Why bootstrapx?

Use bootstrapx when ordinary IID resampling is not enough or when you want one API for IID intervals, block bootstrap, clustered/stratified resampling, Bayesian bootstrap, pandas summaries, and bootstrap cross-validation.

For a simple IID interval for a standard statistic, SciPy may be all you need. bootstrapx is most useful when the resampling design or the surrounding analysis workflow needs to be explicit.

The library keeps resample matrices in bounded batches. The returned bootstrap distribution and some method-specific state still grow with n_resamples or sample size, so this is not a claim of constant total memory.

The audited 0.5.0 experiment suite completed 9,900 interval trials without a failure or invalid result. Across the 15 cells directly matched with SciPy, the mean absolute coverage difference was 0.42 percentage points and the largest was 1.67 points. On the recorded Apple Silicon runtime grid, bootstrapx was 1.26–2.60× faster than SciPy's scalar (vectorized=False) configuration. Against bounded-vectorized SciPy, it was slower for the two small-sample cells and 1.56–2.24× faster for the three larger-sample cells. These machine- and workload-specific measurements are not a blanket performance guarantee. See the benchmark evidence for methods, uncertainty, difficult cases, and reproducible inputs.

Installation

pip install bootstrapx-lib                  # core (numpy + scipy + joblib)
pip install "bootstrapx-lib[pandas]"        # + pandas accessor
pip install "bootstrapx-lib[sklearn]"       # + scikit-learn CV integration
pip install "bootstrapx-lib[numba]"         # + faster MBB/CBB/stationary indexing
pip install "bootstrapx-lib[pandas,sklearn]"  # pandas + scikit-learn integrations
pip install "bootstrapx-lib[pandas,sklearn,numba]"  # all optional features

Quick Start

Basic usage

import numpy as np
from bootstrapx import bootstrap

data = np.random.default_rng(42).normal(5, 2, size=300)

result = bootstrap(data, np.mean, random_state=42)
print(result)

print(result.confidence_interval.low, result.confidence_interval.high)
print(5.0 in result.confidence_interval)  # True

# Compact exports for reports and experiment tracking
print(result.to_dict())
print(result.to_frame())  # requires bootstrapx-lib[pandas]

Independent A/B experiment

import numpy as np
from bootstrapx import bootstrap_two_sample

rng = np.random.default_rng(42)
control = rng.binomial(1, 0.10, size=2_000)
treatment = rng.binomial(1, 0.12, size=2_200)

effect = bootstrap_two_sample(
    control,
    treatment,
    np.mean,
    effect="difference",
    method="bca",
    n_resamples=4_999,
    random_state=42,
)

print(effect.control_estimate, effect.treatment_estimate)
print(effect.estimate, effect.confidence_interval)

This estimates the treatment-minus-control conversion difference directly. Use effect="relative_lift" only when a ratio to the control estimate is scientifically meaningful and the control baseline is safely away from zero.

Complete A/B walkthroughs

Start with the product A/B reference. Its executable notebook defines one primary metric and decision threshold before generating a reproducible user-randomized experiment whose true effect is known.

Then use the Hillstrom real-data case study to see what changes when the truth is unknown and conversion and revenue are sparse. Its notebook verifies the public source and keeps the raw customer-level CSV out of the repository.

pandas accessor

import pandas as pd
import numpy as np
import bootstrapx  # registers .bootstrap accessor

s = pd.Series(np.random.default_rng(0).exponential(scale=2, size=500))

# On a Series
r = s.bootstrap.bca(np.mean, random_state=42)
print(r)

# On a DataFrame — column-wise summary
df = pd.DataFrame({"control": s, "treatment": s * 1.1 + 0.3})
print(df.bootstrap.summary(np.mean, random_state=42))

This DataFrame helper estimates each column separately. It does not estimate the difference or lift between columns. Extract the control and treatment columns and pass them to bootstrap_two_sample() for an experiment effect.

scikit-learn cross-validation

from bootstrapx import BootstrapCV
from sklearn.ensemble import GradientBoostingClassifier
from sklearn.model_selection import cross_val_score
from sklearn.datasets import load_breast_cancer

