bbstat

A lightweight library for Bayesian bootstrapping and statistical evaluation designed for learning, experimentation, and exploring Bayesian nonparametric ideas.

The Bayesian bootstrap (Rubin, 1981) is a simple nonparametric Bayesian method for estimating uncertainty in statistics without assuming a likelihood model. It replaces resampling with random Dirichlet-distributed weights on the observed data, producing a posterior-like distribution for any statistic (mean, quantile, regression, etc.). Results reflect uncertainty in the weights (not in unobserved data) and are asymptotically similar to the classical bootstrap. Assumes i.i.d. data; results may be overconfident if the sample is small or unrepresentative.

This package implements the core logic of Bayesian bootstrapping in Python, along with a few weighted statistic functions, as a way to learn and experiment with Bayesian nonparametric ideas. It's meant as an educational and exploratory project rather than a production-ready library, but may be useful for understanding or demonstrating how Bayesian bootstrap inference works in practice.

Why use this package?

• Learn and experiment with Bayesian bootstrap inference in Python
• Quickly compute posterior-like uncertainty intervals for arbitrary statistics
• Extend easily with your own weighted statistic functions

Installation

• From PyPI:

pip install bbstat

• From GitHub source code:

git clone https://github.com/cwehmeyer/bbstat.git
cd bbstat
pip install .

Quickstart

import numpy as np
from bbstat import bootstrap

# Data preparation: simulated income for a small population (e.g., a survey of 25 people)
income = np.array([
    24_000, 26_000, 28_000, 30_000, 32_000,
    35_000, 36_000, 38_000, 40_000, 41_000,
    45_000, 48_000, 50_000, 52_000, 54_000,
    58_000, 60_000, 62_000, 65_000, 68_000,
    70_000, 75_000, 80_000, 90_000, 100_000,
], dtype=np.float64)

# Direct estimate of mean income
print(np.mean(income))  # => 52280.0

# Bootstrapped distribution of the mean income.
distribution = bootstrap(data=income, statistic_fn="mean", seed=1)
print(distribution)  # => BootstrapDistribution(mean=52263.8..., size=1000)

# Summarize the bootstrapped distribution of the mean income.
summary = distribution.summarize(level=0.87)
print(summary)  # => BootstrapSummary(mean=52263.8..., ci_low=46566.8..., ci_high=58453.6..., level=0.87)
print(summary.round())  # => BootstrapSummary(mean=52000.0, ci_low=47000.0, ci_high=58000.0, level=0.87)

API Overview

bootstrap(data, statistic_fn, n_boot=1000, ...)

Performs Bayesian bootstrapping on data using the given statistic.

Parameters

• data: 1D NumPy array, or tuple/list of arrays
• statistic_fn: string or callable (e.g. "mean", "median", or custom function)
• n_boot: number of bootstrap samples
• seed: random seed (optional)
• blocksize: number of resamples processed per block
• n_jobs: number of worker threads for parallel computation
• fn_kwargs: optional dict of extra parameters for statistic_fn

Returns

A BootstrapDistribution object with:

• .estimates: array of bootstrapped statistic values
• .summarize(level, precision): returns a BootstrapSummary with mean, ci_low, ci_high, and level; rounded if precision is integer-valued or "auto"

Weighted statistic functions included

The module bbstat.statistics includes several univariate and bivariate weighted statistics, such as:

• "mean" – compute_weighted_mean(data, weights)
• "median" – compute_weighted_median(data, weights)
• "quantile" / "percentile"
• "variance" / "std" / "sum"
• "entropy" / "log_odds" / "probability" / "self_information"
• "pearson_dependence" / "spearman_dependence"
• "eta_square_dependency" / "mutual_information"

You can also supply your own functions following this pattern:

def custom_statistic(data, weights, **kwargs) -> float:
    ...

where:

• data: 1D NumPy array or tuple/list of 1D arrays
• weights: 1D NumPy array of non-negative values summing to 1
• **kwargs: optional keyword arguments passed by fn_kwargs

If you want to use your own custom functions, please adhere to this pattern.

License

This project is licensed under the MIT License.

Contributing

Contributions are welcome! Please open an issue or submit a pull request.