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The horizontal magnetic primitive equations approximation of the anisotropic MHD equations in a thin 3D domain

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arXiv 2023年

作者： Zhang, Jie Liu, Wenjun School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing210044 China

In this paper, we give a rigorous justification of the deviation of the primitive equations with only horizontal viscosity and magnetic diffusivity (PEHM) as the small aspect ratio limit of the incompressible three-dimensional scaled horizontal viscous MHD (SHMHD) equations. Choosing an aspect ratio parameter Ε ∈ (0, ∞), we consider the case that if the horizontal and vertical viscous coefficients are of µ = O(1) and ν = O(Εα), and the orders of magnetic diffusion coefficients k and σ are k = O(1) and σ = O(Εα), with α > 2, then the limiting system is the PEHM as Ε goes to zero. For H1-initial data, we prove that the global weak solutions of the SHMHD equations converge strongly to the local-in-time strong solutions of the PEHM, as Ε tends to zero. For H1-initial data with additional regularity (∂zÃ0, ∂zB˜0) ∈ Lp(Ω)(2 2-initial data, we show that the local-in-time strong solutions of the SHMHD equations converge strongly to the global-in-time strong solutions of the PEHM, as Ε goes to zero. Moreover, the rate of convergence is of the order O(Εγ/2), where γ = min{2, α − 2} with α ∈ (2, ∞). It should be noted that in contrast to the case α > 2, the case α = 2 has been investigated by Du and Li in [14], in which they consider the PEM and the rate of global-in-time convergences is of the order O(Ε).MSC Codes 35Q30, 76D03, 76D05, 35Q86, 76W05 Copyright © 2023, The Authors. All rights reserved.

关键词： Aspect ratio

Continuous data assimilation for the three dimensional primitive equations with magnetic field

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arXiv 2023年

作者： Zhao, Yongqing Liu, Wenjun Lv, Guangying Wang, Yuepeng School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing210044 China

In this paper, the problem of continuous data assimilation of three dimensional primitive equations with magnetic field in thin domain is studied. We establish the well-posedness of the assimilation system and prove that the H2-strong solution of the assimilation system converges exponentially to the reference solution in the sense of L2 as t → ∞. We also study the sensitivity analysis of the assimilation system and prove that a sequence of solutions of the difference quotient equation converge to the unique solution of the formal sensitivity *** Codes 35Q35, 34D06, 37C50 Copyright © 2023, The Authors. All rights reserved.

关键词： Sensitivity analysis

Combining Experimental and Historical data for Policy Evaluation

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arXiv 2024年

作者： Li, Ting Shi, Chengchun Wen, Qianglin Sui, Yang Qin, Yongli Lai, Chunbo Zhu, Hongtu School of Statistics and Management Shanghai University of Finance and Economics China Department of Statistics London School of Economics and Political Science United Kingdom Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University China Didi Chuxing China Department of Biostatistics The University of North Carolina Chapel Hill United States

This paper studies policy evaluation with multiple data sources, especially in scenarios that involve one experimental dataset with two arms, complemented by a historical dataset generated under a single control arm. We propose novel data integration methods that linearly integrate base policy value estimators constructed based on the experimental and historical data, with weights optimized to minimize the mean square error (MSE) of the resulting combined estimator. We further apply the pessimistic principle to obtain more robust estimators, and extend these developments to sequential decision making. Theoretically, we establish non-asymptotic error bounds for the MSEs of our proposed estimators, and derive their oracle, efficiency and robustness properties across a broad spectrum of reward shift scenarios. Numerical experiments and real-data-based analyses from a ridesharing company demonstrate the superior performance of the proposed estimators. Copyright © 2024, The Authors. All rights reserved.

关键词： Mean square error

Sequential Cauchy Combination Test for Multiple Testing Problems with Financial Applications

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arXiv 2023年

作者： Bouamara, Nabil Laurent, Sébastien Shi, Shuping Louvain Institute of Data Analysis and Modeling in economics and statistics Université catholique de Louvain Belgium Aix-Marseille University Aix-Marseille School of Economics CNRS & EHESS Aix-Marseille Graduate School of Management – IAE France Department of Economics Macquarie University Australia

