Communications in Mathematics and Statistics最新文献

Nested Group Testing Procedure. 嵌套组测试程序。

IF 0.9 4区数学

Communications in Mathematics and Statistics Pub Date : 2022-10-01 DOI: 10.1007/s40304-021-00269-0

Wenjun Xiong, Juan Ding, Wei Zhang, Aiyi Liu, Qizhai Li

{"title":"Nested Group Testing Procedure.","authors":"Wenjun Xiong, Juan Ding, Wei Zhang, Aiyi Liu, Qizhai Li","doi":"10.1007/s40304-021-00269-0","DOIUrl":"10.1007/s40304-021-00269-0","url":null,"abstract":"We investigated the false-negative, true-negative, false-positive, and true-positive predictive values from a general group testing procedure for a heterogeneous population. We show that its false (true)-negative predictive value of a specimen is larger (smaller), and the false (true)-positive predictive value is smaller (larger) than that from individual testing procedure, where the former is in aversion. Then we propose a nested group testing procedure, and show that it can keep the sterling characteristics and also improve the false-negative predictive values for a specimen, not larger than that from individual testing. These characteristics are studied from both theoretical and numerical points of view. The nested group testing procedure is better than individual testing on both false-positive and false-negative predictive values, while retains the efficiency as a basic characteristic of a group testing procedure. Applications to Dorfman's, Halving and Sterrett procedures are discussed. Results from extensive simulation studies and an application to malaria infection in microscopy-negative Malawian women exemplify the findings.","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":" ","pages":"1-31"},"PeriodicalIF":0.9,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9525165/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33498339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Effects of Nonmonotonic Functional Responses on a Disease Transmission Model: Modeling and Simulation. 非单调功能反应对疾病传播模型的影响:建模与仿真。

IF 0.9 4区数学

Communications in Mathematics and Statistics Pub Date : 2022-01-01 Epub Date: 2021-03-02 DOI: 10.1007/s40304-020-00217-4

Abhishek Kumar, Nilam

{"title":"Effects of Nonmonotonic Functional Responses on a Disease Transmission Model: Modeling and Simulation.","authors":"Abhishek Kumar, Nilam","doi":"10.1007/s40304-020-00217-4","DOIUrl":"https://doi.org/10.1007/s40304-020-00217-4","url":null,"abstract":"In this article, a novel susceptible-infected-recovered epidemic model with nonmonotonic incidence and treatment rates is proposed and analyzed mathematically. The Monod-Haldane functional response is considered for nonmonotonic behavior of both incidence rate and treatment rate. The model analysis shows that the model has two equilibria which are named as disease-free equilibrium (DFE) and endemic equilibrium (EE). The stability analysis has been performed for the local and global behavior of the DFE and EE. With the help of the basic reproduction number <math> <mfenced><msub><mi>R</mi> <mn>0</mn></msub> </mfenced> </math> , we investigate that DFE is locally asymptotically stable when <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo><</mo> <mn>1</mn></mrow> </math> and unstable when <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></mrow> </math> . The local stability of DFE at <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>=</mo> <mn>1</mn></mrow> </math> has been analyzed, and it is obtained that DFE exhibits a forward transcritical bifurcation. Further, we identify conditions for the existence of EE and show the local stability of EE under certain conditions. Moreover, the global stability behavior of DFE and EE has been investigated. Lastly, numerical simulations have been done in the support of our theoretical findings.","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":"10 2","pages":"195-214"},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40304-020-00217-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25445444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Multicategory Classification via Forward-Backward Support Vector Machine. 通过前向-后向支持向量机进行多类别分类

IF 0.9 4区数学

Communications in Mathematics and Statistics Pub Date : 2020-09-01 Epub Date: 2019-05-15 DOI: 10.1007/s40304-019-00179-2

Xuan Zhou, Yuanjia Wang, Donglin Zeng

{"title":"Multicategory Classification via Forward-Backward Support Vector Machine.","authors":"Xuan Zhou, Yuanjia Wang, Donglin Zeng","doi":"10.1007/s40304-019-00179-2","DOIUrl":"10.1007/s40304-019-00179-2","url":null,"abstract":"In this paper, we propose a new algorithm to extend support vector machine (SVM) for binary classification to multicategory classification. The proposed method is based on a sequential binary classification algorithm: we first classify a target class by excluding the possibility of labeling as any other classes using a forward step of sequential SVM; we then exclude the already classified classes and repeat the same procedure for the remaining classes in a backward step. The proposed algorithm relies on SVM for each binary classification and utilizes only feasible data in each step; therefore, the method guarantees convergence and entails light computational burden. We prove Fisher consistency of the proposed forward-backward-SVM (FB-SVM) and obtain a stochastic bound for the predicted misclassification rate. We conduct extensive simulations and analyze real-world data to demonstrate the superior performance of FB-SVM, for example, FB-SVM achieves a classification accuracy much higher than the current standard for predicting conversion from mild cognitive impairment to Alzheimer's disease.","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":"8 3","pages":"319-339"},"PeriodicalIF":0.9,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7962596/pdf/nihms-1529357.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25494891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Sharp Convergence of Nonlinear Functionals of a Class of Gaussian Random Fields. 一类高斯随机场非线性泛函的急剧收敛性。

IF 0.9 4区数学

Communications in Mathematics and Statistics Pub Date : 2018-01-01 Epub Date: 2018-11-10 DOI: 10.1007/s40304-018-0162-9

Weijun Xu

引用次数: 4

Regularity Properties for Sparse Regression. 稀疏回归的正则特性

IF 0.9 4区数学

Communications in Mathematics and Statistics Pub Date : 2016-03-01 Epub Date: 2016-03-14 DOI: 10.1007/s40304-015-0078-6

Edgar Dobriban, Jianqing Fan

{"title":"Regularity Properties for Sparse Regression.","authors":"Edgar Dobriban, Jianqing Fan","doi":"10.1007/s40304-015-0078-6","DOIUrl":"10.1007/s40304-015-0078-6","url":null,"abstract":"Statistical and machine learning theory has developed several conditions ensuring that popular estimators such as the Lasso or the Dantzig selector perform well in high-dimensional sparse regression, including the restricted eigenvalue, compatibility, and [Formula: see text] sensitivity properties. However, some of the central aspects of these conditions are not well understood. For instance, it is unknown if these conditions can be checked efficiently on any given data set. This is problematic, because they are at the core of the theory of sparse regression. Here we provide a rigorous proof that these conditions are NP-hard to check. This shows that the conditions are computationally infeasible to verify, and raises some questions about their practical applications. However, by taking an average-case perspective instead of the worst-case view of NP-hardness, we show that a particular condition, [Formula: see text] sensitivity, has certain desirable properties. This condition is weaker and more general than the others. We show that it holds with high probability in models where the parent population is well behaved, and that it is robust to certain data processing steps. These results are desirable, as they provide guidance about when the condition, and more generally the theory of sparse regression, may be relevant in the analysis of high-dimensional correlated observational data.","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":"4 1","pages":"1-19"},"PeriodicalIF":0.9,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4909155/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34502569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0