Risk-Averse Importance Sampling of Tree Attributes in High-Risk Forested Areas

Abstract

This study develops the theory of risk-averse importance sampling and explains its potential application to forest inventory estimation through the use of a heuristic simulation. When the risk-producing elements of the landscape are known, a risk-averse sampling strategy can be created that results in fewer samples in high-risk areas. Our simulation shows that for certain high-risk populations, risk-averse importance sampling can be highly effective at reducing both risk to field crew members (requiring only 10% of the plot visits in the riskiest category) and sample variance relative to simple random sampling. The method is shown to be especially helpful when a population of values of interest decreases with increasing risk, with a reduction in mean square error (MSE) of 84% to 99% in these cases. The simulation also showed the opposite effect on MSE can be expected when values of interest increase with increasing risk. By increasing field crew safety, risk-averse importance sampling should also improve the frequency and accuracy of field observations, potentially leading to even bigger gains in estimate precision. We recommend risk-averse importance sampling any time hazardous conditions can result in a high number of missing observations and reasonably accurate characterizations of landscape risks can be developed. Study Implications: During the collection of forest inventory data, the safety of field personnel is always of primary importance, but never has the safety of personnel been a component of the sample design. This study develops a risk-averse importance sampling strategy that provides a low-risk probability sample of field observations in high-risk areas for interested practitioners. The low-risk probability sample can be created when the risk-producing elements of the forested area are known and can be described in functional form. The method is shown to be especially helpful when a population of values of interest decrease with increasing risk. It is hypothesized that if a probability sample is defined that will reduce the sample in the riskiest areas and increase safety in the field, both response rates and the accuracy of field measurements will increase, and, in turn, will lead to a reduction in the variance of the final estimates. Risk-averse importance sampling is recommended any time it is likely to lead to a higher level of safety and observational success.