resampling

This is a python module for doing resampling error analysis using the Jackknife, the Bootstrap or the Subsampling method.

Why to use resampling methods?

Suppose you take N samples X_i from a randomly distributed quantity X, e.g. by actual measurements in the laboratory or by Monte Carlo simulations, and store them in a numpy array x_measurements Good estimators for the mean mean_x of the quantity X and its standard error mean_x_error can be calculated using the standard numpy routines by

mean_x = x_measurements.mean()
mean_x_error = x_measurements.std() / math.sqrt(x.size() - 1)

This is totally enough if you want to calculate the mean of X or any linear function of X. But what if you are interested in a non-linear function func of the quantity, e.g. if you are interested in the squared mean <X>**2 and its errors? Then one can show that the following estimates are biased and should not be used:

func_mean_x = func(x_measurements).mean()
func_mean_x_error = func(x_measurements).std() / math.sqrt(x.size() - 1)

Instead you should use resampling methods as the Jackknife, the Bootstrap or the subsampling approach.

Installation

Until now there is no installation routine. Just download (or clone) resampling.py into your source directory or a directory that is visible to your python interpreter.

Usage

The following code snippet shows the usage of the resampling package for estimating the square of the expectation value of a uniform distribution:

import numpy
import resampling

a = numpy.random.random(200)

# Resampling using Jackknife
squared_mean_a, squared_mean_a_error = resampling.jackknife(a, func=lambda x: x**2)

Documentation

The full documentation of all functions can be found here.