EMPIRICAL BAYES ESTIMATION OF PROPORTIONS WITH APPLICATION TO COWBIRDPARASITISM RATES

Bayesian models provide a structure for studying collections of parame ters such as are considered in the investigation of communities, ecosy stems, and landscapes. This structure allows for improved estimation o f individual parameters by considering them in the context of a group of related parameters. Individual estimates are differentially adjuste d toward an overall mean, with the magnitude of their adjustment based on their precision. Consequently, Bayesian estimation allows for a mo re reliable ranking of parameters and, in particular, a more credible identification of extreme values from a collection of estimates.In Bay esian models, individual parameters are regarded as values sampled fro m a specified probability distribution, called a prior. The requiremen t that the prior be known is often regarded as an unattractive feature of Bayesian analysis and may be the reason Bayesian analyses are not frequently applied in ecological studies. Empirical Bayes methods prov ide an alternative approach that incorporates the structural advantage s of Bayesian models while requiring a less stringent specification of prior knowledge. Empirical Bayes methods require only that the prior be in a certain family of distributions, indexed by hyperparameters th at can be estimated from the available data. This structure is of inte rest per se, in addition to its value in allowing for improved estimat ion of individual parameters: for example, hypotheses regarding the ex istence of distinct subgroups in a collection of parameters can be con sidered under the empirical Bayes framework by allowing the hyperparam eters to vary among subgroups. We describe the empirical Bayes approac h in application to estimation of proportions, rising data obtained in a community-wide study of Brown-headed Cowbird parasitism rates for i llustration. Empirical Bayes estimates identify those species for whic h there is the greatest evidence of extreme parasitism rates. Subgroup analysis of our data on cowbird parasitism rates indicates that paras itism rater For neotropical migrants as a group are no greater than th ose of resident/short-distance migrant species in this forest communit y. Our data and analyses demonstrate that the parasitism rates for cer tain neotropical migrant species (Wood Thrush and nose-breasted Grosbe ak) are remarkably low while those for others (Ovenbird and Red-eyed V ireo) are remarkably high.