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Analysis of multinomial models with unknown index using data augmentation

Journal of Computational and Graphical Statistics

6818_Royle.pdf
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Abstract

Multinomial models with unknown index ('sample size') arise in many practical settings. In practice, Bayesian analysis of such models has proved difficult because the dimension of the parameter space is not fixed, being in some cases a function of the unknown index. We describe a data augmentation approach to the analysis of this class of models that provides for a generic and efficient Bayesian implementation. Under this approach, the data are augmented with all-zero detection histories. The resulting augmented dataset is modeled as a zero-inflated version of the complete-data model where an estimable zero-inflation parameter takes the place of the unknown multinomial index. Interestingly, data augmentation can be justified as being equivalent to imposing a discrete uniform prior on the multinomial index. We provide three examples involving estimating the size of an animal population, estimating the number of diabetes cases in a population using the Rasch model, and the motivating example of estimating the number of species in an animal community with latent probabilities of species occurrence and detection.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Analysis of multinomial models with unknown index using data augmentation
Series title:
Journal of Computational and Graphical Statistics
Volume
16
Issue:
1
Year Published:
2007
Language:
English
Contributing office(s):
Patuxent Wildlife Research Center
Description:
67-85
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
First page:
67
Last page:
85
Number of Pages:
19