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Two-dimensional (2D) nuclear magnetic resonance (nmr) methods have become increasingly popular in metabolomics, since they have considerable potential to accurately identify and quantify metabolites within complex biological samples. 2D 1H J-resolved (jres) nmr spectroscopy is a widely used method that expands overlapping resonances into a second dimension. However, existing analytical processing methods do not fully exploit the information in the jres spectrum and, more importantly, do not provide measures of uncertainty associated with the estimates of quantities of interest, such as metabolite concentration. Combining the data-generating mechanisms and the extensive prior knowledge available in online databases, we develop a Bayesian method to analyse 2D jres data, which allows for automatic deconvolution, identification and quantification of metabolites. The model extends and improves previous work on one-dimensional nmr spectral data. Our approach is based on a combination of B-spline tight wavelet frames and theoretical templates, and thus enables the automatic incorporation of expert knowledge within the inferential framework. Posterior inference is performed through specially devised Markov chain Monte Carlo methods. We demonstrate the performance of our approach via analyses of datasets from serum and urine, showing the advantages of our proposed approach in terms of identification and quantification of metabolites. [ABSTRACT FROM AUTHOR]

In observational studies, estimation of a causal effect of a treatment on an outcome relies on proper adjustment for confounding. If the number of the potential confounders (p) is larger than the number of observations (n), then direct control for all potential confounders is infeasible. Existing approaches for dimension reduction and penalization are generally aimed at predicting the outcome, and are less suited for estimation of causal effects. Under standard penalization approaches (e.g. Lasso), if a variable Xj is strongly associated with the treatment T but weakly with the outcome Y, the coefficient ßj will be shrunk towards zero thus leading to confounding bias. Under the assumption of a linear model for the outcome and sparsity, we propose continuous spike and slab priors on the regression coefficients ßj corresponding to the potential confounders Xj. Specifically, we introduce a prior distribution that does not heavily shrink to zero the coefficients (ßjs) of the Xjs that are strongly associated with T but weakly associated with Y. We compare our proposed approach to several state of the art methods proposed in the literature. Our proposed approach has the following features: 1) it reduces confounding bias in high dimensional settings; 2) it shrinks towards zero coefficients of instrumental variables; and 3) it achieves good coverages even in small sample sizes. We apply our approach to the National Health and Nutrition Examination Survey (NHANES) data to estimate the causal effects of persistent pesticide exposure on triglyceride levels. [ABSTRACT FROM AUTHOR]

There has been an intense development in the Bayesian graphical model literature over the past decade; however, most of the existing methods are restricted to moderate dimensions. We propose a novel graphical model selection approach for large dimensional settings where the dimension increases with the sample size, by decoupling model fitting and covariance selection. First, a full model based on a complete graph is fit under a novel class of mixtures of inverse- Wishart priors, which induce shrinkage on the precision matrix under an equivalence with Cholesky-based regularization, while enabling conjugate updates. Subsequently, a post-fitting model selection step uses penalized joint credible regions to perform model selection. This allows our methods to be computationally feasible for large dimensional settings using a combination of straightforward Gibbs samplers and efficient post-fitting inferences. Theoretical guarantees in terms of selection consistency are also established. Simulations show that the proposed approach compares favorably with competing methods, both in terms of accuracy metrics and computation times. We apply this approach to a cancer genomics data example. [ABSTRACT FROM AUTHOR]