rejection-sampler 0.1.1

A statistical computing toolkit for validating proposal distributions and computing optimal rejection-sampling constants.

rejection-sampler

A small Python package for validating rejection sampling setups and computing the optimal rejection constant (M). The package supports both callable Python functions and symbolic SymPy expressions for target and proposal PDFs.

Installation

pip install rejection-sampler
# or 
uv add rejection-sampler

Usage

Import the main function:

from rejection_sampler import find_optimal_M

Example 1: Callable input

def target_pdf(x):
    return 2 * x if 0 <= x <= 1 else 0.0

def proposal_pdf(x):
    return 1.0 if 0 <= x <= 1 else 0.0

M = find_optimal_M(
    target_pdf=target_pdf,
    target_support=(0.0, 1.0),
    proposal_pdf=proposal_pdf,
    proposal_support=(0.0, 1.0),
)

print(M)

Example 2: SymPy input

import sympy as sp

x = sp.Symbol("x", real=True)

target_pdf = 2 * x
proposal_pdf = sp.Integer(1)

M = find_optimal_M(
    target_pdf=target_pdf,
    target_support=(0, 1),
    proposal_pdf=proposal_pdf,
    proposal_support=(0, 1),
)

print(M)

Infinite support

For numerical inputs with infinite support, provide finite optimization bounds:

import numpy as np
from rejection_sampler import find_optimal_M

def target_pdf(x):
    return np.exp(-0.5 * x * x) / np.sqrt(2 * np.pi)

def proposal_pdf(x):
    return 1.0 / (np.pi * (1 + x * x))

M = find_optimal_M(
    target_pdf=target_pdf,
    target_support=(-np.inf, np.inf),
    # or use (-float("inf"), float("inf")) for infinite support
    proposal_pdf=proposal_pdf,
    proposal_support=(-np.inf, np.inf),
    bounds=(-10.0, 10.0),
)

print(M)

Parameters

• target_pdf: target probability density function, either callable or SymPy expression
• target_support: support of the target PDF
• proposal_pdf: proposal probability density function, either callable or SymPy expression
• proposal_support: support of the proposal PDF
• error: numerical tolerance for validation
• bounds: search interval for numerical optimization for pdfs with infinite support

Note

• When writing mathemtatical expressions (eg. exp, log, sqrt, inf), use numpy instead of the built-in math module.
• Provide a sufficiently large bounds to ensure correctness of optimization and prevent finding local optima.

License

This project is licensed under the MIT License.