检索结果-内蒙古大学图书馆

Estimation of the Error Structure in Multivariate Response Linear Regression Models

学校读者我要写书评

暂无评论

Wiley Interdisciplinary Reviews: Computational statistics 2025年第2期17卷

作者： Liu, Ruobin Yu, Guo Department of Statistics and Applied Probability University of California Santa BarbaraCA United States

Multivariate response linear regression model considers how a set of covariates affects multiple responses. In contrast to separately running univariate regression for each response, multivariate response regression can better estimate the coefficient matrix by exploiting shared information among the responses. A key to effectively borrowing strength across different responses is to estimate and utilize the structure among random errors in responses. Moreover, certain applications seek to understand the interrelationships of the responses, which are directly encoded in the error structure. These observations call for the development of methods for estimating the error structure in multivariate response linear regression models. This article aims at providing a review of recent progress in this challenging and important problem. We also provide simulation studies demonstrating the empirical performance of recently developed methods for error structure estimation, as well as the benefit by exploiting these estimates for regression coefficients estimation. © 2025 The Author(s). WIREs Computational statistics published by Wiley Periodicals LLC.

关键词： Multivariant analysis

Heterogenous Macro-Finance Model: A Mean-field Game Approach

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Vu, Hoang Huy Ichiba, Tomoyuki Department of Statistics and Applied Probability University of California Santa BarbaraCA93106 United States

We investigate the full dynamics of capital allocation and wealth distribution of heterogeneous agents in a frictional economy during booms and busts using tools from mean-field games. Two groups in our models, namely the expert and the household, are interconnected within and between their classes through the law of capital processes and are bound by financial constraints. Such a mean-field interaction explains why experts accumulate a lot of capital in the good times and reverse their behavior quickly in the bad times even in the absence of aggregate macro-shocks. When common noises from the market are involved, financial friction amplifies the mean-field effect and leads to capital fire sales by experts. In addition, the implicit interlink between and within heterogeneous groups demonstrates the slow economic recovery and characterizes the deviating and fear-of-missing-out (FOMO) behaviors of households compared to their counterparts. Our model also gives a fairly explicit representation of the equilibrium solution without exploiting complicated numerical approaches. Copyright © 2025, The Authors. All rights reserved.

关键词： Friction

Integrating Sequential Hypothesis Testing into Adversarial Games: A Sun Zi-Inspired Framework

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Zhou, Haosheng Ralston, Daniel Yang, Xu Hu, Ruimeng Department of Statistics and Applied Probability University of California Santa BarbaraCA93106 United States Department of Mathematics University of California Santa BarbaraCA93106 United States Department of Mathematics Department of Statistics and Applied Probability University of California Santa BarbaraCA93106 United States

This paper investigates the interplay between sequential hypothesis testing (SHT) and adversarial decision-making in partially observable games, focusing on the deceptive strategies of red and blue teams. Inspired by Sun Zi’s The Art of War and its emphasis on deception, we develop a novel framework to both deceive adversaries and counter their deceptive tactics. We model this interaction as a Stackelberg game where the blue team, as the follower, optimizes its controls to achieve its goals while misleading the red team into forming incorrect beliefs on its intentions. The red team, as the leader, strategically constructs and instills false beliefs through the blue team’s envisioned SHT to manipulate the blue team’s behavior and reveal its true objectives. The blue team’s optimization problem balances the fulfillment of its primary objectives and the level of misdirection, while the red team coaxes the blue team into behaving consistently with its actual intentions. We derive a semi-explicit solution for the blue team’s control problem within a linear-quadratic framework, and illustrate how the red team leverages leaked information from the blue team to counteract deception. Numerical experiments validate the model, showcasing the effectiveness of deception-driven strategies in adversarial systems. These findings integrate ancient strategic insights with modern control and game theory, providing a foundation for further exploration in adversarial decision-making, such as cybersecurity, autonomous systems, and financial markets. Copyright © 2025, The Authors. All rights reserved.

关键词： Financial markets

FAST DATA INVERSION FOR HIGH-DIMENSIONAL DYNAMICAL SYSTEMS FROM NOISY MEASUREMENTS

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Lin, Yizi Liu, Xubo Segall, Paul Gu, Mengyang Department of Statistics and Applied Probability University of California Santa Barbara United States Department of Geophysics Stanford University United States

In this work, we develop a scalable approach for a flexible latent factor model for high-dimensional dynamical systems. Each latent factor process has its own correlation and variance parameters, and the orthogonal factor loading matrix can be either fixed or estimated. We utilize an orthogonal factor loading matrix that avoids computing the inversion of the posterior covariance matrix at each time of the Kalman filter, and derive closed-form expressions in an expectation-maximization algorithm for parameter estimation, which substantially reduces the computational complexity without approximation. Our study is motivated by inversely estimating slow slip events from geodetic data, such as continuous GPS measurements. Extensive simulated studies illustrate higher accuracy and scalability of our approach compared to alternatives. By applying our method to geodetic measurements in the Cascadia region, our estimated slip better agrees with independently measured seismic data of tremor events. The substantial acceleration from our method enables the use of massive noisy data for geological hazard quantification and other applications. Copyright © 2025, The Authors. All rights reserved.

