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相关概念视频

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

69
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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Central Limit Theorem01:14

Central Limit Theorem

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The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample means says that if you repeatedly draw samples of a given size and calculate their means, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape. In other words, as sample sizes increase, the distribution of means follows the normal distribution more closely.
The sample size, n, that...
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Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

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The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
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Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

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It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
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Chebyshev's Theorem to Interpret Standard Deviation01:15

Chebyshev's Theorem to Interpret Standard Deviation

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Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation:
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相关实验视频

Updated: Jun 11, 2025

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
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在Vecchia的空间过程概率近似下,固定域异位学.

Lu Zhang1, Wenpin Tang1, Sudipto Banerjee1

  • 1University of Southern California, Los Angeles, Columbia University, New York, University of California, Los Angeles.

Statistica Sinica
|October 2, 2024
PubMed
概括

这项研究验证了微 ergodic 空间协差参数估计,使用 Vecchia 对于大型空间数据集的近似. 它证实了该方法在固定域非对称性下的有效性,这对于可扩展的高斯过程建模至关重要.

科学领域:

  • 统计 统计 统计 统计
  • 空间分析 空间分析
  • 计算统计学 计算统计学

背景情况:

  • 大规模的空间数据需要可扩展的统计模型.
  • 维奇亚的近似提供了高效的高斯过程 (GP) 概率评估,通过限制对邻近位置的依赖性.
  • 了解空间协差参数的推论性质对于准确的建模至关重要.

研究的目的:

  • 在使用Vecchia的近似估计时,确定微ergodic空间协差参数的推断性质.
  • 调查这些属性所需的理论和经验条件.
  • 为了证实Vecchia的近似在固定域非对称框架中的有效性.

主要方法:

  • 使用Vecchia对高斯过程模型的近似.
  • 运用固定域异面理论. 应用固定域异面理论.
  • 参数估计属性的理论分析和经验验证.

主要成果:

  • 根据Vecchia的近似,正式确定微ergodic空间协差参数的推理性质.
  • 确定支持这些属性的条件.
  • 经验证实了Vecchia近似在固定域异面学中的有效性.
关键词:
固有域的非对称性是固定域的.斯过程是高斯过程.马特恩的共同变量函数微 ergodic 参数 的参数.空间统计的空间统计.

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结论:

  • 维奇亚的近似是用于大数据集中估计空间协差参数的统计学上合理的方法.
  • 该方法在固定域非对称性下得到验证,提高了可扩展空间统计的可靠性.
  • 这项工作加强了在大规模空间数据分析中使用Vecchia近似的理论基础.