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'.

Bayesian Analyses for One- and Two-Sample Inference and Regression Methods

Perform fundamental analyses using Bayesian parametric and non-parametric inference (regression, anova, 1 and 2 sample inference, non-parametric tests, etc.). (Practically) no Markov chain Monte Carlo (MCMC) is used; all exact finite sample inference is completed via closed form solutions or else through posterior sampling automated to ensure precision in interval estimate bounds. Diagnostic plots for model assessment, and key inferential quantities (point and interval estimates, probability of direction, region of practical equivalence, and Bayes factors) and model visualizations are provided. Bayes factors are computed either by the Savage Dickey ratio given in Dickey (1971) or by Chib's method as given in . Interpretations are from Kass and Raftery (1995) . ROPE bounds are based on discussions in Kruschke (2018) . Methods for determining the number of posterior samples required are described in Doss et al. (2014) . Bayesian model averaging is done in part by Feldkircher and Zeugner (2015) . Methods for contingency table analysis is described in Gunel et al. (1974) . Variational Bayes (VB) methods are described in Salimans and Knowles (2013) . Mediation analysis uses the framework described in Imai et al. (2010) . The loss-likelihood bootstrap used in the non-parametric regression modeling is described in Lyddon et al. (2019) . Non-parametric survival methods are described in Qing et al. (2023) . Methods used for the Bayesian Wilcoxon signed-rank analysis is given in Chechile (2018) and for the Bayesian Wilcoxon rank sum analysis in Chechile (2020) . Correlation analysis methods are carried out by Barch and Chechile (2023) , and described in Lindley and Phillips (1976) and Chechile and Barch (2021) . See also Chechile (2020, ISBN: 9780262044585).

Bayesian Marginal Effects for 'brms' Models

Calculate Bayesian marginal effects, average marginal effects, and marginal coefficients (also called population averaged coefficients) for models fit using the 'brms' package including fixed effects, mixed effects, and location scale models. These are based on marginal predictions that integrate out random effects if necessary (see for example and ).

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.

Adjust Longitudinal Regression Models Using Bayesian Methodology

Adjusts longitudinal regression models using Bayesian methodology for covariance structures of composite symmetry (SC), autoregressive ones of order 1 AR (1) and autoregressive moving average of order (1,1) ARMA (1,1).

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.

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.

Bayesian Regression Models using 'Stan'

Fit Bayesian generalized (non-)linear multivariate multilevel models using 'Stan' for full Bayesian inference. A wide range of distributions and link functions are supported, allowing users to fit -- among others -- linear, robust linear, count data, survival, response times, ordinal, zero-inflated, hurdle, and even self-defined mixture models all in a multilevel context. Further modeling options include both theory-driven and data-driven non-linear terms, auto-correlation structures, censoring and truncation, meta-analytic standard errors, and quite a few more. In addition, all parameters of the response distribution can be predicted in order to perform distributional regression. Prior specifications are flexible and explicitly encourage users to apply prior distributions that actually reflect their prior knowledge. Models can easily be evaluated and compared using several methods assessing posterior or prior predictions. References: Bürkner (2017) ; Bürkner (2018) ; Bürkner (2021) ; Carpenter et al. (2017) .