Discussion of ‘Beyond mean regression’

Abstract

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

LGM Split Sampler: An Efficient MCMC Sampling Scheme for Latent Gaussian Models

“…This paper focuses specifically on LGMs where the data density function of each data point can depend on more than a single linear predictor of the latent parameters, as discussed in Martins et al (2013b). We refer to this framework as extended LGMs when the need for such clarity is necessary.…”

“…However, R-INLA only provides support for LGMs in which the data density of each data point only depends on a single linear predictor of the latent parameters, although the INLA idea has already been reimplemented in a special case of an extended LGM; see (Ferkingstad et al, 2008). The extension of INLA to extended LGMs might seem trivial but it is not (Martins et al, 2013b). Thus, in order to provide an efficient framework for extended LGMs we propose a novel efficient Markov chain Monte Carlo (MCMC) inferential algorithm which is adapted to extended LGMs.…”