Accurate knowledge of indoor radon concentration is crucial for assessing radon-related health effects or identifying radon-prone areas. Indoor radon concentration at the national scale is usually estimated on the basis of extensive measurement campaigns. However, characteristics of the sampled households often differ from the characteristics of the target population owing to the large number of relevant factors that control the indoor radon concentration, such as the availability of geogenic radon or floor level. 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. A modeling approach was used by applying a quantile regression forest to estimate the probability distribution function of indoor radon for each floor level of each residential building in Germany. Based on the estimated probability distribution function,a probabilistic Monte Carlo sampling technique was applied, enabling 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 show an approximate lognormal distribution of indoor radon in dwellings in Germany with an arithmetic mean of 63 Bq/m3, a geometric mean of 41 Bq/m3, and a 95th percentile of 180 Bq/m3. The exceedance probabilities for 100 and 300 Bq/m3 are 12.5% (10.5 million people affected) and 2.2 % (1.9 million people affected), respectively. The advantages of our approach are that it yields a) an accurate estimation of indoor radon concentration even if the survey is not fully representative with respect to floor level and radon concentration in soil, and b) an estimate of the indoor radon distribution with a much higher spatial resolution than basic descriptive statistics.

翻译：准确掌握室内氡气浓度对于评估氡相关健康效应或识别氡易发区域至关重要。国家尺度的室内氡气浓度通常基于大规模测量活动进行估算。然而，由于控制室内氡气浓度的相关因素众多（如地质来源氡气的可获取性、楼层位置等），抽样住户的特征常与目标总体特征存在差异。本研究提出一种基于模型的方法，相比纯数据驱动方法，能以更高空间分辨率实现更贴近现实的室内氡气分布估算。该建模方法通过应用分位数回归森林，估算了德国每栋住宅建筑各楼层的室内氡气概率分布函数。基于估算的概率分布函数，进一步采用概率蒙特卡洛抽样技术，实现了楼层预测结果的组合与人口加权。通过这种方式，个体预测的不确定性被有效传递至聚合层面的变异性估计中。结果显示，德国住宅室内氡气浓度近似服从对数正态分布，其算术平均值为63 Bq/m³，几何平均值为41 Bq/m³，第95百分位数为180 Bq/m³。浓度超过100 Bq/m³与300 Bq/m³的概率分别为12.5%（影响约1050万人）和2.2%（影响约190万人）。本方法的优势在于：a) 即使调查在楼层和土壤氡浓度方面不具备完全代表性，仍能获得准确的室内氡浓度估计；b) 相比基础描述性统计，能以更高的空间分辨率估算室内氡气分布。