A fundamental pattern in ecology is that smaller organisms are more abundant than larger organisms. This pattern is known as the individual size distribution (ISD), which is the frequency distribution of all individual body sizes in an ecosystem. The ISD is described by a power law and a major goal of size spectra analyses is to estimate the exponent of the power law, λ. However, while numerous methods have been developed to do this, they have focused almost exclusively on estimating λ from single samples. Here, we develop an extension of the truncated Pareto distribution within the probabilistic modelling language Stan. We use it to estimate multiple λs simultaneously in a hierarchical modelling approach. The most important result is the ability to examine hypotheses related to size spectra, including the assessment of fixed and random effects, within a single Bayesian generalized mixed model. While the example here uses size spectra, the technique can also be generalized to any data that follow a power law distribution.

中文翻译：

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尺寸谱的贝叶斯分层建模

生态学的一个基本模式是较小的生物体比较大的生物体更丰富。这种模式被称为个体尺寸分布（ISD），它是生态系统中所有个体体型的频率分布。 ISD 由幂律描述，尺寸谱分析的主要目标是估计幂律的指数，λ。然而，虽然已经开发了许多方法来做到这一点，但它们几乎完全专注于估计λ来自单个样本。 在这里，我们在概率建模语言 Stan 中开发了截断帕累托分布的扩展。我们用它来估计多个λ在分层建模方法中同时进行。 最重要的结果是能够在单个贝叶斯广义混合模型中检查与尺寸谱相关的假设，包括评估固定和随机效应。虽然此处的示例使用尺寸谱，但该技术也可以推广到遵循幂律分布的任何数据。