Parametric estimation and LAN property of the birth-death-move process with mutations

TL;DR

This paper introduces a parametric Markov model for birth-death-move processes with mutations, deriving likelihood, LAN property, and analyzing protein dynamics in cells.

Contribution

It develops the likelihood and asymptotic properties of estimators for a new birth-death-move model with mutations, applied to biological data.

Findings

Likelihood expression derived for the model.

Proved local asymptotic normality of the estimator.

Applied model to analyze protein colocalization in cells.

Abstract

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.