Adaptive Stratification (ADSS)

This package provides an implementation of the adaptive stratification sampling method to estimate quantities of interest of the form

where the random vector satisfies

is a given function.

Using the code

To use the Python code provided here, see the INSTALL.md file for further instructions.

Alternatively, if you would like to use the adaptive stratification sampling method without cloning the repository, then you can simply use the adaptive-stratification package as part of the Python Package Index (PyPi), which is available here. The PyPi package contains the implementation of the basic adaptive stratification sampling method, but not the visualisation features (cf., example.ipnyb).

Using the Sampler

The code snippet below indicates the basic usage of the adaptive stratification sampling method provided by the AdaptiveStratification function.

# Import the module containing the sampling routines
from stratification import AdaptiveStratification

# Create a sampler for function func
sampler = AdaptiveStratification(func, d, N_max, N_new_per_stratum, alpha, type='hyperrect')

# Solve
result = sampler.solve()

The input arguments for the constructor AdaptiveStratification are:

• func: implementation of the given function that defines the quantity of interest. It needs to be callable, accepting one m-times-n-dimensional numpy array as input, and returns an m-dimensional numpy array;
• d: dimension of the stochastic domain;
• N_max: number of total samples to be used;
• N_new_per_stratum: targeted average number of samples per stratum, controlling the adaptation;
• alpha: number between zero and one, defining the hybrid allocation rule;
• type: type of tessellation procedure, i.e., hyper-rectangles (type='hyperrect') or simplices (type='simplex')

The solve routine executes the adaptive stratified sampling algorithm. It returns:

• the stratified sampling estimator for the quantity of interest Q;
• a list containing all strata created in the adaptive process;
• the number of strata created;
• an estimate of the variance of the stratified sampling estimator.

Example

A more complete worked out example is available in the Jupyter Notebook example.ipnyb.

Documentation

The package comes with a Sphinx documentation that can be generated as described here. Once created, the documentation will be located in the ./doc folder.

Citing

If you benefit from this package, please cite:

@article{PetterssonKrumscheid22,
author = {P. Pettersson and S. Krumscheid},
title = {Adaptive stratified sampling for non-smooth problems},
journal = {International Journal for Uncertainty Quantification},
year    = {2022},
volume  = {12},
number  = {6},
pages   = {71--99}
}

You can also refer to the code via the persistent identifier: