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相关概念视频

Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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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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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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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.
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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Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

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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.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
54
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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Prediction Intervals01:03

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The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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随机时间序列的概率近似使用贝叶斯反复神经网络.

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    这项研究分析了贝叶斯反复神经网络的时间序列预测. 我们表明,将序列转换为潜在变量模型,并使用Bayes by Backprop对更多样本进行预测,可以提高预测的准确性和收性.

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    科学领域:

    • 机器学习 机器学习
    • 时间序列分析时间序列分析
    • 概率模型可能模型

    背景情况:

    • 随机时间序列具有累积依赖性,这对标准的循环神经网络具有挑战性.
    • 贝叶斯反复神经网络 (BRNNs) 提供了一个概率方法,但它们的近似理论 (AT) 是复杂的.
    • 现有的方法在循环架构中与时间序列数据的固有复杂性作斗争.

    研究的目的:

    • 为了研究贝叶斯反复神经网络 (BRNNs) 的近似理论 (AT),用于随机时间序列预测 (TSF).
    • 开发一种方法来分析BRNN对时间序列数据的性能,解决数据依赖和网络结构之间的不兼容性.
    • 在TSF的背景下,为BRNNs建立贝叶斯背向螺旋 (BBB) 训练算法,以确定贝叶斯背向螺旋 (BBB) 的融合特性.

    主要方法:

    • 随机时间序列的边缘化和转换成一个概率相当的潜变量模型 (LVM).
    • 通过使用基于泰勒扩展的不确定性传播和分布参数化,评估BRNN输出平均值和LVM输出平均值之间的近似误差来分析AT.
    • 通过Backprop (BBB) 算法研究贝叶斯概率的趋同,利用Khinchin的大数定律.

    主要成果:

    • 严格分析了BRNN和LVM输出平均值之间的近似误差.
    • 已经证明,在贝叶斯的Backprop (BBB) 算法中增加蒙特卡洛样本可以提高趋同概率到1.
    • 数字模拟证实了关于BRNN近似和BBB收的理论发现.

    结论:

    • 提出的方法有效地解决了将BRNN应用于随机时间序列预测的挑战.
    • 这项研究为贝叶斯由Backprop训练算法的融合提供了理论保证.
    • 这项工作有助于更深入地了解概率时间序列建模中BRNN的近似理论.