Bayesium 0.0.0

A Python package for Bayesian Inference modeling and diagnostics.

Bayesian Inference for Python

A unified probabilistic programming library, bringing JAX-powered Bayesian inference to the Python, R and Julia ecosystem.
Run bespoke models on CPU, GPU, or TPU with Julia's native syntax.

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One Mental Model. Three Languages.

BayesianInference (BI) provides a unified experience across Julia, Python, and R. 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 across all implementations.
• ✅ NumPyro Power: All interfaces compile down to XLA via JAX for blazing fast inference.
• ✅ Rich Diagnostics: Seamless integration with ArviZ for posterior analysis.

Compare the Syntax

Python Syntax	Julia Syntax	R Syntax
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	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) }

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Built for Speed

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

Benchmark: Network Size 400 (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 Python

Download and install Python 3.10 or later

2. Install Package

From pip

pip install BayesInference

Development Installation

pip install git+https://github.com/BGN-for-ASNA/BI.git

Or clone the repository and activate it locally:

git clone https://github.com/BGN-for-ASNA/BI.git
cd BI

Then in Python:

pip install -e .

3. Initialize Environment

from BI import bi
m = bi()

4. Select Backend

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

# Initialize on CPU (default)
m = bi(platform="cpu")

# Or on GPU (requires JAX GPU installation)
m = bi(platform="gpu")

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Quick Start

from BI import bi

# Initialize BI
m = bi()

# Generate some data
x = m.dist.normal(0, 1, shape=(100,), sample=True)
y = m.dist.normal(0.2 + 0.6 * x, 1.2, sample=True)

# Define a Bayesian linear regression model
def linear_model(x, y):
    alpha = m.dist.normal(loc=0, scale=1, name="alpha")
    beta  = m.dist.normal(loc=0, scale=1, name="beta")
    sigma = m.dist.exponential(1, name="sigma")
    mu = alpha + beta * x
    m.dist.normal(mu, sigma, obs=y)


# Fit the model
m.fit(linear_model, num_warmup=1000, num_samples=1000, num_chains=1)

# Display results
m.summary()

# Plot results with @pyplot
m.plot_trace()

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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

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

Discrete

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

Multivariate

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

Time Series & Stochastic Processes

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

Mixtures & Truncated

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

(See package documentation for the full list)

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Documentation

For full documentation and examples:

# See the Quick Start guide
# QUICKSTART.md

# Explore example notebooks
# test/usage_example.ipynb

For help with specific functions in the underlying BI library, refer to the BayesianInference documentation.

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Platform Support

• ✅ Linux
• ✅ macOS
• ✅ Windows

GPU support available on compatible systems with JAX GPU installation.

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Related Packages

• BIR - R implementation
• BIJ - Julia implementation

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**BayesianInference**\ Based on "The Bayesian Inference library for Python, R, Julia" by [Sosa, McElreath, & Ross (2026)](https://www.biorxiv.org/content/10.64898/2026.01.19.700318v1).

Official website | Issues | Quick Start

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