Forest inventories and surveys, accounting for time and cost constraints, are typically designed to yield accurate and precise estimates of population means and totals over large spatial domains. In many instances, these inventories and surveys also offer reliable inference for smaller subpopulations with sufficient sample observations; however, there is growing demand for valid and precise estimates at levels that have smaller sample sizes based on the original sample design. One solution to this problem is application of small area estimationmethods. Small area estimation (SAE) is a model-based approach that couples a direct estimate and possible covariates to improve the estimate precision and, in some cases, accuracy. Unlike a standard linear regression, the SAE framework is comprised of two components: a sampling model and a linking model. Estimation of the SAE parameter of interest accounts for and balances between the sampling (i.e., direct estimator) and linking model errors. The linking model is a linear model with random effects that relate the small areas of interest with some error. Additional spatial structure might still remain in the linking model after accounting for possible covariates. Such residual structure can be further modeled using spatial random effects.This dissertation presents SAE methods within a hierarchical Bayesian (HB) framework. This framework is applied to common biophysical forest inventory outcomes of interest (i.e., aboveground biomass, basal area, volume, and tree density) at the stand level, and to thesocial forestry survey outcomes of private forest landowner populations. Furthermore, an in depth examination of the direst estimator, in the presence of nonresponse, is assessed for private forest landowner population size. The primary objectives of this dissertationare: i) to apply a HB framework to increase the precision of estimates for biophysical forest variables at the stand level by borrowing strength across all stands through the use of LiDAR covariates; ii) to apply a conditional autoregressive structure to the stand-levelrandom effects to assess gains in precision of biophysical forest variables; iii) to evaluate the current National Woodland Owner Survey estimators of private forest area and private forest landowner population size for a known population at the state level; iv) to presentan alternative estimator of private forest landowner population size that explicitly accounts for various nonresponse scenarios; v) to evaluate the impacts of nonresponse biases on each of these estimators; vi) to produce county-level private forest ownership datasets for two complete states; vi) to define and assess SAE models to improve county-level inference of the number of private forest ownerships, and; vii) to develop open source software to fit proposed SAE models.
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