Quantification of Uncertainty for Emission Estimates using Bootstrap Methods

Abstract

Mitigating global warming problems initially involves reducing greenhouse gas (GHG) emissions, in which the uncertainty of GHG emission estimates is assessed concisely. Although the uncertainty of GHG emission estimates is generally evaluated using classical confidence intervals, quantifying the uncertainty based on non-normal GHG emission estimates or small dataset may lead to a significant bias. Using bootstrap confidence intervals is an effective means of reducing such a bias. This study presents a procedure for constructing the four bootstrap confidence intervals to assess the uncertainty of GHG emission estimates for non-normal distributions. These bootstrap confidence intervals are standard bootstrap (SB) confidence interval, percentile bootstrap (PB) confidence interval, Bias-corrected percentiles bootstrap (BCPB) confidence interval and bias-corrected and accelerated (BCa) confidence interval. The sensitivity of bootstrap intervals for emission data is examined under various combinations of sample size and parameter values of normal and non-normal distributions by using three indices: coverage performance, interval mean, and interval standard deviation. Additionally, this study finds the minimum sample size when constructing bootstrap confidence intervals for emission estimates without considering the distribution of the emission data. Simulation results indicate that the bootstrap intervals are more applicable than the classical confidence interval for the non-normal dataset and small sample size. Moreover, when sample size n is less than 30, the bootstrap confidence interval has a smaller interval length with a smaller deviation than that of the classical 95% confidence interval regardless of whether the data distribution is normal or non-normal. This study recommends a sample size greater than or equal to 15 for estimating the uncertainty of emission estimates without checking the distribution of the data. When the sample size n exceeds 30, either the normality-based 95% confidence interval or bootstrap confidence intervals may be used regardless of whether the data distribution is normal or non-normal. Two case studies with emission data were utilized to demonstrate the effectiveness of the proposed procedure.

Mitigating global warming problems initially involves reducing greenhouse gas (GHG) emissions, in which the uncertainty of GHG emission estimates is assessed concisely. Although the uncertainty of GHG emission estimates is generally evaluated using classical confidence intervals, quantifying the uncertainty based on non-normal GHG emission estimates or small dataset may lead to a significant bias. Using bootstrap confidence intervals is an effective means of reducing such a bias. This study presents a procedure for constructing the four bootstrap confidence intervals to assess the uncertainty of GHG emission estimates for non-normal distributions. These bootstrap confidence intervals are standard bootstrap (SB) confidence interval, percentile bootstrap (PB) confidence interval, Bias-corrected percentiles bootstrap (BCPB) confidence interval and bias-corrected and accelerated (BCa) confidence interval. The sensitivity of bootstrap intervals for emission data is examined under various combinations of sample size and parameter values of normal and non-normal distributions by using three indices: coverage performance, interval mean, and interval standard deviation. Additionally, this study finds the minimum sample size when constructing bootstrap confidence intervals for emission estimates without considering the distribution of the emission data. Simulation results indicate that the bootstrap intervals are more applicable than the classical confidence interval for the non-normal dataset and small sample size. Moreover, when sample size n is less than 30, the bootstrap confidence interval has a smaller interval length with a smaller deviation than that of the classical 95% confidence interval regardless of whether the data distribution is normal or non-normal. This study recommends a sample size greater than or equal to 15 for estimating the uncertainty of emission estimates without checking the distribution of the data. When the sample size n exceeds 30, either the normality-based 95% confidence interval or bootstrap confidence intervals may be used regardless of whether the data distribution is normal or non-normal. Two case studies with emission data were utilized to demonstrate the effectiveness of the proposed procedure.