Bayesian Mediation Analysis with High-Dimensional Data

Mediation analysis is used to identify and quantify intermediate effects from factors that intervene the observed relationship between an exposure/predicting variable and an outcome. We use a Bayesian adaptive lasso method to take care of the hierarchical structures and high dimensional exposures or mediators.

Dependent Gaussian Processes for Longitudinal Correlated Factors

Functionalities for analyzing high-dimensional and longitudinal biomarker data to facilitate precision medicine, using a joint model of Bayesian sparse factor analysis and dependent Gaussian processes. This paper illustrates the method in detail: J Cai, RJB Goudie, C Starr, BDM Tom (2023) .

Distribution-Free Bayesian Analysis

A set of functions to perform distribution-free Bayesian analyses. Included are Bayesian analogues to the frequentist Mann-Whitney U test, the Wilcoxon Signed-Ranks test, Kendall's Tau Rank Correlation Coefficient, Goodman and Kruskal's Gamma, McNemar's Test, the binomial test, the sign test, the median test, as well as distribution-free methods for testing contrasts among condition and for computing Bayes factors for hypotheses. The package also includes procedures to estimate the power of distribution-free Bayesian tests based on data simulations using various probability models for the data. The set of functions provide data analysts with a set of Bayesian procedures that avoids requiring parametric assumptions about measurement error and is robust to problem of extreme outlier scores.

Large-Scale Bayesian Variable Selection Using Variational Methods

Fast algorithms for fitting Bayesian variable selection models and computing Bayes factors, in which the outcome (or response variable) is modeled using a linear regression or a logistic regression. The algorithms are based on the variational approximations described in "Scalable variational inference for Bayesian variable selection in regression, and its accuracy in genetic association studies" (P. Carbonetto & M. Stephens, 2012, ). This software has been applied to large data sets with over a million variables and thousands of samples.

Algorithm for Searching the Space of Gaussian Directed Acyclic Graph Models Through Moment Fractional Bayes Factors

We propose an objective Bayesian algorithm for searching the space of Gaussian directed acyclic graph (DAG) models. The algorithm proposed makes use of moment fractional Bayes factors (MFBF) and thus it is suitable for learning sparse graph. The algorithm is implemented by using Armadillo: an open-source C++ linear algebra library.

Bayes Factors for Hierarchical Linear Models with Continuous Predictors

Runs hierarchical linear Bayesian models. Samples from the posterior distributions of model parameters in JAGS (Just Another Gibbs Sampler; Plummer, 2017, < http://mcmc-jags.sourceforge.net>). Computes Bayes factors for group parameters of interest with the Savage-Dickey density ratio (Wetzels, Raaijmakers, Jakab, Wagenmakers, 2009, ).

Omega-Generic: Composite Reliability of Multidimensional Measures

It is a computer tool to estimate the item-sum score's reliability (composite reliability, CR) in multidimensional scales with overlapping items. An item that measures more than one domain construct is called an overlapping item. The estimation is based on factor models allowing unlimited cross-factor loadings such as exploratory structural equation modeling (ESEM) and Bayesian structural equation modeling (BSEM). The factor models include correlated-factor models and bi-factor models. Specifically for bi-factor models, a type of hierarchical factor model, the package estimates the CR hierarchical subscale/hierarchy and CR subscale/scale total. The CR estimator 'Omega-generic' was proposed by Mai, Srivastava, and Krull (2021) < https://whova.com/embedded/subsession/enars_202103/1450751/1452993/>. The current version can only handle continuous data. Yujiao Mai contributes to the algorithms, R programming, and application example. Deo Kumar Srivastava contributes to the algorithms and the application example. Kevin R. Krull contributes to the application example. The package 'OmegaG' was sponsored by American Lebanese Syrian Associated Charities (ALSAC). However, the contents of 'OmegaG' do not necessarily represent the policy of the ALSAC.

Bayesian Informative Hypotheses Evaluation Web Applications

Researchers often have expectations about the relations between means of different groups or standardized regression coefficients; using informative hypothesis testing to incorporate these expectations into the analysis through order constraints increases statistical power Vanbrabant and Rosseel (2020) . Another valuable tool, the Bayes factor, can evaluate evidence for multiple hypotheses without concerns about multiple testing, and can be used in Bayesian updating Hoijtink, Mulder, van Lissa & Gu (2019) . The 'bain' R package enables informative hypothesis testing using the Bayes factor. The 'mmibain' package provides 'shiny' web applications based on 'bain'. The RepliCrisis() function launches a 'shiny' card game to simulate the evaluation of replication studies while the mmibain() function launches a 'shiny' application to fit Bayesian informative hypotheses evaluation models from 'bain'.

A Multistate Life Table (MSLT) Methodology Based on Bayesian Approach

Create life tables with a Bayesian approach, which can be very useful for modelling a complex health process when considering multiple predisposing factors and multiple coexisting health conditions. Details for this method can be found in: Lynch, Scott, et al., (2022) ; Zang, Emma, et al., (2022) .

Perform Tensor-on-Tensor Regression

Functions to predict one multi-way array (i.e., a tensor) from another multi-way array, using a low-rank CANDECOMP/PARAFAC (CP) factorization and a ridge (L_2) penalty [Lock, EF (2018) ]. Also includes functions to sample from the Bayesian posterior of a tensor-on-tensor model.