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October 2014

Bootstrap.jl: Statistical Bootstrapping


Bootstrapping is a widely applicable technique for statistical estimation.



  • Bootstrapping statistics with different resampling methods:

    • Random resampling with replacement (BasicSampling)
    • Antithetic resampling, introducing negative correlation between samples (AntitheticSampling)
    • Balanced random resampling, reducing bias (BalancedSampling)
    • Exact resampling, iterating through all unique resamples (ExactSampling): deterministic bootstrap, suited for small samples sizes
    • Resampling of residuals in generalized linear models (ResidualSampling, WildSampling)
    • Maximum Entropy bootstrapping for dependent and non-stationary datasets (MaximumEntropySampling)
  • Confidence intervals:

    • Basic (BasicConfInt)
    • Percentile (PercentileConfInt)
    • Normal distribution (NormalConfInt)
    • Studendized (StudentConfInt)
    • Bias-corrected and accelerated (BCa) (BCaConfInt)


The Bootstrap package is part of the Julia ecosphere and the latest release version can be installed with

using Pkg

More details on packages and how to manage them can be found in the package section of the Julia documentation.


This example illustrates the basic usage and cornerstone functions of the package. More elaborate cases are covered in the documentation notebooks.

  using Bootstrap

Our observations in some_data are sampled from a standard normal distribution.

  some_data = randn(100);

Let's bootstrap the standard deviation (std) of our data, based on 1000 resamples and with different bootstrapping approaches.

  using Statistics  # the `std` methods live here
  n_boot = 1000

  ## basic bootstrap
  bs1 = bootstrap(std, some_data, BasicSampling(n_boot))

  ## balanced bootstrap
  bs2 = bootstrap(std, some_data, BalancedSampling(n_boot))

We can explore the properties of the bootstrapped samples, for example, the estimated bias and standard error of our statistic.


Furthermore, we can estimate confidence intervals (CIs) for our statistic of interest, based on the bootstrapped samples.

  ## calculate 95% confidence intervals
  cil = 0.95;

  ## basic CI
  bci1 = confint(bs1, BasicConfInt(cil));

  ## percentile CI
  bci2 = confint(bs1, PercentileConfInt(cil));

  ## BCa CI
  bci3 = confint(bs1, BCaConfInt(cil));

  ## Normal CI
  bci4 = confint(bs1, NormalConfInt(cil));


The bootstrapping wikipedia article is a comprehensive introduction into the topic. An extensive description of the bootstrap is the focus of the book Davison and Hinkley (1997): Bootstrap Methods and Their Application. Most of the methodology covered in the book is implemented in the boot package for the R programming language. More references are listed in the documentation for further reading.

Contributions and Feedback

Contributions of any kind are very welcome. Please feel free to open pull requests or issues if you have suggestions for changes, ideas or questions.

Frequently Asked Questions

  • Does it have anything to do with twitter themes, webpage frameworks, compiling, ...?

    No, not really. This package focuses on an interesting area in statistics, but the term bootstrapping is also used in other contexts. You can check wikipedia for a longer list of meanings associated with bootstrapping.

Package Status





The package uses semantic versioning.