Approximate Bayesian Computation by Modelling Summary Statistics in a Quasi-likelihood Framework

Approximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy between prior and posterior. Therefore, more elaborate methods, such as ABC with the Markov chain Monte Carlo algorithm (ABC-MCMC), should be used. However, the elaboration of a proposal density for MCMC is a sensitive issue and very difficult in the ABC setting, where the likelihood is intractable. We discuss an automatic proposal distribution useful for ABC-MCMC algorithms. This proposal is inspired by the theory of quasi-likelihood (QL) functions and is obtained by modelling the distribution of the summary statistics as a function of the parameters. Essentially, given a real-valued vector of summary statistics, we reparametrize the model by means of a regression function of the statistics on parameters, obtained by sampling from the original model in a pilot-run simulation study. The QL theory is well established for a scalar parameter, and it is shown that when the conditional variance of the summary statistic is assumed constant, the QL has a closed-form normal density. This idea of constructing proposal distributions is extended to non constant variance and to real-valued parameter vectors. The method is illustrated by several examples and by an application to a real problem in population genetics.Comment: Published at http://dx.doi.org/10.1214/14-BA921 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

Helicobacter pylori and intestinal parasites are not detrimental to the nutritional status of Amerindians

Gastrointestinal parasites have evolved with humans and colonize many asymptomatic subjects. We in- vestigated 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. Helico- bacter 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