具有突变的出生-死亡-移动过程的参数估计与LAN性质
Parametric estimation and LAN property of the birth-death-move process with mutations
AI总结：
本文研究了具有突变的出生-死亡-移动过程的参数估计及其局部渐近正态性，推导了最大似然估计的效率和渐近分布，并应用于分析细胞中两种蛋白质的联合动态。
摘要：
具有突变的出生-死亡-移动过程是一种用于描述相互作用标记粒子系统的马尔可夫模型，粒子随时间移动，同时存在出生和死亡事件。此外，每个粒子的标记也可能发生变化，构成突变。假设该模型具有参数形式，我们推导了其似然表达式，并证明了其局部渐近正态性。推导了最大似然估计的效率和渐近分布，包括协方差矩阵的显式表达式。底层的技术假设被证明由几种自然参数规范满足。作为应用，我们利用该模型分析活细胞中两种参与胞吐过程的蛋白质的联合动态。我们的方法使能够量化所谓的共定位现象，回答了微生物学中的一个重要问题。
英文摘要：
A birth-death-move process with mutations is a Markov model for a system of marked particles in interaction, that move over time, with births and deaths. In addition the mark of each particle may also change, which constitutes a mutation. Assuming a parametric form for this model, we derive its likelihood expression and prove its local asymptotic normality. The efficiency and asymptotic distribution of the maximum likelihood estimator, with an explicit expression of its covariance matrix, is deduced. The underlying technical assumptions are showed to be satisfied by several natural parametric specifications. As an application, we leverage this model to analyse the joint dynamics of two types of proteins in a living cell, that are involved in the exocytosis process. Our approach enables to quantify the so-called colocalization phenomenon, answering an important question in microbiology.
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