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Polya Posterior Frequency Distributions for Stratified Double Sampling of Categorical Data

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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. FOR. SCI. 48(3):569–581.
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Keywords: Dirichlet prior; Edgeworth expansions; Polya urns; environmental management; forest; forest management; forest resources; forestry; forestry research; forestry science; natural resource management; natural resources; probability generating functions; variance estimators

Document Type: Miscellaneous

Affiliations: 1: Canadian Forestry Service, Natural Resources Canada, 506 Burnside Rd. West, Victoria, B.C., Canada, V8Z 1M5, Phone: +1 250 363 0712. Fax: +1 363 0775 smagnuss@pfc.forestry.ca 2: Institute of Forest Growth and Computer Sciences, Dresden University of Technology, Wilsdruffer Str. 18, Tharandt, Germany, D 01737, Phone: +49 35203-38 1620 koehl@forst.tu-dresden.de

Publication date: 2002-08-01

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2016 Impact Factor: 1.782 (Rank 17/64 in forestry)

    Average time from submission to first decision: 62.5 days*
    June 1, 2016 to Feb. 28, 2017

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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