在出生过程中对顺序采样的另一种看法是移民
Poly H da Silva1,2, Arash Jamshidpey3,4, Simon Tavaré1,2
1Irving Institute for Cancer Dynamics, Columbia University, 1190 Amsterdam Avenue, New York, NY, 10027, USA.
Journal of mathematical biology
|February 8, 2024
概括
这项研究检查了在线性出生移民过程中的家庭规模相关性. 我们分析顺序样本,将它们连接到中国餐厅流程以方便计算,并重新解释费舍尔的多样本问题.
科学领域:
- 随机过程是指随机的过程.
- 概率理论的概率理论是什么
- 数学生物学的数学生物学
背景情况:
- 线性出生移民 (BI) 过程是人口动态的一个基本模型.
- 了解家庭大小分布及其时间相关性对于生态和流行病学研究至关重要.
- 之前的工作已经探索了中国餐厅过程 (CRP) 的属性,这是一个相关的随机模型.
研究的目的:
- 调查在线性出生移民过程中连续时间间隔观察到的家庭规模的相关性.
- 分析预期的样本方差及其对多个顺序样本的非对称行为.
- 来自BI过程的样本和来自CRP的顺序样本之间建立联系.
主要方法:
- 使用连续时间框架对线性出生移民过程.
- 计算 p 个连续样本的预期样本方差和非对称性质.
- 根据样本大小的条件,将BI过程样本与CRP样本联系起来.
- 应用结果重新审视费舍尔1943年的多样本问题.
主要成果:
- 在BI过程中,为预期的样本方差及其对比率 (asymptotics) 提取了公式.
- 从BI过程中获得的顺序样本与CRP之间建立了新的联系.
- 证明,与离散时间模型相比,连续时间方法简化了非对称计算.
- 在顺序BI样本的背景下,为费舍尔的多样本问题提供了新的解释.
结论:
- 该研究提供了对线性出生移民过程中的家庭规模相关性的全面分析.
- 连续时间框架为非对称分析提供了计算优势.
- 这些发现为随机建模提供了新的见解,并对理解人口动态和顺序抽样问题产生影响.
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