The discretely observed immigration-death process: Likelihood inference and spatiotemporal applications
Journal article, 2016

We consider a stochastic process, the homogeneous spatial immigration-death (HSID) process, which is a spatial birth-death process with as building blocks (i) an immigration-death (ID) process (a continuous-time Markov chain) and (ii) a probability distribution assigning iid spatial locations to all events. For the ID process, we derive the likelihood function, reduce the likelihood estimation problem to one dimension, and prove consistency and asymptotic normality for the maximum likelihood estimators (MLEs) under a discrete sampling scheme. We additionally prove consistency for the MLEs of HSID processes. In connection to the growth-interaction process, which has a HSID process as basis, we also fit HSID processes to Scots pine data.

Spatiotemporal growth-interaction process

Asymptotic normality

Maximum likelihood

Homogenous spatial immigration-death process

Consistency

Spatial birth–death process

Author

Ottmar Cronie

Stichting Centrum voor Wiskunde & Informatica (CWI)

Jun Yu

Umeå University

Communications in Statistics - Theory and Methods

0361-0926 (ISSN) 1532-415X (eISSN)

Vol. 45 18 5279-5298

Subject Categories

Computational Mathematics

Ecology

Probability Theory and Statistics

DOI

10.1080/03610926.2014.942433

More information

Latest update

11/3/2023