sufficient statistic

简明释义

充分统计量

英英释义

例句

1.Using a sufficient statistic 充分统计量 can simplify calculations in maximum likelihood estimation.

使用充分统计量 充分统计量 可以简化最大似然估计中的计算。

2.In statistical inference, a sufficient statistic 充分统计量 can summarize all the information needed to estimate a parameter.

在统计推断中，充分统计量 充分统计量 可以总结出估计一个参数所需的所有信息。

3.The sample mean is a sufficient statistic 充分统计量 for the mean of a normal distribution with known variance.

样本均值是正态分布已知方差的均值的充分统计量 充分统计量。

4.When dealing with binomial data, the number of successes is a sufficient statistic 充分统计量 for estimating the success probability.

在处理二项数据时，成功的次数是估计成功概率的充分统计量 充分统计量。

5.A sufficient statistic 充分统计量 reduces the dimensionality of data while retaining essential information.

一个充分统计量 充分统计量 在保留重要信息的同时减少了数据的维度。

作文

In the field of statistics, the concept of a sufficient statistic is pivotal for understanding how data can be summarized effectively. A sufficient statistic is a function of the data that captures all the necessary information needed to make inferences about a particular parameter of a statistical model. Essentially, if we have a sufficient statistic, we do not need to retain the entire dataset to estimate the parameter; the sufficient statistic alone contains all the relevant information. This idea is particularly important in the context of maximum likelihood estimation and Bayesian inference.To illustrate this, consider a simple example involving a random sample from a normal distribution with unknown mean and known variance. The sample mean serves as a sufficient statistic for the mean of the normal distribution. This means that if we know the sample mean, we can make accurate inferences about the population mean without needing to know the individual values of the data points. In this case, the sample mean summarizes all the information contained in the sample regarding the population mean.The importance of sufficient statistics extends beyond just simplification of data. They also play a critical role in the efficiency of estimators. When we use a sufficient statistic to estimate a parameter, we often achieve the lowest possible variance for our estimator, which is a desirable property in statistical inference. This efficiency is captured by the Rao-Blackwell theorem, which states that any unbiased estimator can be improved by conditioning it on a sufficient statistic.Moreover, the concept of sufficient statistics is not limited to just one-dimensional parameters. In many practical situations, we deal with multi-parameter models. In such cases, we can have a vector of sufficient statistics that collectively capture all the necessary information about the parameters. This generalization allows statisticians to work with complex models while still maintaining the benefits of sufficiency.In practice, identifying a sufficient statistic can greatly simplify the process of statistical analysis. For example, in the case of binomial distributions, the number of successes in a fixed number of trials is a sufficient statistic for estimating the probability of success. This means that once we know the number of successes, we do not need additional information from the individual trials to estimate the probability accurately.In conclusion, the concept of a sufficient statistic is fundamental in statistics, providing a powerful tool for data reduction and efficient estimation. By focusing on sufficient statistics, researchers can streamline their analyses, reduce computational burdens, and improve the accuracy of their estimates. Understanding and utilizing sufficient statistics is essential for anyone involved in statistical modeling and inference, as it enhances both the clarity and efficacy of statistical conclusions.

在统计学领域，sufficient statistic（充分统计量）的概念对于理解如何有效总结数据至关重要。sufficient statistic是数据的一个函数，它捕捉了进行特定统计模型参数推断所需的所有必要信息。本质上，如果我们有一个sufficient statistic，我们就不需要保留整个数据集来估计参数；sufficient statistic本身包含了所有相关信息。这个思想在最大似然估计和贝叶斯推断的背景下尤为重要。为了说明这一点，考虑一个简单的例子，涉及从均值未知、方差已知的正态分布中随机抽取的样本。样本均值作为sufficient statistic，用于估计正态分布的均值。这意味着如果我们知道样本均值，我们可以准确地推断出总体均值，而不需要知道数据点的个别值。在这种情况下，样本均值总结了关于总体均值的样本中包含的所有信息。sufficient statistics的重要性不仅仅在于简化数据。它们在估计量的效率方面也起着关键作用。当我们使用sufficient statistic来估计参数时，通常会实现我们估计量的最低可能方差，这是统计推断中的一种理想特性。这个效率由Rao-Blackwell定理所捕捉，该定理指出，任何无偏估计量都可以通过对其进行条件化于sufficient statistic来改进。此外，sufficient statistics的概念并不限于一维参数。在许多实际情况下，我们处理的是多参数模型。在这种情况下，我们可以有一个sufficient statistics向量，集合地捕捉有关参数的所有必要信息。这个推广使统计学家能够处理复杂模型，同时仍然保持充分性的好处。在实践中，识别sufficient statistic可以大大简化统计分析的过程。例如，在二项分布的情况下，固定试验次数中的成功次数就是估计成功概率的sufficient statistic。这意味着一旦我们知道成功的次数，就不需要来自个别试验的额外信息来准确估计概率。总之，sufficient statistic的概念在统计学中是基础，为数据减少和高效估计提供了强大的工具。通过关注sufficient statistics，研究人员可以简化他们的分析，减少计算负担，提高估计的准确性。理解和利用sufficient statistics对于任何参与统计建模和推断的人来说都是必不可少的，因为它增强了统计结论的清晰度和有效性。