X, y = load_breast_cancer(return_X_y=True)

cv = BootstrapCV(n_splits=200, random_state=42)
scores = cross_val_score(
    GradientBoostingClassifier(n_estimators=100),
    X, y, cv=cv, scoring="roc_auc"
)
print(f"AUC: {scores.mean():.4f} ± {scores.std():.4f}")

Time-series bootstrap

import numpy as np
from bootstrapx import bootstrap

rng = np.random.default_rng(0)
y = np.zeros(500)
for t in range(1, 500):
    y[t] = 0.7 * y[t-1] + rng.normal()

# Moving Block Bootstrap — preserves serial correlation
result = bootstrap(
    y,
    np.mean,
    method="mbb",
    block_length=15,
    n_resamples=4999,
    random_state=42,
)
print(result)

# Sieve Bootstrap — fits AR(p) model to residuals
result = bootstrap(y, np.mean, method="sieve", n_resamples=9999, random_state=42)
print(result)

A/B test with repeated events per user

import numpy as np
from bootstrapx import bootstrap_two_sample

rng = np.random.default_rng(1)
control_user_ids = np.repeat(np.arange(50), 5)
treatment_user_ids = np.repeat(np.arange(60), 5)
control_events = rng.normal(10.0, 2.0, len(control_user_ids))
treatment_events = rng.normal(10.5, 2.0, len(treatment_user_ids))

result = bootstrap_two_sample(
    control_events,
    treatment_events,
    np.mean,
    effect="difference",
    control_cluster_ids=control_user_ids,
    treatment_cluster_ids=treatment_user_ids,
    method="percentile",
    n_resamples=4_999,
    random_state=42,
)
print(result)

This resamples complete users within each experiment arm. If the estimand is an equally weighted mean per user, aggregate to one row per user first instead.

Bayesian bootstrap with a custom statistic

Bayesian bootstrap evaluates a functional directly under Dirichlet weights. np.mean, np.nanmean, and np.average work without extra configuration. For a custom statistic, provide its weighted form explicitly:

def second_moment(x):
    return np.mean(x**2)

def weighted_second_moment(x, weights):
    return np.sum(weights * x**2)

result = bootstrap(
    data,
    second_moment,
    method="bayesian",
    weighted_statistic=weighted_second_moment,
    random_state=42,
)

Benchmarks

bootstrapx is not faster than SciPy in every regime. The audited 0.4.4 release run on Apple Silicon/macOS 15.7.4, Python 3.11.5, NumPy 2.4.6, and SciPy 1.17.1 found:

Values above 1 mean bootstrapx was faster; below 1 mean SciPy was faster. They are local measurements, not cross-machine guarantees. The complete table, memory-method caveats, arbitrary-callable results, and optional Numba scope are in the benchmark documentation. The versioned raw results and environment metadata live in benchmark_runs/v0.4.4-release.

A matched coverage study completed 160 cells: BCa and percentile intervals for mean, median, and standard deviation over four sample sizes and the documented distributions. Each cell used 300 independently generated datasets and 4,999 resamples; no trial failed or produced an invalid interval. Mean empirical coverage was 94.2% for both libraries, and their largest cell-level difference was 0.67 percentage points. This compares implementations rather than proving nominal coverage in every finite-sample setting: the 95% Wilson interval for a single 300-dataset cell is still about six percentage points wide, and both libraries under-covered the standard deviation of exponential data at n=200.

Run the safe local suite without overwriting previous results:

pip install -e ".[dev,numba]"
python benchmarks/run_release.py --profile quick
python benchmarks/run_comparison_release.py --profile quick

For release-candidate coverage with checkpoints, use --profile release. Commands and resume instructions are in the benchmark documentation.

Documentation

📖 Full docs: artyerokhin.github.io/bootstrapx

• Getting Started
• Methods Guide
• API Reference
• Benchmarks

All supported methods

Contributing

git clone https://github.com/artyerokhin/bootstrapx.git
cd bootstrapx
pip install -e ".[dev,pandas]"
pytest tests/ -v

Citation

If you use bootstrapx in academic work:

@software{bootstrapx,
  author  = {Erokhin, Artem},
  title   = {bootstrapx: Practical bootstrap uncertainty estimation},
  url     = {https://github.com/artyerokhin/bootstrapx},
  version = {0.5.1},
  year    = {2026},
}

License

MIT — see LICENSE.