Canadian Forest Service Publications
Polya posterior frequency distributions for stratified double sampling of categorical data. 2002. Magnussen, S.; Köhl, M. Forest Science 48(3): 569-581.
Available from: Pacific Forestry Centre
Catalog ID: 20589
Estimates of category frequencies in stratified double sampling are generally obtained by methods of maximum likelihood assuming a multinomial distribution of data. Although the distribution of estimation errors is asymptotically normal, a reliance on the normal assumption for inference can be problematic for low frequency categories (<10%) and small sample sizes (<1,000). In these situations, a Bayesian approach appears more robust. A vague Dirichlet prior is adopted to compute a Polya posterior distribution. In a simulation study of sampling from eight small- to medium- sized populations, we found that the resampling distributions of maximum likelihood estimates were generally closer to the Polya posteriors than to the assumed normal distributions. Resampling distributions and Polya posteriors deviated frequently and significantly from a normal distribution. A Polya posterior was often orders of magnitude faster to compute than a resampling distribution.