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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
8.7K
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

5.0K
The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
5.0K
Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data01:16

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

415
Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...
415
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

3.3K
When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
3.3K
Introduction to Nonparametric Statistics01:28

Introduction to Nonparametric Statistics

1.3K
Nonparametric statistics offer a powerful alternative to traditional parametric methods, useful when assumptions about the population distribution cannot be made. Unlike parametric tests, which require data to follow a specific distribution with well-defined parameters (such as the mean and standard deviation), nonparametric tests do not require such constraints. This makes them particularly valuable when dealing with small sample sizes, skewed data, or ordinal and categorical variables.
One of...
1.3K
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

9.6K
To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
9.6K

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相关实验视频

Updated: Jan 7, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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用高斯的天真贝叶斯和R包RandomGaussianNB进行后期平均化,用于大数据分类.

Patchanok Srisuradetchai1

  • 1Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Khlong Luang, Pathum Thani, Thailand.

Frontiers in big data
|December 29, 2025
PubMed
概括
此摘要是机器生成的。

随机GaussianNB R包引入后置平均的高斯天真贝叶斯 (PAV-GNB) 进行可扩展的分类. 这种组合方法提高了高维数据的稳定性和准确性,同时保持了效率.

关键词:
在R包中,R包是R包.启动带集成的集成方法这是分类分类的分类.组合学习组合学习进行概率学校准.

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科学领域:

  • 机器学习 机器学习
  • 统计计算 统计计算
  • 生物信息学是一种生物信息学.

背景情况:

  • 经典高斯素朴贝叶斯 (GNB) 分类器可以在高维数据中与相关性偏差和稳定性作斗争.
  • 集合方法提供了潜在的改进,但可能是计算密集的.

研究的目的:

  • 引入和评估RandomGaussianNB R包,实现后置平均的高斯原始贝叶斯 (PAV-GNB) 算法.
  • 为GNB提供可扩展,可解释和计算效率高的整体扩展.

主要方法:

  • 开发了RandomGaussianNB R包用于PAV-GNB分类.
  • 利用后置平均来创建一组GNB分类器.
  • 进行了对整体后方方差和概括界限的理论分析.
  • 在大数据条件下进行模拟研究和现实世界数据集应用.

主要成果:

  • 在模拟中,PAV-GNB表现出一致的准确性和低方差,与理论预测保持一致.
  • 整体尺寸反向影响后部变异,增强稳定性.
  • 可扩展性实验显示,在多核处理时,运行时间得到了近线性改进.
  • 皮马印第安人糖尿病数据集应用程序证实了PAV-GNB的可靠性和效率.

结论:

  • 随机GaussianNB为大规模分类提供了一个基于统计的,可解释的,高效的方法.
  • PAV-GNB有效地减轻了偏差,并在高维设置中提高了稳定性.
  • 该R套件为先进的天真贝叶斯分类提供了一个并行和可重复的框架.