Spatial prediction of naturally occurring gamma radiation in Great Britain.

Gamma radiation from natural sources is an important component of background radiation, and correlates with childhood leukaemia risk in Great Britain. The geographic variation of indoor gamma radiation dose-rates in Great Britain is explored using various geo-statistical methods. A multi-resolution Gaussian-process model using radial basis functions with 2, 4, or 8 components, is fitted via maximum likelihood, and a non-spatial model is also used, fitted by ordinary least squares. Because of the dataset size (N = 10,199), four other parametric spatial models are fitted by variogram-fitting. A randomly selected 70:30 split is used for fitting:validation. The models are evaluated based on their predictive performance as measured by Mean Absolute Error, Mean Squared Error, as well as Pearson correlation and rank-correlation between predicted and actual dose-rates. Each of the four parametric models (Matérn, Gaussian, Bessel, Spherical) fitted the empirical variogram well, and yielded similar predictions at >50 km separation, although with more substantial differences in predicted variograms at <50 km. The multi-resolution Gaussian-process model with 8 components had the best predictive accuracy among the models considered. The Spherical, Bessel, Matérn, Gaussian and ordinary least squares models had progressively worse predictive performance, the ordinary least squares model being particularly poor in this respect.