Bayesian Inference

Beta version of 'Bayesian Inference' (BI) using 'python' and BI. It 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, GPU, or TPU.

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