We propose a computationally efficient statistical method to obtain distributional properties of annual maximum 24 hour precipitation on a 1 km by 1 km regular grid over Iceland. A latent Gaussian model is built which takes into account observations, spatial variations and outputs from a local meteorological model. A covariate based on the meteorological model is constructed at each observational site and each grid point in order to assimilate available scientific knowledge about precipitation into the statistical model. The model is applied to two data sets on extreme precipitation, one uncorrected data set and one data set that is corrected for phase and wind. The observations are assumed to follow the generalized extreme value distribution. At the latent level, we implement SPDE spatial models for both the location and scale parameters of the likelihood. An efficient MCMC sampler which exploits the model structure is constructed, which yields fast continuous spatial predictions for spatially varying model parameters and quantiles.

During 30 days follow-up, AMA and WBS patients had an increased rate of repeat ED visits compared with those patients who completed their ED visits. AMA patients also had an increased rate of hospitalisations.

A general and flexible class of latent Gaussian models is proposed in this paper. The latent Gaussian model is adapted to the generalized additive model for location, scale and shape (GAMLSS), that is, the data density function of each data point can depend on more than a single linear predictor of the latent parameters. We refer to this framework as extended latent Gaussian models. The most commonly applied latent Gaussian models (LGMs) are such that a linear predictor is proposed only for the location parameter. Extended LGMs allow proposing linear predictors also for the scale parameter and potentially other parameters. We propose a novel computationally efficient Markov chain Monte Carlo sampling scheme for the extended LGMs which we refer to as the LGM split sampler. It is a two block Gibbs sampling scheme designed to exploit the model structure of the extended LGMs. An extended LGM is constructed for a simulated dataset and the LGM split sampler is implemented for posterior simulations. The results demonstrate the flexibility of the extended LGM framework and the efficiency of the LGM split sampler.

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First of all, we would like to congratulate the author on an interesting paper that we have enjoyed discussing-it has been a pleasure to share our opinions on this topic.The author correctly points out that there is much more out there than 'regression models for the mean', and discusses quantile regression in particular. While we agree with the first statement, from an academic point of view we do not share the enthusiasm about replacing the likelihood model with the generic quantile model. In a Bayesian context, this leads to results that are far from easy to interpret (see Yue and Rue, 2011). In addition, we do not advocate inferential schemes that do not yield good/reasonable estimates for the uncertainty involved. However, we agree that from a practical point of view 'A man's got to do what a man's got to do', and sometimes just providing a (quantile) estimate for a specific dataset by using any reasonable approach with appropriate software is the only thing one can do. Since this is a research discussion, however, the following focuses on how we think things should be done rather than on how things are currently done in practice by applied researchers.Since this paper does not explicitly distinguish between'modelling' and 'inference', it is not clear to us if the author favours the non-parametric quantile approach due to its non-parametric nature or due to the availability of fast inferential algorithms for it. Our general approach to modelling complex problems is to design a sensible statistical model for a specific problem, to then develop a formal Bayesian machinery that is able to provide posterior distributions and to then approximate all the quantities of interest, such as quantiles, means, credible intervals, etc., from these posteriors.Regarding the design of a sensible statistical model, we think that the focus of the paper should not only be on going 'beyond mean regression', also beyond 'beyond mean regression', i.e., with emphasis on regression, in the sense that it is perhaps