Radon is a carcinogenic, radioactive gas that can accumulate indoors. Indoor radon exposure at the national scale is usually estimated on the basis of extensive measurement campaigns. However, characteristics of the sample often differ from the characteristics of the population due to the large number of relevant factors such as the availability of geogenic radon or floor level. Furthermore, the sample size usually does not allow exposure estimation with high spatial resolution. We propose a model-based approach that allows a more realistic estimation of indoor radon distribution with a higher spatial resolution than a purely data-based approach. We applied a two-stage modelling approach: 1) a quantile regression forest using environmental and building data as predictors was applied to estimate the probability distribution function of indoor radon for each floor level of each residential building in Germany; (2) a probabilistic Monte Carlo sampling technique enabled the combination and population weighting of floor-level predictions. In this way, the uncertainty of the individual predictions is effectively propagated into the estimate of variability at the aggregated level. The results give an arithmetic mean of 63 Bq/m3, a geometric mean of 41 Bq/m3 and a 95 %ile of 180 Bq/m3. The exceedance probability for 100 Bq/m3 and 300 Bq/m3 are 12.5 % (10.5 million people) and 2.2 % (1.9 million people), respectively. In large cities, individual indoor radon exposure is generally lower than in rural areas, which is a due to the different distribution of the population on floor levels. The advantages of our approach are 1) an accurate exposure estimation even if the survey was not fully representative with respect to the main controlling factors, and 2) an estimate of the exposure distribution with a much higher spatial resolution than basic descriptive statistics.

翻译：氡是一种具有致癌性的放射性气体，可在室内积聚。国家尺度的室内氡暴露通常基于大规模测量活动进行评估。然而，由于地生氡可用性、楼层等大量相关因素的影响，样本特征往往与人群特征存在差异。此外，有限的样本量通常无法实现高空间分辨率的暴露评估。我们提出一种基于模型的方法，相较于纯数据驱动方法，能够以更高空间分辨率实现更真实的室内氡分布估算。该方法采用两阶段建模策略：(1) 利用环境与建筑数据作为预测变量，通过分位数回归森林估算德国每栋住宅建筑各楼层的室内氡概率分布函数；(2) 采用概率蒙特卡洛采样技术对各楼层预测值进行组合与人口加权。通过这种方式，单个预测的不确定性被有效传递至聚合层级的变异估计中。结果显示：算术均值为63 Bq/m³，几何均值为41 Bq/m³，95%分位值为180 Bq/m³。超过100 Bq/m³和300 Bq/m³的概率分别为12.5%（约1050万人）和2.2%（约190万人）。大城市居民室内氡暴露普遍低于农村地区，这归因于人口在楼层分布上的差异。本方法的优势在于：(1) 即使调查数据在主要控制因素上缺乏完全代表性，仍能实现精准暴露估算；(2) 相较基础描述性统计，能以更高空间分辨率提供暴露分布估算。