Why bootstrapx?

scipy.stats.bootstrap covers 3 CI types and only iid data. The R boot package is comprehensive but not Pythonic. bootstrapx bridges this gap.

Installation

pip install bootstrapx-lib                  # core (numpy + scipy only)
pip install "bootstrapx-lib[pandas]"        # + pandas accessor
pip install "bootstrapx-lib[sklearn]"       # + scikit-learn CV integration
pip install "bootstrapx-lib[pandas,sklearn]"  # all integrations

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)
print(result)
# BootstrapResult(method='bca', theta_hat=4.97, se=0.11, CI=[4.75, 5.19])

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

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)
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))
#              theta_hat    ci_low   ci_high        se method
# column
# control       1.9973    1.8215    2.1862    0.0941    bca
# treatment     2.4970    2.3036    2.7048    0.1035    bca

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}")
# AUC: 0.9921 ± 0.0071

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)
print(result)

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

A/B test with clustered data

import numpy as np
from bootstrapx import bootstrap

n_clusters = 50
cluster_ids = np.repeat(np.arange(n_clusters), 20)
rng = np.random.default_rng(1)
data = rng.normal(loc=cluster_ids * 0.1, scale=1.0)

result = bootstrap(
    data, np.mean,
    method="cluster",
    cluster_ids=cluster_ids,
    n_resamples=4999,
)
print(result)
# Correctly wider CI that accounts for within-cluster correlation

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,
)

Performance

Measured on Apple M1, Python 3.12, n_resamples=4 999, median of 5 runs. Run yourself: python benchmarks/bench_speed.py --quick

BCa (bias-corrected and accelerated):

At n < 1 000, scipy and bootstrapx are comparable; bootstrapx applies a vectorised fast path for numpy built-ins (mean, median, std, etc.) at n < 500. Speedup grows with sample size due to O(n) vectorised jackknife vs O(n²) in scipy.

Coverage accuracy

BCa empirical coverage at nominal 95%, 1 000 Monte Carlo simulations across normal, log-normal, exponential and t(3) distributions: bootstrapx matches scipy to within simulation noise (< 0.01) for mean and median.

Note: BCa coverage for np.std on heavy-tailed distributions (exponential) is ~91–93% at n = 200 — identical behaviour in both bootstrapx and scipy. This reflects known instability of jackknife acceleration for scale statistics, not a library-specific issue. Use n_resamples ≥ 9 999 or method="studentized" for better coverage when estimating variance.

Run yourself: python benchmarks/bench_coverage_accuracy.py --fast

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: Production-grade bootstrap uncertainty estimation},
  url     = {https://github.com/artyerokhin/bootstrapx},
  version = {0.4.2},
  year    = {2026},
}

License

MIT — see LICENSE.