Bayesian Penalized Quantile Regression

Bayesian regularized quantile regression utilizing sparse priors to impose exact sparsity leads to efficient Bayesian shrinkage estimation, variable selection and statistical inference. In this package, we have implemented robust Bayesian variable selection with spike-and-slab priors under high-dimensional linear regression models (Fan et al. (2024) and Ren et al. (2023) ), and regularized quantile varying coefficient models (Zhou et al.(2023) ). In particular, valid robust Bayesian inferences under both models in the presence of heavy-tailed errors can be validated on finite samples. Additional models including robust Bayesian group LASSO and robust Bayesian binary LASSO are also included. The Markov Chain Monte Carlo (MCMC) algorithms of the proposed and alternative models are implemented in C++.

Choice Item Response Theory

Jointly model the accuracy of cognitive responses and item choices within a Bayesian hierarchical framework as described by Culpepper and Balamuta (2015) . In addition, the package contains the datasets used within the analysis of the paper.

Model Selection in Multivariate Longitudinal Data Analysis

An efficient Gibbs sampling algorithm is developed for Bayesian multivariate longitudinal data analysis with the focus on selection of important elements in the generalized autoregressive matrix. It provides posterior samples and estimates of parameters. In addition, estimates of several information criteria such as Akaike information criterion (AIC), Bayesian information criterion (BIC), deviance information criterion (DIC) and prediction accuracy such as the marginal predictive likelihood (MPL) and the mean squared prediction error (MSPE) are provided for model selection.

Utilising Normalisation Constant Optimisation via Edge Removal (UNCOVER)

Model data with a suspected clustering structure (either in co-variate space, regression space or both) using a Bayesian product model with a logistic regression likelihood. Observations are represented graphically and clusters are formed through various edge removals or additions. Cluster quality is assessed through the log Bayesian evidence of the overall model, which is estimated using either a Sequential Monte Carlo sampler or a suitable transformation of the Bayesian Information Criterion as a fast approximation of the former. The internal Iterated Batch Importance Sampling scheme (Chopin (2002 )) is made available as a free standing function.

Contrast-Based Bayesian Network Meta Analysis

A function that facilitates fitting three types of models for contrast-based Bayesian Network Meta Analysis. The first model is that which is described in Lu and Ades (2006) . The other two models are based on a Bayesian nonparametric methods that permit ties when comparing treatment or for a treatment effect to be exactly equal to zero. In addition to the model fits, the package provides a summary of the interplay between treatment effects based on the procedure described in Barrientos, Page, and Lin (2023) .

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'.

Additive Model for Ordinal Data using Laplace P-Splines

Additive proportional odds model for ordinal data using Laplace P-splines. The combination of Laplace approximations and P-splines enable fast and flexible inference in a Bayesian framework. Specific approximations are proposed to account for the asymmetry in the marginal posterior distributions of non-penalized parameters. For more details, see Lambert and Gressani (2023) ; Preprint: ).

Multivariate (Dynamic) Generalized Additive Models

Fit Bayesian Dynamic Generalized Additive Models to multivariate observations. Users can build nonlinear State-Space models that can incorporate semiparametric effects in observation and process components, using a wide range of observation families. Estimation is performed using Markov Chain Monte Carlo with Hamiltonian Monte Carlo in the software 'Stan'. References: Clark & Wells (2023) .

Bayesian Distributed Lag Model Fitting for Binary and Count Response Data

Tools for fitting Bayesian Distributed Lag Models (DLMs) to longitudinal response data that is a count or binary. Count data is fit using negative binomial regression and binary is fit using quantile regression. The contribution of the lags are fit via b-splines. In addition, infers the predictor inclusion uncertainty. Multimomial models are not supported. Based on Dempsey and Wyse (2025) .

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.