Bayesian Analysis of the Linear Model with Heterogeneous Variance

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Abstract:

Linear models are among the most common statistical tools in forestry, and indeed in all science. It is widely known that when linear models are applied to attributes of size (e.g., individual tree volumes), the conditional variance may be heterogeneous. Under these circumstances, the usual least squares estimator remains consistent, but is no longer efficient. This has been appreciated in forestry for some time, and various solutions have been recommended over the years. In this paper, we propose a Bayesian solution. Bayesians would prefer this method to previous solutions for many reasons. However, even non-Bayesians may wish to consider the method as it yields (as will be shown) solutions quite close to the maximum likelihood solution, along with the marginal posterior distribution of each parameter. For. Sci. 44(1):134-138.

Keywords: Bayesian inference; Ioblolly pine; Markov Chain Monte Carlo; Regression

Document Type: Journal Article

Affiliations: Forest Sciences Laboratory, USDA Forest Service, PO Box 640, Durham, NH 03824-640

Publication date: February 1, 1998

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.
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