Improving the precision of estimates of the frequency of rare events
Improving the precision of estimates of the frequency of rare events
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DOI：
10.1890/04-0601
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发表时间：
2005-05-01
期刊：
影响因子：
4.8
通讯作者：
Gotelli, NJ
中科院分区：
文献类型：
--
作者：
Dixon, PM;Ellison, AM;Gotelli, NJ
罕见事件的概率通常直接估计为事件发生的次数除以总样本量。不幸的是，这种估计的精度很低。对于生态学研究中N < 100的典型样本量，这种罕见事件概率估计的变异系数（cv）可以超过300%。需要10（3）-10（4）次观察的样本量，以将CV降至10%以下。如果增加样本量不切实际或不可能，可以使用辅助数据来提高估计的精度。我们描述了四种使用辅助数据来提高罕见事件概率估计精度的方法：（1）包括有关概率的先验信息的贝叶斯分析;（2）纳入人群异质性信息的分层;（3）解释与概率相关的信息的回归模型;以及（4）包括在更大的空间或时间尺度上收集的汇总数据。这些方法说明了使用数据的食虫植物Darlingtonia californica的胡蜂捕获的概率。相对于简单的基于频率的估计，所有四种方法都提高了估计的精度（绝对精密度= 1.26，相对精密度[CV] = 70%）：分层（绝对精度= 1.10，cv = 62%）;回归模型（绝对精密度= 1.59，cv = 55%）;贝叶斯分析，先验概率分布信息（绝对精度= 4.28，CV = 47%）;以及使用时间聚集数据（绝对精度6.75，CV = 36%）。当有信息丰富的辅助数据时，我们建议在估计罕见事件的概率时将其包括在内。
The probability of a rare event is usually estimated directly as the number of times the event occurs divided by the total sample size. Unfortunately, the precision of this estimate is low. For typical sample sizes of N < 100 in ecological studies, the coefficient of variation (cv) of this estimate of the probability of a rare event can exceed 300%. Sample sizes on the order of 10(3)-10(4) observations are needed to reduce the cv to below 10%. If it is impractical or impossible to increase the sample size, auxiliary data can be used to improve the precision of the estimate. We describe four approaches for using auxiliary data to improve the precision of estimates of the probability of a rare event: (1) Bayesian analysis that includes prior information about the probability; (2) stratification that incorporates information on the heterogeneity in the population; (3) regression models that account for information correlated with the probability; and (4) inclusion of aggregated data collected at larger spatial or temporal scales. These approaches are illustrated using data on the probability of capture of vespulid wasps by the insectivorous plant Darlingtonia californica. All four methods increase the precision of the estimate relative to the simple frequency-based estimate (absolute precision = 1.26, relative precision [cv] = 70%): stratification (absolute precision = 1.10, cv = 62%); regression models (absolute precision = 1.59, cv = 55%); Bayesian analysis with an informative prior probability distribution (absolute precision = 4.28, cv = 47%); and using temporally aggregated data (absolute precision 6.75, cv = 36%). When informative auxiliary data is available, we recommend including it when estimating the probability of rare events.