We introduce a simple tool to control for false discoveries and identify individual signals in scenarios involving many tests, dependent test statistics, and potentially sparse signals. The tool applies the Cauchy combination test recursively on a sequence of expanding subsets of p-values and is referred to as the sequential Cauchy combination test. While the original Cauchy combination test aims to make a global statement about a set of null hypotheses by summing transformed p-values, our sequential version determines which p-values trigger the rejection of the global null. The sequential test achieves strong familywise error rate control, exhibits less conservatism compared to existing controlling procedures when dealing with dependent test statistics, and provides a power boost. As illustrations, we revisit two well-known large-scale multiple testing problems in finance for which the test statistics have either serial dependence or cross-sectional dependence, namely monitoring drift bursts in asset prices and searching for assets with a nonzero alpha. In both applications, the sequential Cauchy combination test proves to be a preferable alternative. It overcomes many of the drawbacks inherent to inequality-based controlling procedures, extreme value approaches, resampling and screening methods, and it improves the power in simulations, leading to distinct empirical outcomes. Copyright © 2023, The Authors. All rights reserved.

关键词： Statistical tests

An explorative system for large-scale table data that combines data visualization and text generation techniques

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Computer Software

Computer Software 2021年第3期38卷 2-22页

作者： Hosokawa, Natsuki Arimoto, Kohei Wakita, Ken School of Computing Tokyo Institute of Technology Japan Teikoku Databank Ltd. Center for TDB Advanced Data Analysis and Modeling Japan The University of Tokyo Graduate School of Interdisciplinary Information Studies Japan School of Computing Tokyo Institute of Technology Teikoku Databank Ltd. Center for TDB Advanced Data Analysis and Modeling Japan

In recent years, data analysis systems that combine natural language generation and visualization are increasing. The medium of text is superior to visualization in that it does not require special knowledge for users to understand the important facts buried in data. However, automatically summarizing large data with texts becomes too long, because in table data, the more attributes there are, the more statistical features there are. In this study, we address this scalability problem by using the hierarchical structure that many large data sets have explicitly or implicitly, in both items and attributes. First, the system focuses text generation and visualization only on the areas that users are interested in. Secondly, it interactively shifts the focus as the user's interest shifts. In this way, we propose an idea for a system that allows users to explore the entire data smoothly while limiting the amount of text presented at once. We also implement the system and show that this idea is effective. © 2021 Japan Society for Software Science and Technology. All rights reserved.

关键词： data visualization

data Classification Algorithms for Complex Heavy-Tailed Distributions

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Data Classification Algorithms for Complex Heavy-Tailed Dist...

2021 CIE International Conference on Radar, Radar 2021

作者： Li, Jianbo Rong, Yao Yang, Liu Liang, Zhifang Du, Xiaolin School of Communication and Information Engineering Chongqing University of Posts and Telecommunications Chongqing400065 China Yunnan University Yunnan Key Laboratory of Statistical Modeling and Data Analysis Kunming650504 China School of Computer and Control Engineering Yantai University Yantai264005 China

ISBN: (纸本)9781665498142

This paper deals with the adaptive classification problem of heavy-tailed data drawn from a multivariate distribution of the complex elliptically symmetric family. The authors assume that the collected data is either homogeneous or partially homogeneous. Based on the GLRT criterion, two adaptive classifiers are devised for the scenarios of Hermitian and persymmetric scatter matrices, respectively. To estimate the unknown parameters, iterative algorithms with convergence property are introduced to solve the developed non-convex maximum likelihood optimization problems. The simulation results show that, compared with the Hermitian scenario, the exploitation of persymmetric structure information can lead to an obvious performance improvement. © 2021 IEEE.

关键词： Classification GLRT heavy-tailed distribution majorization-minimization persymmetric structure

Inference on high-dimensional single-index models with streaming data

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2024年第1期25卷 16489-16556页

作者： Dongxiao Han Jinhan Xie Jin Liu Liuquan Sun Jian Huang Bei Jiang Linglong Kong School of Statistics and Data Science KLMDASR LEBPS and LPMC Nankai University Tianjin China Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University Kunming China and Department of Mathematical and Statistical Sciences University of Alberta Edmonton AB Canada Academy of Mathematics and Systems Science Chinese Academy of Sciences and School of Mathematical Sciences University of Chinese Academy of Sciences Beijing China Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong China Department of Mathematical and Statistical Sciences University of Alberta Edmonton AB Canada

