Dunson, David B.Hsu, Ching-Lung2025-07-022025-07-022025https://hdl.handle.net/10161/32751<p>Ecology aims to quantify and predict interactions between organisms and their environment, necessitating rigorous statistical frameworks for reliable inference. This dissertation presents statistical methodologies for addressing two fundamental ecological problems: biodiversity estimation and joint species distribution modeling. In Chapter 2, we generalize the notion of biodiversity estimation by extending Hubbell’s fundamental biodiversity number α to σ-diversity and conditional σ-diversity. This extension allows for flexible taxon accumulation growth and enables biodiversity estimation across different layers of the Linnean taxonomy. In Chapter 3, we propose a Bayesian mixture framework for joint species distribution modeling. This approach explicitly accounts for rare and previously unobserved species, mitigating biases in traditional models that underestimate biodiversity. Together, these contributions provide a principled statistical foundation for biodiversity estimation and species distribution modeling. Theoretical and empirical results are provided.</p>https://creativecommons.org/licenses/by-nc-nd/4.0/StatisticsMathematicsBayesian non-parametricsEnriched Dirichlet processGibbs-type priorJoint species distribution modelsMixture modelsSpecies sampling modelsBiodiversity Estimation and Joint Species Distribution ModelingDissertation