Bayesian population models can be exceedingly slow due, in part, to the choice to simulate discrete latent states. Here, we discuss an alternative approach to discrete latent states, marginalization, that forms the basis of maximum likelihood population models and is much faster. Our manuscript has two goals: (1) to introduce readers unfamiliar with marginalization to the concept and provide worked examples and (2) to address topics associated with marginalization that have not been previously synthesized and are relevant to both Bayesian and maximum likelihood models. We begin by explaining marginalization using a Cormack‐Jolly‐Seber model. Next, we apply marginalization to multistate capture–recapture, community occupancy, and integrated population models and briefly discuss random effects, priors, and pseudo‐R ². Then, we focus on recovery of discrete latent states, defining different types of conditional probabilities and showing how quantities such as population abundance or species richness can be estimated in marginalized code. Last, we show that occupancy and site‐abundance models with auto‐covariates can be fit with marginalized code with minimal impact on parameter estimates. Marginalized code was anywhere from five to >1,000 times faster than discrete code and differences in inferences were minimal. Discrete latent states and fully conditional approaches provide the best estimates of conditional probabilities for a given site or individual. However, estimates for parameters and derived quantities such as species richness and abundance are minimally affected by marginalization. In the case of abundance, marginalized code is both quicker and has lower bias than an N ‐augmentation approach. Understanding how marginalization works shrinks the divide between Bayesian and maximum likelihood approaches to population models. Some models that have only been presented in a Bayesian framework can easily be fit in maximum likelihood. On the other hand, factors such as informative priors, random effects, or pseudo‐R ² values may motivate a Bayesian approach in some applications. An understanding of marginalization allows users to minimize the speed that is sacrificed when switching from a maximum likelihood approach. Widespread application of marginalization in Bayesian population models will facilitate more thorough simulation studies, comparisons of alternative model structures, and faster learning.

中文翻译：

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贝叶斯人口模型中对速度的需求：边缘化和恢复离散潜伏状态的实用指南。

贝叶斯种群模型可能会非常慢，部分原因是选择模拟离散的潜在状态。在这里，我们讨论了离散潜在状态的一种替代方法，即边缘化，它形成了最大似然总体模型的基础，并且速度更快。我们的手稿有两个目标：（1）向不熟悉边缘化的读者介绍该概念并提供有效的示例；（2）解决与边缘化相关的主题，这些主题以前没有综合在一起，与贝叶斯模型和最大似然模型都相关。我们首先使用Cormack-Jolly-Seber模型解释边缘化。接下来，我们将边缘化应用于多州捕获，重新捕获，社区占用和综合人口模型，并简要讨论随机效应，先验和伪R²。然后，我们专注于离散潜在状态的恢复，定义不同类型的条件概率，并说明如何在边缘化代码中估算诸如种群数量或物种丰富度之类的数量。最后，我们表明具有自动协变量的占用率和站点数量模型可以与边际化代码拟合，并且对参数估计的影响最小。边缘化代码的速度是离散代码的5到> 1,000倍，推理的差异也很小。离散的潜在状态和完全条件的方法可以为给定的站点或个人提供条件概率的最佳估计。但是，边缘化对参数和派生数量（例如物种丰富度和丰度）的估计影响最小。如果有很多，N增强方法。了解边缘化的工作原理可缩小人口模型的贝叶斯方法和最大似然方法之间的鸿沟。仅在贝叶斯框架中提出的某些模型很容易以最大可能性拟合。另一方面，在某些应用中，诸如信息先验，随机效应或伪R ²值等因素可能会激发贝叶斯方法。对边缘化的理解允许用户最小化从最大可能性方法切换时牺牲的速度。在贝叶斯人口模型中边缘化的广泛应用将促进更彻底的模拟研究，替代模型结构的比较和更快的学习。