Browsing by Subject "MCMC"

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    Learning Hamiltonian Monte Carlo in R
    (Taylor & Francis, 2021) Thomas, Samuel; Tu, Wanzhu; Biostatistics, School of Public Health
    Hamiltonian Monte Carlo (HMC) is a powerful tool for Bayesian computation. In comparison with the traditional Metropolis–Hastings algorithm, HMC offers greater computational efficiency, especially in higher dimensional or more complex modeling situations. To most statisticians, however, the idea of HMC comes from a less familiar origin, one that is based on the theory of classical mechanics. Its implementation, either through Stan or one of its derivative programs, can appear opaque to beginners. A lack of understanding of the inner working of HMC, in our opinion, has hindered its application to a broader range of statistical problems. In this article, we review the basic concepts of HMC in a language that is more familiar to statisticians, and we describe an HMC implementation in R, one of the most frequently used statistical software environments. We also present hmclearn, an R package for learning HMC. This package contains a general-purpose HMC function for data analysis. We illustrate the use of this package in common statistical models. In doing so, we hope to promote this powerful computational tool for wider use. Example code for common statistical models is presented as supplementary material for online publication.
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    Robust Bayesian variable selection for gene-environment interactions
    (Wiley, 2022-06) Ren, Jie; Zhou, Fei; Li, Xiaoxi; Ma, Shuangge; Jiang, Yu; Wu, Cen; Biostatistics and Health Data Science, School of Medicine
    Gene–environment (G× E) interactions have important implications to elucidate the etiology of complex diseases beyond the main genetic and environmental effects. Outliers and data contamination in disease phenotypes of G× E studies have been commonly encountered, leading to the development of a broad spectrum of robust regularization methods. Nevertheless, within the Bayesian framework, the issue has not been taken care of in existing studies. We develop a fully Bayesian robust variable selection method for G× E interaction studies. The proposed Bayesian method can effectively accommodate heavy-tailed errors and outliers in the response variable while conducting variable selection by accounting for structural sparsity. In particular, for the robust sparse group selection, the spike-and-slab priors have been imposed on both individual and group levels to identify important main and interaction effects robustly. An efficient Gibbs sampler has been developed to facilitate fast computation. Extensive simulation studies, analysis of diabetes data with single-nucleotide polymorphism measurements from the Nurses' Health Study, and The Cancer Genome Atlas melanoma data with gene expression measurements demonstrate the superior performance of the proposed method over multiple competing alternatives.