Belief propagation methods in Bayesian Networks to propagate evidence through the network. The implementation of these methods are based on the article: Cowell, RG (2005). Local Propagation in Conditional Gaussian Bayesian Networks <https://www.jmlr.org/papers/v6/cowell05a.html>. For details please see Yu et. al. (2020) BayesNetBP: An R Package for Probabilistic Reasoning in Bayesian Networks <doi:10.18637/jss.v094.i03>. The optional cyjShiny package for running the Shiny app is available at <https://github.com/cytoscape/cyjShiny>. Please see the example in the documentation of runBayesNetApp function for installing cyjShiny package from GitHub.

Bayesian Latent Class Analysis using several different methods.

Bayesian kernel machine regression (from the bkmr package) is a Bayesian semi-parametric generalized linear model approach under identity and probit links. There are a number of functions in this package that extend Bayesian kernel machine regression fits to allow multiple-chain inference and diagnostics, which leverage functions from the future', rstan', and coda packages. Reference: Bobb, J. F., Henn, B. C., Valeri, L., & Coull, B. A. (2018). Statistical software for analyzing the health effects of multiple concurrent exposures via Bayesian kernel machine regression. ; <doi:10.1186/s12940-018-0413-y>.

Comprehensive toolkit for valid spatial, temporal, and grouped model evaluation. Automatically detects data dependencies (spatial autocorrelation, temporal structure, clustered observations), generates appropriate cross-validation schemes (spatial blocking, checkerboard, hexagonal, KNNDM, environmental blocking, leave-location-out, purged CV), and validates evaluation pipelines for leakage. Includes area of applicability (AOA) assessment following Meyer & Pebesma (2021) <doi:10.1111/2041-210X.13650>, forward feature selection with blocked CV, spatial thinning, block-permutation variable importance, extrapolation detection, and interactive visualizations. Integrates with tidymodels', caret', mlr3', ENMeval', and biomod2'. Based on evaluation principles described in Roberts et al. (2017) <doi:10.1111/ecog.02881>, Kaufman et al. (2012) <doi:10.1145/2382577.2382579>, Kapoor & Narayanan (2023) <doi:10.1016/j.patter.2023.100804>, and Linnenbrink et al. (2024) <doi:10.5194/gmd-17-5897-2024>.

This package implements the Bayesian Clustering Factor Models (BCFM) for simultaneous clustering and latent factor analysis of multivariate longitudinal data. The model accounts for within-cluster dependence through shared latent factors while allowing heterogeneity across clusters, enabling flexible covariance modeling in high-dimensional settings. Inference is performed using Markov chain Monte Carlo (MCMC) methods with computationally intensive steps implemented via Rcpp'. Model selection and visualization tools are provided. The methodology is described in Shin, Ferreira, and Tegge (2018) <doi:10.1002/sim.70350>.

Download data from the time-series databases of the Bundesbank, the German central bank. See the overview at the Bundesbank website (<https://www.bundesbank.de/en/statistics/time-series-databases>) for available series. The package provides only a single function, getSeries(), which supports both traditional and real-time datasets; it will also download meta data if available. Downloaded data can automatically be arranged in various formats, such as data frames or zoo series. The data may optionally be cached, so as to avoid repeated downloads of the same series.

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) <doi:10.1214/aoms/1177693507> or by Chib's method as given in xxx. Interpretations are from Kass and Raftery (1995) <doi:10.1080/01621459.1995.10476572>. ROPE bounds are based on discussions in Kruschke (2018) <doi:10.1177/2515245918771304>. Methods for determining the number of posterior samples required are described in Doss et al. (2014) <doi:10.1214/14-EJS957>. Bayesian model averaging is done in part by Feldkircher and Zeugner (2015) <doi:10.18637/jss.v068.i04>. Methods for contingency table analysis is described in Gunel et al. (1974) <doi:10.1093/biomet/61.3.545>. Variational Bayes (VB) methods are described in Salimans and Knowles (2013) <doi:10.1214/13-BA858>. Mediation analysis uses the framework described in Imai et al. (2010) <doi:10.1037/a0020761>. The loss-likelihood bootstrap used in the non-parametric regression modeling is described in Lyddon et al. (2019) <doi:10.1093/biomet/asz006>. Non-parametric survival methods are described in Qing et al. (2023) <doi:10.1002/pst.2256>. Methods used for the Bayesian Wilcoxon signed-rank analysis is given in Chechile (2018) <doi:10.1080/03610926.2017.1388402> and for the Bayesian Wilcoxon rank sum analysis in Chechile (2020) <doi:10.1080/03610926.2018.1549247>. Correlation analysis methods are carried out by Barch and Chechile (2023) <doi:10.32614/CRAN.package.DFBA>, and described in Lindley and Phillips (1976) <doi:10.1080/00031305.1976.10479154> and Chechile and Barch (2021) <doi:10.1016/j.jmp.2021.102638>. See also Chechile (2020, ISBN: 9780262044585).

Decomposition of time series into trend, seasonal, and remainder components with methods for detecting and characterizing abrupt changes within the trend and seasonal components. BFAST can be used to analyze different types of satellite image time series and can be applied to other disciplines dealing with seasonal or non-seasonal time series, such as hydrology, climatology, and econometrics. The algorithm can be extended to label detected changes with information on the parameters of the fitted piecewise linear models. BFAST monitoring functionality is described in Verbesselt et al. (2010) <doi:10.1016/j.rse.2009.08.014>. BFAST monitor provides functionality to detect disturbance in near real-time based on BFAST'- type models, and is described in Verbesselt et al. (2012) <doi:10.1016/j.rse.2012.02.022>. BFAST Lite approach is a flexible approach that handles missing data without interpolation, and will be described in an upcoming paper. Furthermore, different models can now be used to fit the time series data and detect structural changes (breaks).

