Publication details

Parameter estimation for discretely-observed linear birth-and-death processes



Year of publication 2021
Type Article in Periodical
Magazine / Source Biometrics
MU Faculty or unit

Faculty of Science

Keywords Galton-Watson process; Gaussian approximation; likelihood; linear birth-and-death process; saddlepoint approximation
Description Birth-and-death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, as the likelihood can become numerically unstable when data arise from the most common sampling schemes, such as annual population censuses. A further difficulty arises when the discrete observations are not equi-spaced, for example, when census data are unavailable for some years. We present two approaches to estimating the birth, death, and growth rates of a discretely observed linear birth-and-death process: via an embedded Galton-Watson process and by maximizing a saddlepoint approximation to the likelihood. We study asymptotic properties of the estimators, compare them on numerical examples, and apply the methodology to data on monitored populations.
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