Bayesian Inference Reimagined for R, Python and Julia

A unified probabilistic programming library bridging the gap between user-friendly R syntax and high-performance JAX computation.
Run bespoke models on CPU, GPU, or TPU with ease.

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One Mental Model. Three Languages.

BFR (BI) provides a unified experience across R, Python, and Julia. Whether you work in R's formula syntax, Python's object-oriented approach, or Julia's mathematical elegance, the model logic remains consistent.

• ✅ Zero Context Switching: Variable names, distribution signatures, and model logic remain consistent.
• ✅ NumPyro Power: Both interfaces compile down to XLA via JAX for blazing fast inference.
• ✅ Rich Diagnostics: Seamless integration with ArviZ for posterior analysis.

Compare the Syntax

R Syntax	Python Syntax	Julia Syntax
model <- function(height, weight){ # Priors sigma = bf.dist.uniform(0, 50, name='sigma', shape=c(1)) alpha = bf.dist.normal(178, 20, name='alpha', shape=c(1)) beta = bf.dist.normal(0, 1, name='beta', shape=c(1)) # Likelihood mu = alpha + beta * weight bf.dist.normal(mu, sigma, obs=height) }	def model(height, weight): # Priors sigma = bf.dist.uniform(0, 50, name='sigma', shape=(1,)) alpha = bf.dist.normal(178, 20, name='alpha', shape=(1,)) beta = bf.dist.normal(0, 1, name='beta', shape=(1,)) # Likelihood mu = alpha + beta * weight bf.dist.normal(mu, sigma, obs=height)	@BI function model(weight, height) # Priors sigma = bf.dist.uniform(0, 50, name='sigma', shape=(1,)) alpha = bf.dist.normal(178, 20, name='alpha', shape=(1,)) beta = bf.dist.normal(0, 1, name='beta', shape=(1,)) # Likelihood mu = alpha + beta * weight bf.dist.normal(mu, sigma, obs=height) end

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Built for Speed

Leveraging Just-In-Time (JIT) compilation, BI outperforms traditional engines on standard hardware and unlocks massive scalability on GPU clusters for large datasets.

Benchmark: Network Size 100 (Lower is Better)

Engine	Execution Time	Relative Performance
STAN (CPU)	████████████████████████████	Baseline
BI (CPU)	████████████	~30x Faster
BI (GPU)	██	~200x Faster

> Comparison of execution time for a Social Relations Model. Source: Sosa et al. (2026).

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Installation & Setup

1. Install Package

Use devtools to pull the latest development version from GitHub.

if (!requireNamespace("devtools", quietly = TRUE)) install.packages("devtools")
devtools::install_github("https://github.com/BGN-for-ASNA/BIR")

2. Initialize Environment

Run the starting test to create the Python virtual environment managed by reticulate.

library(BayesForge)
# Run the starting test to install Python dependencies
BF_starting_test()

3. Select Backend

Choose 'cpu', 'gpu', or 'tpu' when importing the library.

# Initialize on CPU (default) or GPU/TPU
m <- importBF(platform = 'cpu')

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Features

Data Manipulation

• One-hot encoding
• Index variable conversion
• Scaling and normalization

Modeling (via NumPyro)

• Linear & Generalized Linear Models: Regression, Binomial, Poisson, Negative Binomial, etc.
• Hierarchical/Multilevel Models: Varying intercepts and slopes.
• Time Series & Processes: Gaussian Processes, Gaussian Random Walks, State Space Models.
• Mixture Models: GMM, Dirichlet Process Mixtures.
• Network Models: Network-based diffusion, Block models.
• Bayesian Neural Networks (BNN).

Diagnostics (via ArviZ)

• Posterior summary statistics and plots.
• Trace plots, Density plots, Autocorrelation.
• WAIC and LOO (ELPD) model comparison.
• R-hat and Effective Sample Size (ESS).

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Available Distributions

The package provides wrappers for a comprehensive set of distributions from NumPyro.

Continuous

• bf.dist.normal, bf.dist.uniform, bf.dist.student_t
• bf.dist.cauchy, bf.dist.halfcauchy, bf.dist.halfnormal
• bf.dist.gamma, bf.dist.inverse_gamma, bf.dist.exponential
• bf.dist.beta, bf.dist.beta_proportion
• bf.dist.laplace, bf.dist.asymmetric_laplace
• bf.dist.log_normal, bf.dist.log_uniform
• bf.dist.pareto, bf.dist.weibull, bf.dist.gumbel
• bf.dist.chi2, bf.dist.gompertz

Discrete

• bf.dist.bernoulli, bf.dist.bfnomial
• bf.dist.poisson, bf.dist.negative_binomial
• bf.dist.geometric, bf.dist.discrete_uniform
• bf.dist.beta_binomial, bf.dist.zero_inflated_poisson

Multivariate

• bf.dist.multivariate_normal, bf.dist.multivariate_student_t
• bf.dist.dirichlet, bf.dist.dirichlet_multinomial
• bf.dist.multinomial
• bf.dist.lkj, bf.dist.lkj_cholesky
• bf.dist.wishart, bf.dist.wishart_cholesky

Time Series & Stochastic Processes

• bf.dist.gaussian_random_walk
• bf.dist.gaussian_state_space
• bf.dist.euler_maruyama
• bf.dist.car (Conditional AutoRegressive)

Mixtures & Truncated

• bf.dist.mixture, bf.dist.mixture_same_family
• bf.dist.truncated_normal, bf.dist.truncated_cauchy
• bf.dist.lower_truncated_power_law

(See package documentation for the full list)

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Documentation

For full documentation of functions and parameters, you can use the built-in R help or the package helper:

# Open package documentation
bf.doc()

# Help for a specific function
?bf.dist.normal

Platform Support

• ✅ Linux
• ✅ macOS
• ✅ Windows

GPU support available on compatible systems with JAX GPU installation.

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Related Packages

• BF - Python implementation
• BFJ - J implementation

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BFR
Based on "The Bayesian Inference library for Python, R, Julia" by Sosa, McElreath, & Ross (2026).

Official website | Issues | Quick Start

© 2026 Bayesian Inference Team. Released under GPL-3.0.