Adjust Longitudinal Regression Models Using Bayesian Methodology

Adjusts longitudinal regression models using Bayesian methodology for covariance structures of composite symmetry (SC), autoregressive ones of order 1 AR (1) and autoregressive moving average of order (1,1) ARMA (1,1).

High-Dimensional Model Selection

Model selection and averaging for regression, generalized linear models, generalized additive models, graphical models and mixtures, focusing on Bayesian model selection and information criteria (Bayesian information criterion etc.). See Rossell (2025) (see the URL field below for its URL) for a hands-on book describing the methods, examples and suggested citations if you use the package.

Combining Subset MCMC Samples to Estimate a Posterior Density

See Miroshnikov and Conlon (2014) . Recent Bayesian Markov chain Monto Carlo (MCMC) methods have been developed for big data sets that are too large to be analyzed using traditional statistical methods. These methods partition the data into non-overlapping subsets, and perform parallel independent Bayesian MCMC analyses on the data subsets, creating independent subposterior samples for each data subset. These independent subposterior samples are combined through four functions in this package, including averaging across subset samples, weighted averaging across subsets samples, and kernel smoothing across subset samples. The four functions assume the user has previously run the Bayesian analysis and has produced the independent subposterior samples outside of the package; the functions use as input the array of subposterior samples. The methods have been demonstrated to be useful for Bayesian MCMC models including Bayesian logistic regression, Bayesian Gaussian mixture models and Bayesian hierarchical Poisson-Gamma models. The methods are appropriate for Bayesian hierarchical models with hyperparameters, as long as data values in a single level of the hierarchy are not split into subsets.

Bayesian Estimation of ARIMAX Model

The Autoregressive Integrated Moving Average (ARIMA) model is very popular univariate time series model. Its application has been widened by the incorporation of exogenous variable(s) (X) in the model and modified as ARIMAX by Bierens (1987) . In this package we estimate the ARIMAX model using Bayesian framework.

Bayesian Additive Regression Trees for Confounder Selection

Fit Bayesian Regression Additive Trees (BART) models to select true confounders from a large set of potential confounders and to estimate average treatment effect. For more information, see Kim et al. (2023) .

Bayesian Optimal INterval (BOIN) Design for Single-Agent and Drug- Combination Phase I Clinical Trials

The Bayesian optimal interval (BOIN) design is a novel phase I clinical trial design for finding the maximum tolerated dose (MTD). It can be used to design both single-agent and drug-combination trials. The BOIN design is motivated by the top priority and concern of clinicians when testing a new drug, which is to effectively treat patients and minimize the chance of exposing them to subtherapeutic or overly toxic doses. The prominent advantage of the BOIN design is that it achieves simplicity and superior performance at the same time. The BOIN design is algorithm-based and can be implemented in a simple way similar to the traditional 3+3 design. The BOIN design yields an average performance that is comparable to that of the continual reassessment method (CRM, one of the best model-based designs) in terms of selecting the MTD, but has a substantially lower risk of assigning patients to subtherapeutic or overly toxic doses. For tutorial, please check Yan et al. (2020) .

Tidy Methods for Bayesian Treatment Effect Models

Functions for extracting tidy data from Bayesian treatment effect models, in particular BART, but extensions are possible. Functionality includes extracting tidy posterior summaries as in 'tidybayes' < https://github.com/mjskay/tidybayes>, estimating (average) treatment effects, common support calculations, and plotting useful summaries of these.

Estimate Causal Effects with Borrowing Between Data Sources

Estimate population average treatment effects from a primary data source with borrowing from supplemental sources. Causal estimation is done with either a Bayesian linear model or with Bayesian additive regression trees (BART) to adjust for confounding. Borrowing is done with multisource exchangeability models (MEMs). For information on BART, see Chipman, George, & McCulloch (2010) . For information on MEMs, see Kaizer, Koopmeiners, & Hobbs (2018) .

Bayesian Model for CACE Analysis

Performs CACE (Complier Average Causal Effect analysis) on either a single study or meta-analysis of datasets with binary outcomes, using either complete or incomplete noncompliance information. Our package implements the Bayesian methods proposed in Zhou et al. (2019) , which introduces a Bayesian hierarchical model for estimating CACE in meta-analysis of clinical trials with noncompliance, and Zhou et al. (2021) , with an application example on Epidural Analgesia.

Efficient Leave-One-Out Cross-Validation and WAIC for Bayesian Models

Efficient approximate leave-one-out cross-validation (LOO) for Bayesian models fit using Markov chain Monte Carlo, as described in Vehtari, Gelman, and Gabry (2017) . The approximation uses Pareto smoothed importance sampling (PSIS), a new procedure for regularizing importance weights. As a byproduct of the calculations, we also obtain approximate standard errors for estimated predictive errors and for the comparison of predictive errors between models. The package also provides methods for using stacking and other model weighting techniques to average Bayesian predictive distributions.