Welcome to Bayesian Inference (BI)

An open-source library for Python, R and Julia

Scalable - Built on top of Numpyro, TensorFlow Probability and Jax, for cpu, gpu and tpu vectorization and parallelization.

Flexibility trade-offs - low-level abstraction coding available but also pre-build function for high-level of abstraction.

Unified - One framework for both Python and R.

Accessibility - 30 documented models.

Intuitive - model-building syntax.

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One Mental Model. Three Languages.

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.

Compare the Syntax

Python 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)

R 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)
}

Julia Syntax

@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

A Unified, Scalable, and Accessible Framework

Pipeline

from BI import bi

# Setup device------------------------------------------------
m = bi(platform='cpu') # cpu, gpu or : tuple

# Import Data ------------------------------------------------
m.data(data_path) 

# Define model ------------------------------------------------
def model(arg1,argb2):
   pass

# Run mcmc ------------------------------------------------
m.fit(model) 

# Summary ------------------------------------------------
m.summary()

# Diagnostics ------------------------------------------------
m.diag()

Full Model definition

def model(kcal_per_g, index_clade):
    alpha = m.bi.dist.normal(0, 0.5, shape=(4,), name = 'a') # shape based on the number of clades
    beta = m.bi.dist.normal(0, 0.5, shape=(4,), name = 'b')
    sigma = m.bi.dist.exponential( 1, name = 's')    
    mu = a[index_clade]+b[index_clade]*mass
    m.normal(mu, s, obs=kcal_per_g)

Prebuilt function

def model(kcal_per_g, index_clade):
    a = m.dist.normal(5, 2,  name = 'a')
    b = m.dist.normal(-1, 0.5, name = 'b')
    sigma = m.dist.exponential( 1,  name = 'sigma')

    varying_intercept, varying_slope = m.effects.varying_effects(
      N_group = N_cafes,
      group = cafe,
      global_intercept= a,
      global_slope= b,
      group_name = 'cafe'
    )

Model to Latex

#| label: model-to-latex
#| results: hold
#| echo: true
from BI import bi
m = bi(platform='cpu')

# define model ------------------------------------------------
def model(weight, height):    
    alpha = m.dist.normal( 178, 20, name = 'a')
    beta = m.dist.log_normal( 0, 1, name = 'b')   
    sigma = m.dist.uniform( 0, 50, name = 's')
    m.dist.normal(alpha + beta * weight , sigma, obs=height)

# Run sampler ------------------------------------------------
m.model = model
m.latex()

\begin{aligned} height &\sim \text{Normal}(\alpha + \beta * weight, \sigma) \\ \sigma &\sim \text{Uniform}(0, 50) \\ \beta &\sim \text{LogNormal}(0, 1) \\ \alpha &\sim \text{Normal}(178, 20) \end{aligned}

Distributions visualization

from BI import bi
m = bi()
m.dist.normal( 0, 1, name = 'a', shape=(100,2, 4), sample = True, to_jax = False).hist()

jax.local_device_count 16

Gallery