Parametric estimation and LAN property of the birth-death-move process with mutations
arxiv(2024)
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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