A Variational Bayesian algorithm for high-dimensional multi-source 
    heterogeneous linear models. More details have been written up in a paper 
    submitted to the journal Statistics in Medicine, and the details of variational
    Bayesian methods can be found in Ray and Szabo (2021) <doi:10.1080/01621459.2020.1847121>.
    It simultaneously performs parameter estimation and variable selection. The 
    algorithm supports two model settings: (1) local models, where variable selection
    is only applied to homogeneous coefficients, and (2) global models, where variable
    selection is also performed on heterogeneous coefficients. Two forms of 
    Spike-and-Slab priors are available: the Laplace distribution and the Gaussian 
    distribution as the Slab component.

Identification of Latent Patient Phenotype from Electronic Health Records (EHR) Data using Variational Bayes Gaussian Mixture Model for Latent Class Analysis and Variational Bayes regression for Biomarker level shifts, both implemented by Coordinate Ascent Variational Inference algorithms.  Variational methods are used to enable Bayesian analysis of very large Electronic Health Records data. For VB GMM details see Bishop (2006,ISBN:9780-387-31073-2). For Logistic VB see Jaakkola and Jordan (2000) <doi:10.1023/A:1008932416310>. Please see preprint of JSS-submitted paper <doi:10.48550/arXiv.2512.14272>.

Add publication-quality custom legends with vertical brackets. Designed for displaying statistical comparisons between groups,
    commonly used in scientific publications for showing significance levels.
    Features include adaptive positioning, automatic bracket spacing for overlapping
    comparisons, font family inheritance, and support for asterisks, p-values,
    or custom labels. Compatible with 'ggplot2' graphics.

Contains functions for a variational Bayesian method for sparse PCA proposed by Ning (2020) <arXiv:2102.00305>. There are two algorithms: the PX-CAVI algorithm (if assuming the loadings matrix is jointly row-sparse) and the batch PX-CAVI algorithm (if without this assumption). The outputs of the main function, VBsparsePCA(), include the mean and covariance of the loadings matrix, the score functions, the variable selection results, and the estimated variance of the random noise.