The paper by P. J. Diggle, J. A. Tawn, and R. A. Moyeed discusses the extension of geostatistical methods to non-Gaussian data. Conventional geostatistics typically assumes that the data follow a Gaussian distribution, but the authors present two applications where this assumption is clearly inappropriate: assessing residual contamination from nuclear weapons testing on Rongelap Island and modeling spatial variation in campylobacter infections in north Lancashire and south Cumbria. For these applications, they propose a generalized linear mixed model framework, where the observations at sample locations form a generalized linear model with the underlying spatial process as an offset term in the linear predictor. The authors use Markov chain Monte Carlo (MCMC) methods to implement Bayesian inference, allowing for proper accounting of parameter uncertainty in the prediction of non-linear functionals of the spatial process. They also discuss the extension of the variogram, a standard tool in conventional geostatistics, to the more general setting. The paper includes a simulated case study and two real-world examples to illustrate the methodology.The paper by P. J. Diggle, J. A. Tawn, and R. A. Moyeed discusses the extension of geostatistical methods to non-Gaussian data. Conventional geostatistics typically assumes that the data follow a Gaussian distribution, but the authors present two applications where this assumption is clearly inappropriate: assessing residual contamination from nuclear weapons testing on Rongelap Island and modeling spatial variation in campylobacter infections in north Lancashire and south Cumbria. For these applications, they propose a generalized linear mixed model framework, where the observations at sample locations form a generalized linear model with the underlying spatial process as an offset term in the linear predictor. The authors use Markov chain Monte Carlo (MCMC) methods to implement Bayesian inference, allowing for proper accounting of parameter uncertainty in the prediction of non-linear functionals of the spatial process. They also discuss the extension of the variogram, a standard tool in conventional geostatistics, to the more general setting. The paper includes a simulated case study and two real-world examples to illustrate the methodology.