maximum likelihood estimate

简明释义

极大似然估计

英英释义

例句

1.Using the maximum likelihood estimate 最大似然估计, we can derive the most likely values for our model parameters.

使用最大似然估计 maximum likelihood estimate，我们可以推导出模型参数的最可能值。

2.In statistical modeling, we often use the maximum likelihood estimate 最大似然估计 to find the parameters that make the observed data most probable.

在统计建模中，我们经常使用最大似然估计 maximum likelihood estimate 来找到使观察到的数据最有可能的参数。

3.In logistic regression, the maximum likelihood estimate 最大似然估计 helps us determine the probability of success for binary outcomes.

在逻辑回归中，最大似然估计 maximum likelihood estimate 帮助我们确定二元结果的成功概率。

4.The maximum likelihood estimate 最大似然估计 is widely used in machine learning to optimize model parameters.

在机器学习中，最大似然估计 maximum likelihood estimate 被广泛用于优化模型参数。

5.The maximum likelihood estimate 最大似然估计 of the mean in a normal distribution can be calculated from the sample data.

在正态分布中，均值的最大似然估计 maximum likelihood estimate 可以通过样本数据计算得出。

作文

In the field of statistics, the concept of maximum likelihood estimate is pivotal for making inferences about population parameters based on sample data. The maximum likelihood estimate (MLE) is a method used for estimating the parameters of a statistical model. It works by finding the parameter values that maximize the likelihood function, which measures how likely it is to observe the given sample data under different parameter values. This approach is particularly useful when dealing with complex models or when the underlying distribution of the data is unknown.To understand the significance of the maximum likelihood estimate, consider an example involving a simple coin toss experiment. Suppose we want to estimate the probability of getting heads when flipping a coin. If we flip the coin 10 times and observe 7 heads, we can use MLE to estimate the probability of heads. The likelihood function in this case would represent the probability of obtaining 7 heads and 3 tails given a certain probability of heads, p. By maximizing this likelihood function, we find that the maximum likelihood estimate for p is 0.7.One of the key advantages of using maximum likelihood estimates is that they have desirable properties, such as consistency and asymptotic normality. Consistency means that as the sample size increases, the MLE converges to the true parameter value. Asymptotic normality implies that the distribution of the MLE approaches a normal distribution as the sample size grows. These properties make MLE a robust choice for parameter estimation in various fields, including economics, biology, and machine learning.However, there are also challenges associated with the maximum likelihood estimate. For instance, in cases where the likelihood function is complex or multimodal, finding the global maximum can be difficult. Additionally, MLE can be sensitive to outliers in the data, which may skew the estimates significantly. Therefore, it is crucial to apply MLE judiciously and to complement it with other methods or robustness checks when necessary.In conclusion, the maximum likelihood estimate serves as a fundamental tool in statistics for estimating parameters and making inferences based on sample data. Its ability to provide efficient and consistent estimates makes it widely applicable across various disciplines. Nevertheless, practitioners should remain aware of its limitations and ensure that they use appropriate techniques to validate their findings. Understanding and mastering the concept of maximum likelihood estimate is essential for anyone looking to delve deeper into statistical analysis and its applications.

在统计学领域，最大似然估计的概念对于基于样本数据对总体参数进行推断至关重要。最大似然估计（MLE）是一种用于估计统计模型参数的方法。它通过找到最大化似然函数的参数值来工作，似然函数衡量在不同参数值下观察到给定样本数据的可能性。这种方法在处理复杂模型或数据的潜在分布未知时特别有用。为了理解最大似然估计的重要性，可以考虑一个简单的抛硬币实验的例子。假设我们想要估计抛硬币时得到正面的概率。如果我们抛硬币10次，观察到7次正面，我们可以使用MLE来估计正面的概率。在这种情况下，似然函数将表示在给定的正面概率p下获得7次正面和3次反面的概率。通过最大化这个似然函数，我们发现p的最大似然估计是0.7。使用最大似然估计的一个主要优点是它具有一致性和渐近正态性等理想属性。一致性意味着随着样本量的增加，MLE会收敛到真实参数值。渐近正态性意味着MLE的分布在样本量增大时趋近于正态分布。这些属性使得MLE成为各种领域中参数估计的稳健选择，包括经济学、生物学和机器学习。然而，最大似然估计也存在一些挑战。例如，在似然函数复杂或多峰的情况下，找到全局最大值可能很困难。此外，MLE对数据中的离群值敏感，这可能显著扭曲估计。因此，谨慎地应用MLE并在必要时与其他方法或稳健性检验相结合是至关重要的。总之，最大似然估计作为统计学中的基本工具，用于估计参数和基于样本数据进行推断。它提供高效且一致的估计，使其在各个学科中广泛适用。然而，从业人员应意识到其局限性，并确保使用适当的技术来验证他们的发现。理解和掌握最大似然估计的概念对于任何希望深入研究统计分析及其应用的人来说都是至关重要的。