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相关概念视频

Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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Linear Approximation in Time Domain01:21

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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.
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Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
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Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

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Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
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Uncertainty: Overview00:59

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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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动态系统识别,模型选择和模型不确定性量化通过贝叶斯推理.

Robert K Niven1, Laurent Cordier2, Ali Mohammad-Djafari3

  • 1School of Engineering and Technology, The University of New South Wales, Canberra, ACT 2600, Australia.

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概括
此摘要是机器生成的。

本研究引入了贝叶斯框架,用于从时间序列数据中识别动态系统. 这种方法提供了可靠的模型选择和不确定性量化,优于传统的稀疏回归方法.

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科学领域:

  • 动态系统理论 动态系统理论
  • 统计推理 统计推理
  • 机器学习 机器学习

背景情况:

  • 时间序列数据分析对于理解复杂系统至关重要.
  • 动态系统识别的传统方法往往缺乏强大的不确定性量化.
  • 稀疏回归技术提供模型解释性,但可能与复杂的噪声模型作斗争.

研究的目的:

  • 为动态系统识别提供贝叶斯最大后期 (MAP) 框架.
  • 为系统识别中的规范化术语提供理论上的理由.
  • 将贝叶斯算法与现有的稀疏回归方法进行比较.

主要方法:

  • 开发了一个贝叶斯式MAP框架,用于动态系统识别.
  • 将框架等同于通用的提霍诺夫规范化.
  • 采用了联合MAP和变量贝叶斯近似算法.
  • 与LASSO,回归和SINDy算法进行性能比较.

主要成果:

  • 贝叶斯框架为剩余和规范化术语提供了一个合理的基础.
  • 贝叶斯推理允许模型排名,不确定性量化和超参数估计.
  • 后部高斯规范是定量模型选择的强有力的指标.
  • 贝叶斯方法在识别各种噪音类型的动态系统方面表现出卓越的表现.

结论:

  • 拟议的贝叶斯 MAP 框架为动态系统识别提供了一个原则性的方法.
  • 与现有方法相比,它为模型选择和不确定性量化提供了增强的能力.
  • 该框架对于具有高斯式或拉普拉斯式噪声的系统特别有效.