Discriminating among common probabilistic models for radon data: a Bayesian approach

Discriminating among competing statistical models for experimental data is of interest for physical science. While right-skewed experimental measurements commonly approximate a lognormal distribution, among many others, substantial deviations occur at the extremes of the distribution, suggesting that alternative models may provide better fits in certain contexts. In many practical contexts, the choice of a single underlying distribution has significant implications, such as estimating the proportion of dwellings exceeding regulatory reference radon levels. We employ a Bayesian approach to model selection, utilizing Bayes factors and posterior model probabilities to compare suitable distributions applied to radon concentration data from Gran Canaria. Using non-informative priors appropriate for shape-scale family distributions, we calculate marginal densities and derive evidence metrics that transcend the limitations of conventional frequentist goodness-of-fit tests. We found strong evidence against the Gamma model and mild/weak evidence for the LogLogistic over the LogNormal distribution. We also offer a Bayesian model averaging strategy that weights the LogLogistic and LogNormal distributions by their posterior probability to create BMA mixture that improves dwelling exceedance frequency estimates across regulatory reference levels.