scholarly journals Detecting Changes under Multivariate Normal Distributions via the Generalized Inference

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Weiyan Mu ◽  
Xin Wang ◽  
Xi Wu ◽  
Shifeng Xiong
Keyword(s):  
Multiple Testing ◽  
Simulation Studies ◽  
Multivariate Normal ◽  
Multivariate Statistical ◽  
Normal Distributions ◽  
Generalized Inference ◽  
Before And After ◽  
Statistical Hypotheses ◽  
Statistical Hypotheses Testing ◽  
Special Process

It is commonly encountered in many fields to detect whether a change occurs on a population after a special process. Based on observations for describing the population before and after the process, we formulate this problem as two statistical hypotheses testing problems within a framework of multivariate statistical analysis and then propose a generalized inference approach to solve them. The corresponding generalized p values and their calculation details are provided. The proposed method is also extended to multiple testing problems. Simulation studies show that the proposed p values have satisfactory frequentist performance. We illustrate our methods with a real application in manufacturing of bearings that are used in medical devices.

scholarly journals Algorithms for 3D Particles Characterization Using X-Ray Microtomography in Proppant Crush Test

2018 ◽  
Vol 4 (11) ◽  
pp. 134 ◽  
Author(s):  
Ilia Safonov ◽  
Ivan Yakimchuk ◽  
Vladimir Abashkin
Keyword(s):  
Laboratory Method ◽  
X Ray ◽  
Geometric Moments ◽  
Before And After ◽  
Statistical Hypotheses ◽  
Image Processing Algorithms ◽  
A New Technique ◽  
Individual Particles ◽  
Remarkable Advantage

We present image processing algorithms for a new technique of ceramic proppant crush resistance characterization. To obtain the images of the proppant material before and after the test we used X-ray microtomography. We propose a watershed-based unsupervised algorithm for segmentation of proppant particles, as well as a set of parameters for the characterization of 3D particle size, shape, and porosity. An effective approach based on central geometric moments is described. The approach is used for calculation of particles’ form factor, compactness, equivalent ellipsoid axes lengths, and lengths of projections to these axes. Obtained grain size distribution and crush resistance fit the results of conventional test measured by sieves. However, our technique has a remarkable advantage over traditional laboratory method since it allows to trace the destruction at the level of individual particles and their fragments; it grants to analyze morphological features of fines. We also provide an example describing how the approach can be used for verification of statistical hypotheses about the correlation between particles’ parameters and their crushing under load.

scholarly journals On Multiple Hypotheses LAO Testing With Rejection of Decision for Two Dependent Objects

2018 ◽  
pp. 110-114
Author(s):  
Evgueni Haroutunian ◽  
Aram Yesayan ◽  
Narine Harutyunyan
Keyword(s):  
Hypotheses Testing ◽  
Asymptotically Optimal ◽  
Discrete Probability ◽  
Multiple Hypotheses ◽  
Optimal Tests ◽  
The Matrix ◽  
Statistical Hypotheses ◽  
Asymptotically Optimal Tests ◽  
Error Probabilities ◽  
Statistical Hypotheses Testing

Multiple statistical hypotheses testing with possibility of rejecting of decisionis considered for model consisting of two dependent objects characterized by joint discrete probability distribution. The matrix of error probabilities exponents (reliabilities) of asymptotically optimal tests is studied.

scholarly journals Interpopulational variability of Pinus sylvestris L. in eight Polish localities expressed in morphological and anatomical traits of needles

2014 ◽  
Vol 63 (1) ◽  
pp. 67-76 ◽  
Author(s):  
Maria A. Bobowicz ◽  
Adolf F. Korczyk
Keyword(s):  
Pinus Sylvestris ◽  
Minimum Spanning Tree ◽  
Multivariate Statistical ◽  
Mahalanobis Distances ◽  
The North ◽  
Flat Side ◽  
Standing Trees ◽  
Statistical Hypotheses ◽  
Resin Canals ◽  
Interpopulational Variability

Two-year old needles were collected from 272 standing trees of <i>Pinus sylvestris</i> L., representing 8 Polish populations. The needles were studied in respect to IS morphological and anatomical traits. The obtained data were subjected to multivariate statistical analysis in an attempt to delineate interpopulational variability. Multivariate analysis of variance with testing of statistical hypotheses and discriminant analysis were conducted. Mahalanobis distances were calculated between each of population in pairs and their significance was estimated using Hotelling T<sup>2</sup> statistics. On the basis of the shortest Mahalanobis distances a minimum spanning tree was constructed and on the basis of Euklidean distances hierarchy grouping was performed. A large majority of the populations was found to differ significantly from the remaining populations. The population from Bolewice proved to be most divergent. The principal variables which proved capable of discriminating between populations were found to include: needle length, the number of stomata on the flat side of the needle and the number of resin canals. Using Bryant's test, the studied populations were found to belong to two geographic groups: the North-Polish one or the South-Polish one.

scholarly journals The Intervention Effects of Acupuncture on Fatigue Induced by Exhaustive Physical Exercises: A Metabolomics Investigation

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Haifeng Ma ◽  
Xia Liu ◽  
Ying Wu ◽  
Naixia Zhang
Keyword(s):  
Acupuncture Treatment ◽  
Young Male ◽  
Short Term ◽  
Multivariate Statistical ◽  
Male Athletes ◽  
Physical Exercises ◽  
Induced Stress ◽  
Choline Metabolism ◽  
Before And After ◽  
Metabolomics Analysis

In this study, the antifatigue effects of acupuncture had been investigated at the metabolic level on the young male athletes with exhaustive physical exercises. After a series of exhaustive physical exercises and a short-term rest, the athletes either were treated with needling acupuncture on selected acupoints (TA group) or enjoyed an extended rest (TR group). NMR-based metabolomics analysis was then applied to depict the metabolic profiles of urine samples, which were collected from the athletes at three time points including the time before exercises, the time before and after the treatment of acupuncture, or taking the extended rest. The results from multivariate statistical analysis indicated that the recoveries of disturbed metabolites in the athletes treated with acupuncture were significantly faster than in those only taking rest. After the treatment with acupuncture, the levels of distinguished metabolites, 2-hydroxybutyrate, 3-hydroxyisovalerate, lactate, pyruvate, citrate, dimethylglycine, choline, glycine, hippurate, and hypoxanthine were recovered at an accelerated speed in the TA group in comparison with the TR group. The above-mentioned results indicated that the acupuncture treatment ameliorated fatigue by backregulating the perturbed energy metabolism, choline metabolism, and attenuating the ROS-induced stress at an accelerated speed, which demonstrated that acupuncture could serve as an alternative fatigue-relieving approach.

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