Traditional statistical methods are faced with new challenges due to streaming data. The major challenge is the rapidly growing volume and velocity of data, which makes storing such huge data sets in memory impossible. The paper presents an online inference framework for regression parameters in high-dimensional semiparametric single-index models with unknown link functions. The proposed online procedure updates only the current data batch and summary statistics of historical data instead of re-accessing the entire raw data set. At the same time, we do not need to estimate the unknown link function, which is a highly challenging task. In addition, a generalized convex loss function is used in the proposed inference procedure. To illustrate the proposed method, we use the Huber loss function and the negative log-likelihood of the logistic regression model. In this study, the asymptotic normality of the proposed online debiased Lasso estimators and the bounds of the proposed online Lasso estimators are investigated. To evaluate the performance of the proposed method, extensive simulation studies have been conducted. We provide applications to Nasdaq stock prices and financial distress data sets.

关键词： high-dimensional data lasso single-index models statistical inference streaming data

More efficient estimation of multivariate additive models based on tensor decomposition and penalization

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2024年第1期25卷 7659-7685页

作者： Xu Liu Heng Lian Jian Huang School of Statistics and Management Shanghai University of Finance and Economics Shanghai China and Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University Kunming China City University of Hong Kong Shenzhen Research Institute Shenzhen China and Department of Mathematics City University of Hong Kong Kowloon Tong Hong Kong China Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong China

We consider parsimonious modeling of high-dimensional multivariate additive models using regression splines, with or without sparsity assumptions. The approach is based on treating the coefficients in the spline expansions as a third-order tensor. Note the data does not have tensor predictors or tensor responses, which distinguishes our study from the existing ones. A Tucker decomposition is used to reduce the number of parameters in the tensor. We also combined the Tucker decomposition with penalization to enable variable selection. The proposed method can avoid the statistical inefficiency caused by estimating a large number of nonparametric functions. We provide sufficient conditions under which the proposed tensor-based estimators achieve the optimal rate of convergence for the nonparametric regression components. We conduct simulation studies to demonstrate the effectiveness of the proposed novel approach in fitting high-dimensional multivariate additive models and illustrate its application on a breast cancer copy number variation and gene expression data set.

关键词： high dimensionality sparse models splines tensor estimation tucker decomposition

Geriatric syndromes in intermediate care resources: Screening, prevalence and inpatient mortality. Multicenter prospective study

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Revista Espanola de Geriatria y Gerontologia 2023年第3期58卷 134-140页

作者： Perea-García, Miquel Martori, Joan Carles del Moral-Pairada, Marta Amblàs-Novellas, Jordi Hospital de Sant Celoni Sant Celoni Barcelona Spain Grupo de Investigación en Cronicidad de la Cataluña Central (C3RG) Universitat de Vic-Universitat Central de Catalunya (UVIC-UCC) Vic Barcelona Spain Grupo de Investigación Data Analysis and Modeling Universitat de Vic-Universitat Central de Catalunya (UVIC-UCC) Vic Barcelona Spain Centro de Atención Primaria Consorcio de Atención Primaria de Salud de Eixample (CAPSBE) Barcelona Spain

Objective: To determine the prevalence of geriatric syndromes (GS) in the geriatric population of the different intermediate care resources, as well as its relationship with intrahospital mortality. Material and methods: A prospective observational descriptive study, carried out in intermediate care resources in the Vic area (Barcelona) between July 2018 and September 2019. All people aged ≥65 years and/or criteria of complex chronic patient and/or advanced chronic disease, who were assessed for the presence of GS using the trigger questions of the Frail VIG-Index (IF-VIG), administered at baseline, on admission, on discharge and 30 days after discharge. Results: Four hundred and forty-two participants were included, of which 55.4% were women, with a mean age of 83.48 years. There are significant differences (P<.05) between frailty, age and number of GS in relation to the intermediate care resource at the time of admission. There were significant differences in the prevalence of GS between the group of patients who died during the hospitalization (24.7% of the sample) in relation to the survivors: both in a situation baseline (malnutrition, dysphagia, delirium, loss of autonomy, pressure ulcers, and insomnia), as well as in the admission assessment (falls, malnutrition, dysphagia, cognitive impairment, delirium, loss of autonomy, and insomnia). Conclusions: There is a close relationship between the prevalence of GS and in-hospital mortality in intermediate care resources. In the absence of more studies, the use of the IF-VIG as a screening checklist for GS could be useful for its detection. © 2023 SEGG

关键词： End-of-life Frailty Frailty index Geriatric syndrome Intermediate care