Plotting for Bayesian Models

Plotting functions for posterior analysis, MCMC diagnostics, prior and posterior predictive checks, and other visualizations to support the applied Bayesian workflow advocated in Gabry, Simpson, Vehtari, Betancourt, and Gelman (2019) . The package is designed not only to provide convenient functionality for users, but also a common set of functions that can be easily used by developers working on a variety of R packages for Bayesian modeling, particularly (but not exclusively) packages interfacing with 'Stan'.

Gaussian Mixture Modelling for Model-Based Clustering, Classification, and Density Estimation

Gaussian finite mixture models fitted via EM algorithm for model-based clustering, classification, and density estimation, including Bayesian regularization, dimension reduction for visualisation, and resampling-based inference.

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.

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.

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) .