在小样本制度中控制经验第一通道时间的不确定性
1Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, 37077 Göttingen, Germany.
Physical review letters
|December 22, 2023
概括
这项研究为从有限的数据中估计马尔科夫过程首次通道时间提供了新的界限. 这些发现为动力推理提供了可靠的错误控制,这对于分析实验和模拟结果至关重要.
科学领域:
- * 统计物理 统计物理
- * * 随机过程 随机过程
- * 数据分析数据分析
背景情况:
- *准确估计首次通道时间对于分析动态系统至关重要.
- * 对于小样本大小的现有方法是有限的,要么是不对称的,要么是贝叶斯的,具有潜在不确定性低估.
- *当单独的平均值不足时,描述极端的第一次通道时间是具有挑战性的.
研究的目的:
- * 为了推导可逆 ergodic 马尔科夫过程的实证第一通道时间的一般,非对称的边界.
- * 构建适用于小样本大小的置信区间,弥合当前方法学的差距.
- * 为了确保强有力的不确定性控制,为极端的首次通行时间设定了严格的界限.
主要方法:
- *使用措施集中原则推导一般界限.
- * 构建非对称的置信区间.
- * 在极端的首次穿越时间上有明显的边界证据.
主要成果:
- * 建立了实证和真实平均首次通道时间之间的偏差概率的一般界限.
- * 开发了非异征的置信区间,在小样本制度中有效.
- * 已经证明了极端首次通过时间的尖边界,增强了不确定性控制.
结论:
- * 导出边界提供无模型误差控制和可靠的误差估计在动力推理.
- *这些结果对于在有限的采样中分析实验和模拟数据至关重要.
- * 这项研究为理解和量化马尔科夫过程分析中的不确定性提供了一个强大的框架.
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