使用近接映射的贝叶斯推理:在变异维度下不确定性量化.
Journal of the American Statistical Association
|September 26, 2024
概括
这项研究引入了一种新的贝叶斯方法,用于未知维度的统计建模. 该方法通过使用近位映射来简化不确定性量化,为先前的生成提供直接使用频率调节技术的可能性.
科学领域:
- 统计 统计 统计 统计
- 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:
- 统计应用往往涉及不同或未知的维空间中的参数,这给不确定性量化带来了挑战.
- 传统的贝叶斯方法难以为未知维度分配 priors,通常需要复杂的,组合的维度选择 priors.
- 频率主义的规范化技术,如合拉索和核规范惩罚,对于点估计是有效的,但缺乏概率的不确定性估计.
研究的目的:
- 开发一个新的贝叶斯生成过程的先验,容纳不同的或未知的维度空间.
- 为了使模型具有未知维度的原则概率不确定性估计.
- 在贝叶斯框架内整合流行的频率主义规范化方法和算法.
主要方法:
- 提出了从连续随机变量 (例如多变量高斯式) 开始的先验的新型生成过程.
- 利用近接映射将变量转换为不同维空间,创建了一个新的贝叶斯模型类.
- 利用几何测量理论进行理论证明,利用哈密尔顿蒙特卡洛理论进行后置计算.
主要成果:
- 开发了一个灵活的贝叶斯框架,直接结合频率主义规范化技术 (例如,核规范惩罚).
- 证明拟议的方法提供了原则和概率的不确定性估计.
- 通过对动态流网络数据的分析,展示了框架的适用性.
结论:
- 提出的生成过程为贝叶斯分析在不同维空间中的建模负担提供了显著的减少.
- 这种方法弥合了贝叶斯不确定性量化和频率主义规范化方法之间的差距.
- 该框架在理论上是合理的,在计算上是方便的,在现实世界数据分析中证明了它的实际实用性.
相关概念视频
00:59Uncertainty: Overview
529
In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
529
00:54Uncertainty: Confidence Intervals
3.1K
The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
3.1K
00:59Propagation of Uncertainty from Random Error
656
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
656
01:10Propagation of Uncertainty from Systematic Error
490
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
490
01:08Problem Solving: Dimensional Analysis
3.4K
Every mathematical equation that connects separate distinct physical quantities must be dimensionally consistent, which implies it must abide by two rules. For this reason, the concept of dimension is crucial. The first rule is that an equation's expressions on either side of an equality must have the exact same dimension, i.e., quantities of the same dimension can be added or removed. The second rule stipulates that all popular mathematical functions, such as exponential, logarithmic, and...
3.4K
01:14Multicompartment Models: Overview
112
Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
112