Mapping indoor radon-222 in Denmark: design and test of the statistical model used in the second nationwide survey

In Denmark, a new survey of indoor radon-222 has been carried out. 1-year alpha track measurements ŽCR-39. have been made in 3019 single-family houses. There are from 3 to 23 house measurements in each of the 275 municipalities. Within each municipality, houses have been selected randomly. One important outcome of the survey is the prediction of the fraction of houses in each municipality with an annual average radon concentration above 200 Bq m 3. To obtain the most accurate estimate and to assess the associated uncertainties, a statistical model has been developed. The purpose of this paper is to describe the design of this model, and to report results of model tests. The model is based on a transformation of the data to normality and on analytical Žconditionally. unbiased estimators of the quantities of interest. Bayesian statistics are used to minimize the effect of small sample size. In each municipality, the correction is dependent on the fraction of area where sand and gravel is a dominating surface geology. The uncertainty analysis is done with a Monte Carlo technique. It is demonstrated that the weighted sum of all municipality model estimates of fractions above 200 Bq m 3 Ž3.9% with 95%-confidence interval 3.4,4.5 . is consistent with the weighted sum of the observations for Denmark taken as a whole Ž4.6% with 95%-confidence interval 3.8,5.6 .. The total number of single-family houses within each municipality is used as weight. Model estimates are also found to be consistent with observations at the level of individual counties. These typically include a few hundred house measurements. These tests indicate that the model is well suited for its purpose.