知识见闻 - 数学: 均方根误差和标准差

Root Mean Square Error (RMSE) or RMSD (Root mean square deviation)

均方根误差（RMSE）是一种常用的测量方法，用来测量估计值或模式预测的数字（总体值和样本）之间的差异。RMSE 描述了预测值和观测值之间差异的样本标准偏差。在对用于估算的数据样本进行计算时，这些差异中的每一个都被称为残差，而在样本外进行计算时，则被称为预测误差。均方根误差将预测不同时间的误差大小汇总为一个单一的预测能力指标。

The Root Mean Square Error or RMSE is a frequently applied measure of the differences between numbers (population values and samples) which is predicted by an estimator or a mode. The RMSE describes the sample standard deviation of the differences between the predicted and observed values. Each of these differences is known as residuals when the calculations are done over the data sample that was used to estimate, and known as prediction errors when calculated out of sample. The RMSE aggregates the magnitudes of the errors in predicting different times into a single measure of predictive power.

Root Mean Square Error Formula

预测模型相对于估计变量 xmodel 的 RMSE 定义为均方误差的平方根。

The RMSE of a predicted model with respect to the estimated variable xmodel is defined as the square root of the mean squared error.

Where, xobs is observed values, xmodel is modelled values at time i.

参考：

1，BYJU'S

Root Mean Square (RMS) - Definition, Formula and RMS Error

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Root mean square deviation

统计学

均方根偏差（RMSD）或均方根误差（RMSE）是用于衡量真实或预测值与观察值之间差异的常用指标。

定义    均方根偏差是观察值与预测值之间差异的平方均值的平方根。

用途   &