The paper revisits the Bayesian group lasso and uses spike and slab priors for group variable selection. In the process, the connection of our model with penalized regression is demonstrated, and the role of posterior median for thresholding is pointed out. We show that the posterior median estimator has the oracle property for group variable selection and estimation under orthogonal designs, while the group lasso has suboptimal asymptotic estimation rate when variable selection consistency is achieved. Next we consider bi-level selection problem and propose the Bayesian sparse group selection again with spike and slab priors to select variables both at the group level and also within a group. We demonstrate via simulation that the posterior median estimator of our spike and slab models has excellent performance for both variable selection and estimation.
C6 compounds are the major fraction of the volatile profiles of grape berries, contributing the typical 'green' aroma to the grape and wine. Hydroperoxide lyase (HPL) catalyzes the cleavage of fatty acid hydroperoxides to produce C6 compounds. Two hypothetical genes, VvHPL1 and VvHPL2 were cloned from grape berries (Vitis vinifera L. Cabernet Sauvignon). Bioinformatics analysis revealed that the proteins encoded by these two genes both belong to subfamily of cytochrome P450 and contain typical conserved domains of HPLs, and have high identity with HPLs from other plants. Prokaryotically-expressed VvHPL1 and VvHPL2 with thioredoxin-6xHis-fusion partner were confirmed to have enzymatic activity. VvHPL1 is specific for 13-HPOD (T) producing C6 aldehydes with relatively higher activity and VvHPL2 catalyzes the cleavage of both 9- and 13-hydroperoxides producing C6 aldehydes and C9 aldehydes respectively. Analysis of real time-PCR showed that VvHPL2 was highly expressed in the leaves and the flowers of the grapes, while relatively low transcript abundance was detected in the berries, tendril and stems; VvHPL1 had high expression in all detected tissues. During grape berry development, the expression of these two isogenes presented similar trends with a rapid increase after veraison and a decrease at full-ripen stage, which roughly corresponded to the accumulation of their volatile products. These data lay an essential foundation for further study on the accumulation and control of C6 volatiles in grape berries.
In this paper, we consider Bayesian variable selection problem of linear regression model with global-local shrinkage priors on the regression coefficients. We propose a variable selection procedure that select a variable if the ratio of the posterior mean to the ordinary least square estimate of the corresponding coefficient is greater than 1/2. Under the assumption of orthogonal designs, we show that if the local parameters have polynomialtailed priors, our proposed method enjoys the oracle property in the sense that it can achieve variable selection consistency and optimal estimation rate at the same time. However, if, instead, an exponential-tailed prior is used for the local parameters, the proposed method does not have the oracle property.
Self-esteem has been associated with neural responses to self-reflection and attitude toward social feedback but in different brain regions. The distinct associations might arise from different tasks or task-related attitudes in the previous studies. The current study aimed to clarify these by investigating the association between self-esteem and neural responses to evaluation of one’s own personality traits and of others’ opinion about one’s own personality traits. We scanned 25 college students using functional MRI during evaluation of oneself or evaluation of social feedback. Trait self-esteem was measured using the Rosenberg self-esteem scale after scanning. Whole-brain regression analyses revealed that trait self-esteem was associated with the bilateral orbitofrontal activity during evaluation of one’s own positive traits but with activities in the medial prefrontal cortex, posterior cingulate, and occipital cortices during evaluation of positive social feedback. Our findings suggest that trait self-esteem modulates the degree of both affective processes in the orbitofrontal cortex during self-reflection and cognitive processes in the medial prefrontal cortex during evaluation of social feedback.
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