Hierarchical models are increasingly used in many applications. Along with this increased use comes a desire to investigate whether the model is compatible with the observed data. Bayesian methods are well suited to eliminate the many (nuisance) parameters in these complicated models; in this paper we investigate Bayesian methods for model checking. Since we contemplate model checking as a preliminary, exploratory analysis, we concentrate on objective Bayesian methods in which careful specification of an informative prior distribution is avoided. Numerous examples are given and different proposals are investigated and critically compared.Comment: This paper commented in: [arXiv:0802.0746], [arXiv:0802.0747], [arXiv:0802.0749], [arXiv:0802.0752]. Rejoinder in [arXiv:0802.0754]. Published in at http://dx.doi.org/10.1214/07-STS235 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Gastrointestinal parasites have evolved with humans and colonize many asymptomatic subjects. We investigated the influence of microbial gastrointestinal colonization on the nutritional status of rural Amerindians (40 males and 61 females). Helicobacter pylori was detected by 13C-breath test, and intestinal parasites were detected in fecal specimens. Body morphometry and bioelectrical impedance measurements were measured. Although Amerindians showed low height and weight for age, they had an adequate body mass index, morphometric parameters, and cell mass. Intestinal parasites were detected in 99% of the subjects, with no detrimental effect on nutritional parameters. Helicobacter pylori was present in 82% of adults and half the children, and was positively correlated with improved nutritional status. Despite the high prevalence of gastrointestinal microbes often associated with disease, the studied population of Amerindians had a body morphometry and composition indicative of good nutritional status, and improved in children positive for gastric H. pylori.

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