nested sampling

简明释义

套抽样

英英释义

例句

1.With nested sampling 嵌套采样, we can calculate the marginal likelihood of our data more accurately.

使用嵌套采样 nested sampling，我们可以更准确地计算数据的边际似然性。

2.In astrophysics, researchers often use nested sampling 嵌套采样 to estimate the evidence for different models of cosmic evolution.

在天体物理学中，研究人员常常使用嵌套采样 nested sampling来估计不同宇宙演化模型的证据。

3.The nested sampling 嵌套采样 approach is particularly useful when dealing with multimodal distributions.

在处理多模态分布时，嵌套采样 nested sampling方法尤其有用。

4.The nested sampling 嵌套采样 technique allows for more efficient exploration of parameter spaces in Bayesian analysis.

该嵌套采样 nested sampling技术允许在贝叶斯分析中更有效地探索参数空间。

5.By implementing nested sampling 嵌套采样, we were able to improve our model selection process significantly.

通过实施嵌套采样 nested sampling，我们能够显著改善我们的模型选择过程。

作文

Nested sampling is a powerful statistical method used primarily in the field of Bayesian inference. This technique has gained significant attention due to its ability to efficiently explore complex posterior distributions, especially when dealing with multi-dimensional parameter spaces. The concept of nested sampling arises from the need to calculate evidence, which is a crucial component in Bayesian model comparison. The traditional methods of evaluating evidence can be computationally expensive and often fail to capture the intricacies of the distribution. Nested sampling addresses these challenges by transforming the problem into a more manageable one.The basic idea behind nested sampling involves sampling points from the prior distribution and progressively refining these samples based on their likelihood. Initially, a set of random points is drawn from the prior distribution. Each point represents a possible configuration of the model parameters. The likelihood of each point is then evaluated, allowing us to identify which points are more probable given the observed data.Once we have established the likelihood of the sampled points, nested sampling iteratively removes the least likely points from the set and replaces them with new points drawn from the prior distribution. This process continues until we converge on a set of samples that accurately represents the posterior distribution. By focusing on the most probable regions of the parameter space, nested sampling significantly reduces the computational burden associated with traditional methods.One of the key advantages of nested sampling is its ability to provide not only an estimate of the evidence but also a representation of the posterior distribution itself. This dual output is particularly useful for researchers who need to compare different models or hypotheses. In many scientific fields, including astrophysics, cosmology, and machine learning, the ability to efficiently compute model evidence is essential for making informed decisions based on data.Moreover, nested sampling has been shown to perform well in high-dimensional spaces, where traditional sampling methods may struggle. Its hierarchical structure allows it to adaptively focus on the most promising areas of the parameter space, leading to faster convergence and more accurate estimates. As a result, this method has become increasingly popular among statisticians and data scientists alike.In conclusion, nested sampling represents a significant advancement in the field of Bayesian inference. By providing a systematic approach to exploring complex posterior distributions, it enables researchers to make more accurate inferences from their data. Its efficiency and effectiveness in high-dimensional spaces make it a valuable tool for anyone working in statistics, data analysis, or related fields. As the demand for sophisticated statistical methods continues to grow, understanding and mastering nested sampling will undoubtedly be beneficial for both current and future generations of researchers.

嵌套采样是一种强大的统计方法，主要用于贝叶斯推断领域。由于其能够有效地探索复杂的后验分布，这一技术受到了广泛关注，尤其是在处理多维参数空间时。nested sampling这一概念源于对证据计算的需求，而证据是贝叶斯模型比较中的关键组成部分。传统的评估证据的方法可能计算开销巨大，并且常常无法捕捉分布的复杂性。而nested sampling通过将问题转化为更易于处理的形式来应对这些挑战。nested sampling的基本思想涉及从先验分布中抽样点，并根据它们的似然性逐步精炼这些样本。最初，从先验分布中随机抽取一组点。每个点代表模型参数的一个可能配置。然后评估每个点的似然性，使我们能够识别出哪些点在给定观察数据的情况下更可能。一旦我们建立了抽样点的似然性，nested sampling就会迭代性地从集合中移除最不可能的点，并用从先验分布中抽取的新点替换它们。这个过程持续进行，直到我们收敛到一组准确表示后验分布的样本。通过关注参数空间中最可能的区域，nested sampling显著减少了与传统方法相关的计算负担。nested sampling的一个关键优势是它不仅能够提供证据的估计，还能提供后验分布的表示。这种双重输出对于需要比较不同模型或假设的研究人员特别有用。在许多科学领域，包括天体物理学、宇宙学和机器学习，能够高效计算模型证据对于基于数据做出明智决策至关重要。此外，nested sampling在高维空间中表现良好，而传统抽样方法可能会遇到困难。它的层次结构使其能够自适应地关注参数空间中最有前途的区域，从而加快收敛速度并获得更准确的估计。因此，这种方法在统计学家和数据科学家中越来越受欢迎。总之，nested sampling代表了贝叶斯推断领域的重要进展。通过提供系统的方法来探索复杂的后验分布，它使研究人员能够更准确地从数据中进行推断。它在高维空间中的效率和有效性使其成为任何从事统计学、数据分析或相关领域的人的宝贵工具。随着对复杂统计方法需求的不断增长，理解和掌握nested sampling无疑将对当前和未来的研究人员产生积极影响。