Number of Newly Discovered Rare Species Estimation

A Bayesian-weighted estimator and two unweighted estimators are developed to estimate the number of newly found rare species in additional ecological samples. Among these methods, the Bayesian-weighted estimator and an unweighted (Chao-derived) estimator are of high accuracy and recommended for practical applications. Technical details of the proposed estimators have been well described in the following paper: Shen TJ, Chen YH (2018) A Bayesian weighted approach to predicting the number of newly discovered rare species. Conservation Biology, In press.

Generalized Additive Mixed Model Interface

An interface for fitting generalized additive models (GAMs) and generalized additive mixed models (GAMMs) using the 'lme4' package as the computational engine, as described in Helwig (2024) . Supports default and formula methods for model specification, additive and tensor product splines for capturing nonlinear effects, and automatic determination of spline type based on the class of each predictor. Includes an S3 plot method for visualizing the (nonlinear) model terms, an S3 predict method for forming predictions from a fit model, and an S3 summary method for conducting significance testing using the Bayesian interpretation of a smoothing spline.

Causal Inference using Bayesian Causal Forests

Causal inference for a binary treatment and continuous outcome using Bayesian Causal Forests. See Hahn, Murray and Carvalho (2020) for additional information. This implementation relies on code originally accompanying Pratola et. al. (2013) .

Computer Model Calibration for Deterministic and Stochastic Simulators

Implements the Bayesian calibration model described in Pratola and Chkrebtii (2018) for stochastic and deterministic simulators. Additive and multiplicative discrepancy models are currently supported. See < http://www.matthewpratola.com/software> for more information and examples.

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 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'.