This package provides functionality for determining the sample size of replication studies using Bayesian design approaches in the normal-normal hierarchical model (Pawel et al., 2022) <doi:10.48550/arXiv.2211.02552>.

Fits and simulates multi-optima Ornstein-Uhlenbeck models to phylogenetic comparative data using Bayesian reversible-jump methods. See Uyeda and Harmon (2014) <DOI:10.1093/sysbio/syu057>.

Bayesian adaptive trial algorithm implements multiple-stage interim analysis. Package includes data generating function, and Bayesian hypothesis testing function.

This package provides a high-performance probabilistic programming library that aims to unify the modeling experience by providing an intuitive model-building syntax together with the flexibility of low-level abstraction coding. It also includes pre-built functions for high-level abstraction and supports hardware-accelerated computation for improved scalability, including parallelization, vectorization, and execution on CPU (Central Processing Unit), GPU (Graphics Processing Unit), or TPU (Tensor Processing Unit) using JAX (Just-In-Time compiled Accelerated linear algebra) as the computational backend: Sosa (2026) <doi:10.64898/2026.01.19.700318>.

Computation of the minimum sample size using the Average Coverage Criterion or the Average Length Criterion for estimating binomial proportions using beta prior distributions. For more details see Costa (2025) <DOI:10.1007/978-3-031-72215-8_14>.

This package provides methods for piecewise smooth regression. A piecewise smooth signal is estimated by applying a bootstrapped test recursively (binary segmentation approach). Each bootstrapped test decides whether the underlying signal is smooth on the currently considered subsegment or contains at least one further change-point.

Bumblebee colonies grow during worker production, then decline after switching to production of reproductive individuals (drones and gynes). This package provides tools for modeling and visualizing this pattern by identifying a switchpoint with a growth rate before and a decline rate after the switchpoint. The mathematical models fit by bumbl are described in Crone and Williams (2016) <doi:10.1111/ele.12581>.

Generating multiple binary and normal variables simultaneously given marginal characteristics and association structure based on the methodology proposed by Demirtas and Doganay (2012) <DOI:10.1080/10543406.2010.521874>.

Prior transcription factor binding knowledge and target gene expression data are integrated in a Bayesian framework for functional cis-regulatory module inference. Using Gibbs sampling, we iteratively estimate transcription factor associations for each gene, regulation strength for each binding event and the hidden activity for each transcription factor.

Implementation of the record linkage methodology proposed by Sadinle (2017) <doi:10.1080/01621459.2016.1148612>. It handles the bipartite record linkage problem, where two duplicate-free datafiles are to be merged.

This package provides a Bayesian framework for estimating distributed lag linear and non-linear models. Model fitting is implemented using Integrated Nested Laplace Approximation (R package INLA'), together with prediction and visualization of exposure-lag-response associations. Additional functions allow estimation of optimal exposure values (e.g., minimum mortality temperature) and computation of attributable fractions and numbers. Models with crossbasis or onebasis terms are supported (R package dlnm').

Fit computational and measurement models using full Bayesian inference. The package provides a simple and accessible interface by translating complex domain-specific models into brms syntax, a powerful and flexible framework for fitting Bayesian regression models using Stan'. The package is designed so that users can easily apply state-of-the-art models in various research fields, and so that researchers can use it as a new model development framework. References: Frischkorn and Popov (2025) <doi:10.3758/s13428-025-02643-0>.

This package provides methods for detecting and visualizing cladogenic shifts in multivariate trait data on phylogenies. Implements penalized-likelihood multivariate generalized least squares models, enabling analyses of high-dimensional trait datasets and large trees via searchOptimalConfiguration(). Includes a greedy step-wise shift-search algorithm following approaches developed in Smith et al. (2023) <doi:10.1111/nph.19099> and Berv et al. (2024) <doi:10.1126/sciadv.adp0114>. Methods build on multivariate GLS approaches described in Clavel et al. (2019) <doi:10.1093/sysbio/syy045> and implemented in the mvgls() function from the mvMORPH package. Documentation and vignettes are available at <https://jakeberv.com/bifrost/>, including worked examples for the jaw-shape dataset.

This package performs Bayesian sample size, precision, and value-of-information analysis for external validation of existing multi-variable prediction models using the approach proposed by Sadatsafavi and colleagues (2026) <doi:10.1002/sim.70389>.

Bayesian methods for predicting the calendar time at which a target number of events is reached in clinical trials. The methodology applies to both blinded and unblinded settings and jointly models enrollment, event-time, and censoring processes. The package provides tools for trial data simulation, model fitting using Stan via the rstan interface, and event time prediction under a wide range of trial designs, including varying sample sizes, enrollment patterns, treatment effects, and event or censoring time distributions. The package is intended to support interim monitoring, operational planning, and decision-making in clinical trial development. Methods are described in Fu et al. (2025) <doi:10.1002/sim.70310>.

The Bayesian Adjustment for Confounding (BAC) algorithm (Wang et al., 2012) can be used to estimate the causal effect of a continuous exposure on a continuous outcome. This package provides an approximate sensitivity analysis of BAC with regards to the hyperparameter omega. BACprior also provides functions to guide the user in their choice of an appropriate omega value. The method is based on Lefebvre, Atherton and Talbot (2014).