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, e.g., 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. This article is protected by copyright. All rights reserved.

中文翻译：

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离散观测线性生死过程的参数估计

生死过程被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，但它们的参数可能难以估计，因为当数据来自最常见的抽样方案（例如年度人口普查）时，可能性在数值上可能变得不稳定。当离散观测不是等间隔时，例如，当人口普查数据在某些年份不可用时，会出现进一步的困难。我们提出了两种方法来估计离散观察的线性生死过程的出生、死亡和增长率：通过嵌入式高尔顿 - 沃森过程和通过最大化可能性的鞍点近似。我们研究估计量的渐近特性，在数值示例上比较它们，并将该方法应用于受监控人群的数据。本文受版权保护。版权所有。