Institute of Mathematics, Ecole Polytechnique Fédérale de Lausanne, EPFL-FSB-MATH-STAT, Lausanne, Switzerland.
School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia.
Biometrics. 2021 Mar;77(1):186-196. doi: 10.1111/biom.13282. Epub 2020 May 8.
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.
birth-and-death 过程广泛用于模拟生物种群的发展。尽管它们是相对简单的模型，但当数据来自最常见的抽样方案（如年度人口普查）时，它们的参数可能难以估计，因为似然函数可能会变得数值不稳定。当离散观测值不均匀时，例如某些年份没有人口普查数据时，会出现另一个困难。我们提出了两种方法来估计离散观测的线性 birth-and-death 过程的出生率、死亡率和增长率：通过嵌入式 Galton-Watson 过程和最大化似然函数的鞍点逼近。我们研究了估计量的渐近性质，在数值示例上进行了比较，并将该方法应用于监测种群的数据。
