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A finite population Bayes procedure for censored categorical abundance data

Holland MD, G Meeden and BR Gray. 2010. A finite population Bayes procedure for censored categorical abundance data. Journal of the Indian Society of Agricultural Statistics 64: 171-175.

Abstract

We propose a Bayes procedure for estimating categorical abundance using data that are observed with error from a random sample form a finite population. The procedure is designed to estimate the proportion of sites in a finite population that belong to each abundance category. Royle and Link (2005) proposed a multinomial mixture model to analyze data of this nature. Holland and Gray (2010) demonstrated that category means would exhibit bias when probabilities of correct category classifications vary among sampling units and this heterogeneity is not modeled. Those authors proposed a modification to the multinomial mixture model that allows correct classification probabilities to vary by sampling unit according to a single normal distribution on a common logit scale. Our proposal allows both correct and incorrect classification probabilities to vary by site and dose not require strong assumptions about the nature of the heterogeneity in classification probabilities. We analyze submerged aquatic vegetation data collected by the Long Term Resource Monitoring Program and compare our results to those of Holland and Gray (2010). We also provide simulation results to demonstrate the performance of our proposal and associated credible intervals under several prior distributions.

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