problem of recognize the causation factor characteristics of emergency in supply chain in different industries, the paper established causation factor index system of emergency in supply chain based on system analytical method, and at the same time, put forward a causation factor characteristics recognition model for emergency in supply chain based on principal component analysis and clustering analysis that utilize eigenvalue and eigenvector of correlation matrix, comprehensive score of principal component and clusering. An empirical analysis is carried out to find the causation factor characteristics of IT, chemical, auto, transportation and other 6 industries under supply chain Emergency, which indicate that the established model is applicable for solving the problem.

Recognition for Causation Factor Characteristics of Emergency in Supply Chain Based on Principal Component and Clustering Analysis

To find the industry characteristics of emergency in supply chain and to solve the problem of recognition about that. The paper established causation factor indexes system of emergency in supply chain based on systems analytical method, and at the same time, put forward a industry characteristics recognition model for emergency supply chain based on fuzzy clustering utilizing fuzzy similarity relation, fuzzy equivalence relation and fuzzy equivalence matrix. An empirical analysis is carried out to find the characteristics of IT, chemical, auto, transportation and other 6 industries under supply chain emergency, which indicates that IT, medicine and chemical, transportation, agriculture, steel have similar characteristics of supply chain emergency respectively, and the established model is applicable for solving the problem.

Lei Xu

Papers

Research on Early-Warning Model for Food Supply Chain Risk Based on Logistic Regression

The Research progress and prospect of data mining methods on corrosion prediction of oil and gas pipelines

Recognition for Causation Factor Characteristics of Emergency in Supply Chain Based on Principal Component and Clustering Analysis

Analysis and Recognition for Industry Characteristics of Emergency in Supply Chain Based on Fuzzy Clustering