Abstract:
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Bayesian models for multinomial-type count data have been developed using non-informative priors. When small observed counts are present, there is little information in the data and prior selection is critical. Traditional non-informative priors often show poor performance here, motivating the use of "sparse" Dirichlet prior distributions. We consider prior selection in the case of hierarchical multinomial data, assessing the performance of several types of priors.
As an example, we look at modeling repeated predator feeding surveys. The great variation often found in species abundances can lead to counts in feeding surveys spanning multiple orders of magnitude, and we show that prior choice has important statistical and ecological implications in this setting. As a second example, we consider analyzing feeding rates based on the contents of predators' stomachs. In this case, the response vectors are the numbers of prey consumed by each predator and frequently contain numerous small counts that complicate traditional modeling efforts.
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