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Free Content Variance Reduction for Sector Sampling

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Abstract:

Variance reduction techniques used in Monte Carlo integration including control variates and importance sampling can use estimated or actual shapes of vegetated land areas to reduce the variance of estimators from sector sampling. The estimated shapes of forested areas could come from maps, aerial photos, or similar sources. Antithetic variates for variance reduction in Monte Carlo integration can be applied to sector sampling without using any estimated shape or map. Sector sampling selects as samples all trees or other vegetation of interest located in randomly chosen sectors that have a vertex at a common point located in the interior of a forested area. Each sector is associated with an angle of fixed magnitude emanating from the interior point. Sector orientation is based on a randomly selected azimuth originating at the interior point that is the vertex for each sector. This technique is well adapted to application on relatively small areas that have irregularly shaped boundaries. Sector sampling can be demonstrated to be unbiased. Unbiasedness holds with angle reduction for adjustment of sample size and with the variance reduction techniques that are proposed. The method is not restricted to application with trees because sector sampling methods could be applied just as well to other vegetation types or any other objects located in the land area of interest.

Keywords: Monte Carlo integration; control variates; importance sampling; polar coordinates; vegetation sampling

Document Type: Research Article

Affiliations: Thomas B. Lynch, Professor, Department of Forestry, Room 008C Ag Hall, Oklahoma State University, Stillwater, OK 74078-6013—Phone: (405) 744-5447; tlynch@okstate.edu., Fax: (405) 744-5437

Publication date: June 1, 2006

More about this publication?
  • 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.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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