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: ).

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'.

Multivariate (Dynamic) Generalized Additive Models

Fit Bayesian Dynamic Generalized Additive Models to sets of time series. Users can build dynamic 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 (2022) .

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.

Reference Analysis for Bayesian Meta-Analysis

Functionality for performing a principled reference analysis in the Bayesian normal-normal hierarchical model used for Bayesian meta-analysis, as described in Ott, Plummer and Roos (2021) . Computes a reference posterior, induced by a minimally informative improper reference prior for the between-study (heterogeneity) standard deviation. Determines additional proper anti-conservative (and conservative) prior benchmarks. Includes functions for reference analyses at both the posterior and the prior level, which, given the data, quantify the informativeness of a heterogeneity prior of interest relative to the minimally informative reference prior and the proper prior benchmarks. The functions operate on data sets which are compatible with the 'bayesmeta' package.

Extracting and Visualizing Bayesian Graphical Models

Fit and visualize the results of a Bayesian analysis of networks commonly found in psychology. The package supports fitting cross-sectional network models fitted using the packages 'BDgraph', 'bgms' and 'BGGM'. The package provides the parameter estimates, posterior inclusion probabilities, inclusion Bayes factor, and the posterior density of the parameters. In addition, for 'BDgraph' and 'bgms' it allows to assess the posterior structure space. Furthermore, the package comes with an extensive suite for visualizing results.

Sparse Generalized Additive Models

Fits sparse frequentist GAMs (SF-GAM) for continuous and discrete responses in the exponential dispersion family with the group lasso, group smoothly clipped absolute deviation (SCAD), and group minimax concave (MCP) penalties . Also fits sparse Bayesian generalized additive models (SB-GAM) with the spike-and-slab group lasso (SSGL) penalty of Bai et al. (2021) . B-spline basis functions are used to model the sparse additive functions. Stand-alone functions for group-regularized negative binomial regression, group-regularized gamma regression, and group-regularized regression in the exponential dispersion family with the SSGL penalty are also provided.

Stepwise Elimination and Term Reordering for Mixed-Effects Regression

Finds the largest possible regression model that will still converge for various types of regression analyses (including mixed models and generalized additive models) and then optionally performs stepwise elimination similar to the forward and backward effect-selection methods in SAS, based on the change in log-likelihood or its significance, Akaike's Information Criterion, the Bayesian Information Criterion, the explained deviance, or the F-test of the change in R².

Bayesian Analysis of Finite Mixtures of Plackett-Luce Models for Partial Rankings/Orderings

Fit finite mixtures of Plackett-Luce models for partial top rankings/orderings within the Bayesian framework. It provides MAP point estimates via EM algorithm and posterior MCMC simulations via Gibbs Sampling. It also fits MLE as a special case of the noninformative Bayesian analysis with vague priors. In addition to inferential techniques, the package assists other fundamental phases of a model-based analysis for partial rankings/orderings, by including functions for data manipulation, simulation, descriptive summary, model selection and goodness-of-fit evaluation. Main references on the methods are Mollica and Tardella (2017) and Mollica and Tardella (2014) .

Bayesian Penalized Quantile Regression

The quantile varying coefficient model is robust to data heterogeneity, outliers and heavy-tailed distributions in the response variable due to the check loss function in quantile regression. In addition, it can flexibly model the dynamic pattern of regression coefficients through nonparametric varying coefficient functions. Although high dimensional quantile varying coefficient model has been examined extensively in the frequentist framework, the corresponding Bayesian variable selection methods have rarely been developed. In this package, we have implemented the Gibbs samplers of the penalized Bayesian quantile varying coefficient model with the spike-and-slab priors [Zhou et al.(2023)]. The Markov Chain Monte Carlo (MCMC) algorithms of the proposed and alternative models can be efficiently performed by using the package.