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.

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.

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'.

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.

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 R package offers functions for simulating, analyzing, and evaluating Bayesian MCPMod trials with normally 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.