关键词： Expectation maximization algorithm

Estimation of anisotropic viscosities for the stochastic primitive equations

学校读者我要写书评

暂无评论

Stochastics and Partial Differential Equations: Analysis and Computations 2025年 1-48页

作者： Cialenco, Igor Hu, Ruimeng Lin, Quyuan Department of Applied Mathematics Illinois Institute of Technology Chicago USA Department of Mathematics Department of Statistics and Applied Probability University of California Santa Barbara USA School of Mathematical and Statistical Sciences Clemson University Clemson USA

The viscosity parameters play a fundamental role in applications involving stochastic primitive equations (SPE), such as accurate weather predictions, climate modeling, and ocean current simulations. In this paper, we develop several novel estimators for the anisotropic viscosities in the SPE, using a finite number of Fourier modes of a single sample path observed within a finite time interval. The focus is on analyzing the consistency and asymptotic normality of these estimators. We consider a torus domain and treat strong, pathwise solutions in the presence of additive white noise (in time). Notably, the analysis for estimating horizontal and vertical viscosities differs due to the unique structure of the SPE and the fact that both parameters of interest are adjacent to the highest-order derivative. To the best of our knowledge, this is the first work addressing the estimation of anisotropic viscosities, with the potential applicability of the developed methodology to other models.

关键词：

Prior distributions for Gaussian processes in computer model emulation and calibration

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Gu, Mengyang De Oliveira, Victor Department of Statistics and Applied Probability University of California Santa BarbaraCA93106 United States Department of Management Science and Statistics University of Texas at San Antonio San AntonioTX78249 United States

This article discusses prior distributions for the parameters of Gaussian processes (GPs) that are widely used as surrogate models to emulate expensive computer simulations. The parameters typically involve mean parameters, a variance parameter, and correlation parameters. These parameters are often estimated by maximum likelihood (MLE). In some scenarios, however, the MLE can be unstable, particularly when the number of simulation runs is small, and some Bayesian estimators display better properties. We introduce default Bayesian priors for the parameters of GPs with isotropic and separable correlation functions for emulating computer simulations with both scalar-valued and vector-valued outputs. We also summarize recent developments of Bayesian priors for calibrating computer models by field or experimental observations. Finally, we review software packages for computer model emulation and calibration. Copyright © 2025, The Authors. All rights reserved.

关键词： Gaussian distribution

ON THE LOCAL WELL-POSEDNESS OF FRACTIONALLY DISSIPATED PRIMITIVE EQUATIONS WITH TRANSPORT NOISE

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Hu, Ruimeng Lin, Quyuan Liu, Rongchang Department of Mathematics Department of Statistics and Applied Probability University of California Santa BarbaraCA93106 United States School of Mathematical and Statistical Sciences Clemson University ClemsonSC29634 United States Department of Mathematics University of Arizona TucsonAZ85721 United States

We investigate the three-dimensional fractionally dissipated primitive equations with transport noise, focusing on subcritical and critical dissipation regimes characterized by (−∆)s/2 with s ∈ (1, 2) and s = 1, respectively. For σ > 3, we establish the local existence of unique pathwise solutions in Sobolev space Hσ. This result applies to arbitrary initial data in the subcritical case (s ∈ (1, 2)), and to small initial data in the critical case (s = 1). The analysis is particularly challenging due to the loss of horizontal derivatives in the nonlinear terms and the lack of full dissipation. To address these challenges, we develop novel commutator estimates involving the hydrostatic Leray *** Codes 35Q86, 60H15, 76M35, 35Q35, 86A10 Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

ON GENERALIZED INVERSES OF A BLOCK IN A PARTITIONED MATRIX

学校读者我要写书评

暂无评论

LINEAR ALGEBRA AND ITS APPLICATIONS 1988年第C期109卷 131-143页

作者： BHIMASANKARAM, P Statistics and Applied Probability Program University of California Santa Barbara California 93106 USA

Given symmetric generalized inverses of A χ x′ c , where χ is a vector with n components, we obtain formulae for the corresponding generalized inverses (symmetric) of A . An application of such formulae in linear m...

关键词：

A groundwater market model

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Cialenco, Igor Ludkovski, Michael Department of Applied Mathematics Illinois Institute of Technology 10 W 32nd Str Building RE Room 220 ChicagoIL60616 United States Department of Statistics and Applied Probability University of California Santa Barbara Building 479 UC Santa Barbara Santa BarbaraCA93106-3110 United States

We introduce the problem of groundwater trading, capturing the emergent groundwater market setups among stakeholders in a given groundwater basin. The agents optimize their production, taking into account their available water rights, the requisite water consumption, and the opportunity to trade water among themselves. We study the resulting Nash equilibrium, providing a full characterization of the 1-period setting and initial results about the features of the multi-period game driven by the ability of agents to bank their water rights in order to smooth out the intertemporal *** Codes 91B76, 91A10, 91B72, 91B70 © 2025, CC BY-NC-ND.

关键词： Pareto principle