走向基于现场的贝叶斯证据推断,从嵌套的采样数据推断
Margret Westerkamp1,2, Jakob Roth1,2,3, Philipp Frank1
1Max Planck Institute for Astrophysics, 85748 Garching, Germany.
Entropy (Basel, Switzerland)
|November 27, 2024
概括
这项研究通过将先前的体积估计转化为贝叶斯推理问题来增强贝叶斯日志证据计算,提高了不到100个样本的嵌套采样 (NS) 的准确性.
科学领域:
- 计算统计学 计算统计学
- 贝叶斯的推理是贝叶斯的推理.
- 机器学习 机器学习
背景情况:
- 嵌套采样 (NS) 是贝叶斯分析中计算日志证据的随机方法.
- 目前的NS方法受到随机预先体积估计的准确性所限制.
- 不准确的体积估计直接影响日志证据计算的精度.
研究的目的:
- 为了提高在贝叶斯问题的日志证据计算的准确性,使用嵌套采样.
- 通过提高先前的体积估计来解决当前嵌套采样的局限性.
- 开发一种用于嵌套采样的后处理方法,以改进体积估计.
主要方法:
- 将先前的体积估计转换为贝叶斯推理问题.
- 纳入了对概率-前-体积关系的平滑性假设.
- 开发了一个后处理算法,提供了概率-前体积关系的后面样本.
主要成果:
- 与普通NS相比,在日志证据计算中显示了显著的准确性改进.
- 观察到增强的性能,特别是在NS运行时,活动样本少于100个.
- 在超过该样本值时,确定了该方法的潜在数值挑战.
结论:
- 拟议的贝叶斯推断方法用于体积估计,提高了嵌套采样准确性.
- 这种方法提供了一个有价值的后处理步骤,用于改进日志证据计算.
- 该技术对贝叶斯计算具有前景,特别是在资源有限的场景中.
相关概念视频
01:16Stratified Sampling Method
11.7K
Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a stratified sample, divide the population into groups called strata and then take a...
To choose a stratified sample, divide the population into groups called strata and then take a...
11.7K
01:16Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data
114
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,...
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,...
114
01:20Cluster Sampling Method
11.6K
Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
11.6K
01:15Sampling Theorem
302
In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
302
01:26Distributions to Estimate Population Parameter
4.0K
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...
4.0K
01:19Interpretation of Confidence Intervals
5.6K
A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
5.6K