在Burr分佈下利用無母數Bootstrap法量化估計溫室氣體排放量之不確定性

Abstract

近幾十年來人類的活動已大幅影響了大氣中溫室氣體greenhouse gases(GHG)的排放量，而GHG排放含量的增加會加劇全球暖化的現象；暖化現象在全世界各地有不同的影響，其中包含降雨量驟變、農業產量劇降、冰川融化造成物種滅絕、海岸侵蝕的增加、某些地區的季節改變以及新型傳染病的出現等，這些影響已經讓世界各地的科學家警覺並積極採取行動以控制溫室氣體的排放，其中包括簽定「聯合國氣候變化綱要公約」以及「京都議定書」。實施「京都議定書」需要詳盡的溫室氣體中之溫室氣體排放清冊數據，根據政府間氣候變遷研究小組(Intergovernmental Panel on Climate Change, IPCC 2006)排放量之不確定性一般可用95%信賴區間來表示，但當排放估計的樣本數據小且不符合常態分配時，以95%信賴區間來量化排放估計的不確定性是不合適的，針對上類小量樣本數據或非常態分配數據，本研究提出利用bootstrap 方法來替代傳統的信賴區間方法來估計溫室氣體排放量之不確定性，由於Burr分佈藉由調動其參數值可呈現各種不同之非常態分佈(右偏、常態、左偏)，因此本研究主要是針對當母體分佈為Burr XII分佈利用bootstrap方法和四種bootstrap的信賴區間(SB, PB, BCPB ,BCa)來量化排放量的不確定性。本研究利用三種評估標準(coverage performance, interval mean, interval standard deviation)來判斷信賴區間的優劣，並找出在Burr分佈下建構量化排放估計的不確定性的bootstrap 信賴區間時所需的最適之樣本數。根據本研究模擬的結果可知，當抽樣樣本數量提升可以明顯改善Coverage Performance並且降低Interval Mean 以及Interval Standard Deviation同時可改善估計之精確度與準確度。不論資料在常態或非常態且樣本數n小於30時，bootstrap信賴區間相較於傳統信賴區間擁有較小的Interval Mean及Interval Standard Deviation且在樣本數n超過12時其Coverage Performance可達到90%以上，而其中又以BCa表現較佳。因此本研究建議在量化估計溫室氣體排放量之不確定性時選擇BCa信賴區間之效果較佳。若是抽樣樣本數超過30時，傳統信賴區間或bootstrap信賴區間皆適合用來量化排放估計的不確定性，本研究成果可撰寫成軟體程式應用相當簡易。

Human activities in recent decades have dramatically influenced the atmospheric changes in terms of the increasing amount of greenhouse gases (GHG). Global warming is caused by the GHG emitted into the atmosphere. The Global warming have very serious impacts worldwide; these impacts include changes in rainfall patterns, changes in agricultural yields, the continued melting of glaciers and species extinctions, etc. These impacts have alerted scientists worldwide to act together aggressively in controlling GHG emissions, including UNFCCC and the Kyoto protocol. Implementing the Kyoto protocol requires high quality greenhouse gas inventory data. According to IPCC guidelines, the uncertainties are generally expressed in the uncertainty range which is described by a 95% confidence interval. The Classical method requires not only a sufficiently large dataset to estimate the uncertainty, but also the data must possess a normal distribution. The Burr distribution can be utilized to describe many non-normal distribution by simply adjusting its parameter values. Therefore the main objective of this study is to develop non-parametric bootstrap mothed to quantify the uncertainty of GHG emission estimates under the Burr distribution when the sample data are small or possess a non-normal distribution. Four bootstrap confidence intervals (SB, PB, BCPB, BCa) are used to quantify the uncertainty of GHG emission estimates. The performance of the proposed bootstrap confidence intervals is evaluated using three indices (i.e., coverage performance, interval mean and interval standard deviation). Furthermore, this study also finds an appropriate sample size when constructing the bootstrap confidence intervals for quantifying the uncertainty of emission estimates using the non-parametric bootstrap confident intervals. According to the sensitivity analysis, this study concludes that larger sample size always results in higher coverage performance, shorter interval mean, and smaller interval standard deviation for four bootstrap confidence intervals. When the sample size (n) is less than 30, the bootstrap confidence intervals generally have smaller interval length with smaller deviation than that of the classical confidence interval, no matter the data is normal or non-normal. The coverage performance is approximately 0.90 or above for n exceeding 12 for all of the four bootstrap confidence intervals. Although four bootstrap confidence intervals behave similar in all three indices, but BCa performs slightly better than other bootstrap intervals with higher coverage performance under right-skewed distribution. In summary this study recommend to employ BCa confident interval to quantify the uncertainty of emission estimates for n≥12. The classical confidence interval and four bootstrap confidence intervals are all suitable for quantifying the uncertainty of emission estimates when the sample size n≥30.