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.

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) .

Mixed GAM Computation Vehicle with Automatic Smoothness Estimation

Generalized additive (mixed) models, some of their extensions and other generalized ridge regression with multiple smoothing parameter estimation by (Restricted) Marginal Likelihood, Cross Validation and similar, or using iterated nested Laplace approximation for fully Bayesian inference. See Wood (2025) for an overview. Includes a gam() function, a wide variety of smoothers, 'JAGS' support and distributions beyond the exponential family.

Linear Mixed-Effects Models using 'Eigen' and S4

Fit linear and generalized linear mixed-effects models. The models and their components are represented using S4 classes and methods. The core computational algorithms are implemented using the 'Eigen' C++ library for numerical linear algebra and 'RcppEigen' "glue".

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.

MCMC, Particle Filtering, and Programmable Hierarchical Modeling

A system for writing hierarchical statistical models largely compatible with 'BUGS' and 'JAGS', writing nimbleFunctions to operate models and do basic R-style math, and compiling both models and nimbleFunctions via custom-generated C++. 'NIMBLE' includes default methods for MCMC, Laplace Approximation, deterministic nested approximations, Monte Carlo Expectation Maximization, and some other tools. The nimbleFunction system makes it easy to do things like implement new MCMC samplers from R, customize the assignment of samplers to different parts of a model from R, and compile the new samplers automatically via C++ alongside the samplers 'NIMBLE' provides. 'NIMBLE' extends the 'BUGS'/'JAGS' language by making it extensible: New distributions and functions can be added, including as calls to external compiled code. Although most people think of MCMC as the main goal of the 'BUGS'/'JAGS' language for writing models, one can use 'NIMBLE' for writing arbitrary other kinds of model-generic algorithms as well. A full User Manual is available at < https://r-nimble.org>.

Simulate, Evaluate, and Analyze Dose Finding Trials with Bayesian MCPMod

Bayesian MCPMod (Fleischer et al. (2022) ) is an innovative method that improves the traditional MCPMod by systematically incorporating historical data, such as previous placebo group data. This package offers functions for simulating, analyzing, and evaluating Bayesian MCPMod trials with normally and binary distributed endpoints. It enables the assessment of trial designs incorporating historical data across various true dose-response relationships and sample sizes. Robust mixture prior distributions, such as those derived with the Meta-Analytic-Predictive approach (Schmidli et al. (2014) ), can be specified for each dose group. Resulting mixture posterior distributions are used in the Bayesian Multiple Comparison Procedure and modeling steps. The modeling step also includes a weighted model averaging approach (Pinheiro et al. (2014) ). Estimated dose-response relationships can be bootstrapped and visualized.

A Shiny Application for End-to-End Bayesian Decision Network Analysis and Web-Deployment

A Shiny application for learning Bayesian Decision Networks from data. This package can be used for probabilistic reasoning (in the observational setting), causal inference (in the presence of interventions) and learning policy decisions (in Decision Network setting). Functionalities include end-to-end implementations for data-preprocessing, structure-learning, exact inference, approximate inference, extending the learned structure to Decision Networks and policy optimization using statistically rigorous methods such as bootstraps, resampling, ensemble-averaging and cross-validation. In addition to Bayesian Decision Networks, it also features correlation networks, community-detection, graph visualizations, graph exports and web-deployment of the learned models as Shiny dashboards.

Neural AutoRegressive Fractionally Integrated Moving Average Model

Methods and tools for forecasting univariate time series using the NARFIMA (Neural AutoRegressive Fractionally Integrated Moving Average) model. It combines neural networks with fractional differencing to capture both nonlinear patterns and long-term dependencies. The NARFIMA model supports seasonal adjustment, Box-Cox transformations, optional exogenous variables, and the computation of prediction intervals. In addition to the NARFIMA model, this package provides alternative forecasting models including NARIMA (Neural ARIMA), NBSTS (Neural Bayesian Structural Time Series), and NNaive (Neural Naive) for performance comparison across different modeling approaches. The methods are based on algorithms introduced by Chakraborty et al. (2025) .