Bayesian Inference Reimagined for R, Python and Julia

One Mental Model. Three Languages.

BayesianInference (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

model <- function(height, weight){
  # Priors
  sigma = bi.dist.uniform(0, 50, name='sigma', shape=c(1))
  alpha = bi.dist.normal(178, 20, name='alpha', shape=c(1))
  beta  = bi.dist.normal(0, 1, name='beta', shape=c(1))

  # Likelihood
  mu = alpha + beta * weight
  bi.dist.normal(mu, sigma, obs=height)
}

def model(height, weight):
    # Priors
    sigma = bi.dist.uniform(0, 50, name='sigma', shape=(1,))
    alpha = bi.dist.normal(178, 20, name='alpha', shape=(1,))
    beta  = bi.dist.normal(0, 1, name='beta', shape=(1,))

    # Likelihood
    mu = alpha + beta * weight
    bi.dist.normal(mu, sigma, obs=height)

@BI function model(weight, height)
    # Priors
    sigma = bi.dist.uniform(0, 50, name='sigma', shape=(1,))
    alpha = bi.dist.normal(178, 20, name='alpha', shape=(1,))
    beta  = bi.dist.normal(0, 1, name='beta', shape=(1,))

    # Likelihood
    mu = alpha + beta * weight
    bi.dist.normal(mu, sigma, obs=height)
end

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)

> Comparison of execution time for a Social Relations Model. Source: Sosa et al. (2025).

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(BayesianInference)
# Run the starting test to install Python dependencies
BI_starting_test()

3. Select Backend

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

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

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).

Available Distributions

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

Continuous

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

Discrete

• bi.dist.bernoulli, bi.dist.binomial
• bi.dist.poisson, bi.dist.negative_binomial
• bi.dist.geometric, bi.dist.discrete_uniform
• bi.dist.beta_binomial, bi.dist.zero_inflated_poisson

Multivariate

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

Time Series & Stochastic Processes

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

Mixtures & Truncated

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

(See package documentation for the full list)

Documentation

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

# Open package documentation
bi.doc()

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

Platform Support

• ✅ Linux
• ✅ macOS
• ✅ Windows

GPU support available on compatible systems with JAX GPU installation.

Related Packages

• BI - Python implementation
• BIJ - J implementation