Bootmedian

Bootmedian estimates robust statistics (median, mean, sum, std) via bootstrapping and returns confidence intervals for the estimates.

This package provides a small set of utilities centered on the bootmedian() function in bootmedian/main.py to compute bootstrapped statistics and an API to run bootstrap-based linear fits.

Highlights

• Robust medians: estimate medians using bootstrap resampling.
• Confidence intervals: returns 1σ, 2σ and 3σ up/down limits for estimates.
• Multiple modes: compute median, mean, std or sum via the mode argument.
• Weighted resampling: supports sample weights in resampling.

Table of Contents

• Overview: short summary and behavior
• Installation: dependencies and install
• Quickstart: minimal usage examples
• API Reference: main functions and parameters
• Notes & Contactn+ Overview

bootmedian() takes a 1-D array-like input and performs nsimul bootstrap resamples. By default it computes the median of each resample and returns the median of that distribution together with percentile-based confidence intervals for 1σ, 2σ and 3σ. NaN values in the input are ignored.

Typical return (dictionary):

• median: median of the bootstrap distribution (or mean/std/sum depending on mode).
• s1_up, s1_down: 1σ upward and downward limits (percentiles).
• s2_up, s2_down: 2σ limits.
• s3_up, s3_down: 3σ limits.
• std1_up, std1_down: optional percentiles of the raw sample (if std provided).
• sims: the full bootstrap simulation array (useful for diagnostics).

Installation

Requirements: Python 3.8+ and the dependencies listed in setup.py / pyproject.toml.

Install editable (dev) mode from the project root:

pip install -e .

Or install via pip (from PyPI when published):

pip install Bootmedian

Quickstart

Example: compute the bootstrapped median and 1/2/3σ intervals for a sample:

import numpy as np
from bootmedian import bootmedian

data = np.array([1.0, 2.1, 2.3, np.nan, 3.5, 2.0])
result = bootmedian(data, nsimul=2000, errors=1, verbose=True)
print(result)
# -> dict with keys: 'median','s1_up','s1_down',...,'sims'

Using weights:

weights = np.array([1, 1, 2, 1, 1, 1.5])
result_w = bootmedian(data, nsimul=2000, weights=weights)

Change the statistic with mode ("median", "mean", "std", "sum"):

# Bootmedian

Bootmedian estimates robust statistics (median, mean, sum, std) via
bootstrapping and returns confidence intervals for the estimates.

This package provides utilities centered on the `bootmedian()` function in
`bootmedian/bootmedian.py` to compute bootstrapped statistics and an API to run
bootstrap-based linear fits.

Highlights

- Robust medians: estimate medians using bootstrap resampling.
- Confidence intervals: returns 1σ, 2σ and 3σ up/down limits for estimates.
- Multiple modes: compute `median`, `mean`, `std` or `sum` via the `mode` argument.
- Weighted resampling: supports sample weights in resampling.

Table of contents

- Overview
- Installation
- Quickstart
- API reference
- Notes & contact

Overview

`bootmedian()` takes a 1-D array-like input and performs `nsimul` bootstrap
resamples. By default it computes the median of each resample and returns the
median of that distribution together with percentile-based confidence intervals
for 1σ, 2σ and 3σ. NaN values in the input are ignored.

Typical return (dictionary)

- `median`: median of the bootstrap distribution (or mean/std/sum depending on `mode`).
- `s1_up`, `s1_down`: 1σ upward and downward limits (percentiles).
- `s2_up`, `s2_down`: 2σ limits.
- `s3_up`, `s3_down`: 3σ limits.
- `std1_up`, `std1_down`: optional percentiles of the raw sample (if `std` provided).
- `sims`: the full bootstrap simulation array (useful for diagnostics).

Installation

Requirements: Python 3.8+ and the dependencies listed in `setup.py` / `pyproject.toml`.

Install in editable (development) mode from the project root:

```bash
pip install -e .

Quickstart

Example: compute the bootstrapped median and 1/2/3σ intervals for a sample:

import numpy as np
from bootmedian import bootmedian

data = np.array([1.0, 2.1, 2.3, np.nan, 3.5, 2.0])
result = bootmedian(data, nsimul=2000, errors=1, verbose=True)
print(result)
# -> dict with keys: 'median','s1_up','s1_down',...,'sims'

Using weights:

weights = np.array([1, 1, 2, 1, 1, 1.5])
result_w = bootmedian(data, nsimul=2000, weights=weights)

Change the statistic with mode ("median", "mean", "std", "sum"):

mean_result = bootmedian(data, nsimul=1500, mode="mean")

Bootstrap linear fit

Use bootfit(x, y, nsimul) to obtain bootstrap distributions for slope (m) and intercept (b). The function returns a dictionary with medians and confidence percentiles for m and b.

from bootmedian import bootfit

x = np.linspace(0, 10, 20)
y = 2.3*x + 1.5 + np.random.normal(scale=0.5, size=x.size)
fit = bootfit(x, y, nsimul=1000)
print(fit['m_median'], fit['b_median'])

API reference (short)

• bootstrap_resample(X, weights=False, seed=None) — Resamples an array-like X with optional weights (weighted sampling). Returns a flattened numpy array with one bootstrap resample.
• median_bootstrap(argument) / mean_bootstrap(argument) / sum_bootstrap(argument) / std_bootstrap(argument) — Internal helpers used by bootmedian when running parallel workers. argument is a tuple/list: (sample, weights, std) where std is optional.
• boot_polyfit(x, y, seed) — Performs a single resampled linear fit and returns [slope, intercept].
• bootfit(x, y, nsimul, errors=1) — Runs nsimul bootstrap fits (currently single-threaded loop with progress). Returns a dict with medians and percentile confidence intervals for m and b.
• bootmedian(sample_input, nsimul=1000, weights=False, errors=1, std=False, verbose=False, nthreads=7, mode="median") — Main function; see docstring in code for parameter details.

Notes & recommendations

• The implementation uses bottleneck and pandas.DataFrame.sample for resampling.
• For reproducibility you can set numpy.random.seed(...) before calling routines that internally use randomness. Some helper functions accept a seed.
• nsimul controls accuracy vs runtime: start with a few hundred simulations, then increase to a few thousand if you need tighter percentiles.
• If your input contains many NaNs ensure weights (if provided) align with non-NaN entries.

Development & tests

• See setup.py and pyproject.toml for declared dependencies.
• A small example is available at examples/simple_example.py — run it after installing dependencies with pip install -e ..

License & contact

This project is released under the BSD license (see setup.py for metadata). Author: Alejandro S. Borlaff a.s.borlaff@nasa.gov