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Bayesian Modeling of Sequential Discoveries.

Alessandro Zito1, Tommaso Rigon2, Otso Ovaskainen3,4,5

  • 1Department of Statistical Science, Duke University, Durham, NC.

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|March 19, 2024
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Summary
This summary is machine-generated.

We introduce a new Bayesian method to model species discovery in sequential data. This approach offers flexibility and includes tractable models, even those accounting for covariates, useful for biodiversity studies.

Keywords:
Accumulation curvesDirichlet processLogistic regressionPoisson-binomial distributionSpecies sampling models

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Area of Science:

  • Ecology
  • Statistics
  • Computational Biology

Background:

  • Sequential data, such as species in ecological samples or words in a corpus, often exhibit patterns of discovery.
  • Accumulation curves are commonly used to summarize the number of distinct entities observed as sample size increases.
  • Existing models may lack flexibility in specifying discovery probabilities.

Purpose of the Study:

  • To propose a novel Bayesian method for modeling species sampling and sequential discoveries.
  • To develop a flexible framework for directly specifying the probability of new discoveries.
  • To investigate the theoretical and practical properties of the proposed models.

Main Methods:

  • Developed a new Bayesian species sampling model by directly parameterizing the probability of a new discovery.
  • Studied the asymptotic behavior and finite sample properties of the proposed sequential processes.
  • Identified a tractable subclass of models, including one related to the Dirichlet process and logistic regression.

Main Results:

  • The proposed Bayesian method allows for flexible specification of discovery probabilities in sequential data.
  • A subclass of models with favorable theoretical and computational properties was identified.
  • The models demonstrate applicability to real-world data, including a fungal biodiversity study.

Conclusions:

  • The novel Bayesian approach provides a flexible and powerful tool for species sampling and sequential discovery modeling.
  • The identified tractable subclass, particularly the model linked to logistic regression, offers practical advantages for covariate analysis.
  • The method is validated through application to both synthetic and real-world ecological data.