Mapping indoor radon-222 in denmark: design and test of the statistical model used in the second nation-wide survey

In Denmark, a new survey of indoor radon-222 has been carried out. One-year alpha trackmeasurements (CR-39) have been done in 3019 single-family houses. There is from 3 to 23 housemeasurements in each of the 275 municipalities. Within each municipality, houses have been selectedrandomly. One important outcome of the survey is the prediction of the fraction of houses in eachmunicipality with an annual average radon concentration above 200 Bqm-3. To obtain the mostaccurate 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 (conditionally)unbiased estimators of the quantities of interest. Bayesian statistics is used to minimize the effect ofsmall sample size. In each municipality, the correction is dependent on the fraction of area where sandand gravel is a dominating surface geology. The uncertainty analysis is done with a Monte Carlotechnique. It is demonstrated that the weighted sum of all municipality model estimates of fractionsabove 200 Bqm-3 (3.9 % with 95 %-confidence interval = [3.4,4.5]) is consistent with the weightedsum of the observations for Denmark taken as a whole (4.6 % 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 wellsuited for its purpose.