Bayesian Analysis
- Bayesian Anal.
- Volume 5, Number 4 (2010), 765-785.
Objective Bayesian estimation for the number of species
Full-text: Open access
Abstract
Objective priors have been used in Bayesian models for estimating the number of species in a population, but they have not been examined in depth. Here we derive the form of two objective priors, using Bernardo's reference method and Jeffreys' rule, based on the mixed-Poisson likelihood used in the single-abundance-sample species problem. These derivations are based on asymptotic results for estimates of integer-valued parameters. The factored form of these priors justifies the use of independent prior distributions for the parameter of interest (the number of species) and the nuisance parameters (of the stochastic abundance distribution). We find that the reference prior is preferable overall to the prior resulting from Jeffreys' rule. Although a comprehensive objective Bayesian approach can become analytically intractable for more complicated models, the essence of the approach can be upheld in practice. We analyze several datasets to show that the method can be implemented in practice and that it yields good results, comparable with current competing methods.
Article information
Source
Bayesian Anal., Volume 5, Number 4 (2010), 765-785.
Dates
First available in Project Euclid: 19 June 2012
Permanent link to this document
https://projecteuclid.org/euclid.ba/1340110854
Digital Object Identifier
doi:10.1214/10-BA527
Mathematical Reviews number (MathSciNet)
MR2740156
Zentralblatt MATH identifier
1330.62110
Keywords
Jeffreys' prior mixed-Poisson noninformative prior reference prior species richness estimation
Citation
Barger, Kathryn; Bunge, John. Objective Bayesian estimation for the number of species. Bayesian Anal. 5 (2010), no. 4, 765--785. doi:10.1214/10-BA527. https://projecteuclid.org/euclid.ba/1340110854
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