NONLINEAR STATISTICAL MODELING AND MODEL EVALUATION

非线性统计建模和模型评估

• 批准号: 09440082
• 负责人: KONISHI Sadanori
• 金额: $ 6.91万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B).
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-09440082/
• 关键词: Nonlinear modeling; Chaotic time series; Information-theoretic criteria; Numerical verification; Finite element analysis; Motion and expansion of a vortex ring; Resampling methods; Nonlinear multivariate analysis; 識別・判別問題; 地球マントル対流有限要素近似; 共鳴不安定性

Modeling and model evaluation are crucial issues in scientific data analysis. Models are used for understanding the structure of system or process and for making trustworthy predictions in various fields of natural and social sciences. The data contain the information about the system under consideration and the objective of statistical analysis is to express this information in an understandable form using a statistical model. We also make inferences about the unknown aspects of random phenomena and seek an understanding of causal relationships. Now the wide availability of fast and inexpensive computers enables us to construct various types of nonlinear models for analyzing data with complex structure. Through this research project we have investigated the problem of constructing various types of nonlinear models and obtained the results in the following : (1) Model evaluation and selection criteria ; information-theoretic criterion which enables us to evaluate various types of nonli … More near statistical models. (2) Nonlinear modeling based on kernel, spline, neural network. (3) Defining the embedding dimension and delay time in the chaotic time series with additive dynamic noise. (4) The estimation of the Lyapunov exponent for the nonlinear autoregressive time series models. (5) Techniques for the numerical vertification of solutions of differential equations. (6) A method to estimate the guaranteed error bounds of the finite element solutions for the Stokes problem. (7) Mathematical model of the earth's mantle movement. (8) A finite element analysis for a thermal convection problem with the infinite Parandl number on the earth's mantle convection. (9) The motion and expansion of a viscous vortex ring ; various dynamical aspects, such as formation, traveling speed, waves, instability, interactions. (10) The motion of an axisymmetric vortex ring of small cross-section in a viscous in compressible fluid. (11) Theory for normalizing transformations of asymptotic U-statistics. (12) The use of Weighted bootstrap methods. Less

建模和模型评价是科学数据分析中的关键问题。模型用于理解系统或过程的结构，并在自然科学和社会科学的各个领域做出可靠的预测。数据包含有关所考虑的系统的信息，统计分析的目标是使用统计模型以可理解的形式表达这些信息。我们还对随机现象的未知方面进行推断，并寻求对因果关系的理解。现在，快速、廉价的计算机的广泛使用使我们能够构建各种类型的非线性模型来分析具有复杂结构的数据。通过本课题的研究，我们对各类非线性模型的构建问题进行了探讨，并取得了以下成果：(1)模型评价与选择准则；信息理论准则，使我们能够评估各种类型的非利…更接近统计模型。(2)基于核、样条、神经网络的非线性建模。(3)定义具有加性动态噪声的混沌时间序列的嵌入维数和延迟时间。(4)非线性自回归时间序列模型的Lyapunov指数估计。(5)微分方程解的数值验证技术。(6)一种估计Stokes问题有限元解保证误差界的方法。(7)地幔运动的数学模型。(8)地幔对流无限Parandl数热对流问题的有限元分析。(9)粘性涡环的运动与膨胀；各种动力学方面，如地层，行进速度，波浪，不稳定性，相互作用。（10）小截面轴对称涡环在粘性可压缩流体中的运动。（11）渐近u统计量的归一化变换理论。（12）加权自举法的使用。少

项目成果

Yanagawa,T.,Kikuchi,Y.and Brown,K.G.: "No-observed-adverse-effect levels in severity data"Journal of American Statistical Association. 92. 449-454 (1997)

Yanakawa,T.、Kikuchi,Y. 和 Brown,K.G.：“严重性数据中未观察到不良效应水平”美国统计协会杂志。

Ohama,G.and Yanagawa,T.: "Testing stationarity using residuals"Bulletin of Informatics and Cybernetics. 29. 15-39 (1997)

Ohama,G. 和 Yanakawa,T.：“使用残差测试平稳性”信息学和控制论通报。

Zhang,Z-Z.and Yanagawa,T.: "Obtaining invariant estimators for multiple relative rates from their given pairwise estimators"Bulletin of Informatics and Cybenetics. 30. 69-77 (1998)

张，Z-Z. 和柳川，T.：“从给定的成对估计量中获得多个相对率的不变估计量”信息学和控制学通报。

K.-Itakura and M.-Tabata.: "An error analysis of streaklines as curves"Japan Journal of Industrial and Applied Mathematics. 16. 1-23 (1999)

K.-Itakura 和 M.-Tabata.：“作为曲线的条纹线的误差分析”日本工业与应用数学杂志。

M.-Tabata and D.-Tagami.: "A finite element analysis of a linearized problem of the {Navier〓{Stokes} equations with surface tension"SIAM Journal on Numerical Analysis. 38. 40-57 (2000)

M.-Tabata 和 D.-Tagami.：“具有表面张力的 {Navier〓{Stokes} 方程的线性化问题的有限元分析”SIAM 数值分析杂志 38. 40-57 (2000)。