A Bayesian theory for estimation of biodiversity
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| author | Rigon, Tommaso Hsu, Ching-Lung Dunson, David B. |
| author_facet | Rigon, Tommaso Hsu, Ching-Lung Dunson, David B. |
| contents | Statistical inference on biodiversity has a rich history going back to RA Fisher. An influential ecological theory suggests the existence of a fundamental biodiversity number, denoted $α$, which coincides with the precision parameter of a Dirichlet process (DP). In this paper, motivated by this theory, we develop Bayesian nonparametric methods for statistical inference on biodiversity, building on the literature on Gibbs-type priors. We argue that $σ$-diversity is the most natural extension of the fundamental biodiversity number and discuss strategies for its estimation. Furthermore, we develop novel theory and methods starting with an Aldous-Pitman (AP) process, which serves as the building block for any Gibbs-type prior with a square-root growth rate. We propose a modeling framework that accommodates the hierarchical structure of Linnean taxonomy, offering a more refined approach to quantifying biodiversity. The analysis of a large and comprehensive dataset on Amazon tree flora provides a motivating application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Bayesian theory for estimation of biodiversity Rigon, Tommaso Hsu, Ching-Lung Dunson, David B. Methodology Applications Statistical inference on biodiversity has a rich history going back to RA Fisher. An influential ecological theory suggests the existence of a fundamental biodiversity number, denoted $α$, which coincides with the precision parameter of a Dirichlet process (DP). In this paper, motivated by this theory, we develop Bayesian nonparametric methods for statistical inference on biodiversity, building on the literature on Gibbs-type priors. We argue that $σ$-diversity is the most natural extension of the fundamental biodiversity number and discuss strategies for its estimation. Furthermore, we develop novel theory and methods starting with an Aldous-Pitman (AP) process, which serves as the building block for any Gibbs-type prior with a square-root growth rate. We propose a modeling framework that accommodates the hierarchical structure of Linnean taxonomy, offering a more refined approach to quantifying biodiversity. The analysis of a large and comprehensive dataset on Amazon tree flora provides a motivating application. |
| title | A Bayesian theory for estimation of biodiversity |
| topic | Methodology Applications |
| url | https://arxiv.org/abs/2502.01333 |