Estimating, Visualizing, and Testing Average Dose-Response Functions

Facilitates estimating, visualizing, and testing average dose-response functions (ADRFs) for characterizing the causal effect of a continuous (i.e., non-discrete) treatment or exposure. Includes support for frequentist and Bayesian regression models, analytical and bootstrap inference, and characterization of subgroup effects.

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) .

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.

Robust Bayesian Meta-Analyses

A framework for Bayesian meta-analysis, including model estimation, prior specification, model comparison, prediction, summaries, visualizations, and diagnostics. The package fits single and model-averaged meta-analytic, meta-regression, multilevel, publication bias adjusted, and generalized linear mixed models The model-averaged meta-analytic models combine competing models based on their predictive performance, weight inference by posterior model probabilities, and test model components using Bayes factors (e.g., effect vs. no effect; Bartoš et al., 2022, ; Maier, Bartoš & Wagenmakers, 2022, ; Bartoš et al., 2025, ). Users can specify flexible prior distributions for effect sizes, heterogeneity, publication bias (including selection models and PET-PEESE), and moderators.

Variational Mixture Models for Clustering Categorical Data

A variational Bayesian finite mixture model for the clustering of categorical data, and can implement variable selection and semi-supervised outcome guiding if desired. Incorporates an option to perform model averaging over multiple initialisations to reduce the effects of local optima and improve the automatic estimation of the true number of clusters. For further details, see the paper by Rao and Kirk (2024) .

Hierarchical Modeling and Frequency Method Checking on Overdispersed Gaussian, Poisson, and Binomial Data

We utilize approximate Bayesian machinery to fit two-level conjugate hierarchical models on overdispersed Gaussian, Poisson, and Binomial data and evaluates whether the resulting approximate Bayesian interval estimates for random effects meet the nominal confidence levels via frequency coverage evaluation. The data that Rgbp assumes comprise observed sufficient statistic for each random effect, such as an average or a proportion of each group, without population-level data. The approximate Bayesian tool equipped with the adjustment for density maximization produces approximate point and interval estimates for model parameters including second-level variance component, regression coefficients, and random effect. For the Binomial data, the package provides an option to produce posterior samples of all the model parameters via the acceptance-rejection method. The package provides a quick way to evaluate coverage rates of the resultant Bayesian interval estimates for random effects via a parametric bootstrapping, which we call frequency method checking.