Refined Stratified Sampling (RSS) is a sequential sampling procedure that adaptively refines the stratification of the parameter space to add samples. There are four variations of RSS currently available in :pyUQpy. First, the procedure works with either rectangular stratification (i.e. using .Rectangular) or Voronoi stratification (i.e. using .Voronoi). For each of these, two refinement procedures are available. The first is a randomized algorithm where strata are selected at random according to their probability weight. This algorithm is described in Rss1. The second is a gradient-enhanced version (so-called GE-RSS) that draws samples in strata that possess both large probability weight and have high variance. This algorithm is described in Rss2.
All variations of Refined Stratifed Sampling are implemented in the .RefinedStratifiedSampling class. This class provides the framework for refined stratified sampling. with the aid of an underlying stratification generated in a previous sampling of type TrueStratifiedSampling, as well as a .Refinement algorithm an adaptive sampling and refinement of the stratification can be performed.
The .RefinedStratifiedSampling class is imported using the following command:
>>> from UQpy.sampling.stratified_sampling.RefinedStratifiedSampling import RefinedStratifiedSampling
UQpy.sampling.RefinedStratifiedSampling
UQpy.sampling.RefinedStratifiedSampling.samples
UQpy.sampling.RefinedStratifiedSampling.samplesU01
Refined Stratified Sampling Examples <../auto_examples/sampling/refined_stratified_sampling/index>
The .RefinedStratifiedSampling allows for an adaptive refinement of existing strata. This adaptive refinement procedure can be performed based on different algorithms. Each algorithm provides a different approach on selecting and refining the available .Strata, which can be either randomly, or based on advanced selection techniques. In order to accommodate all possible refinement procedures, the .Refinement baseclass is created. The user only needs to implement the :pyupdate_samples method, thus allowing the implementation of different adaptive strata refinement techniques.
UQpy.sampling.stratified_sampling.refinement.baseclass.Refinement
The .RandomRefinement class is imported using the following command:
>>> from UQpy.sampling.stratified_sampling.refinement.RandomRefinement import RandomRefinement
UQpy.sampling.stratified_sampling.refinement.RandomRefinement
The .GradientEnhancedRefinement class is imported using the following command:
>>> from UQpy.sampling.stratified_sampling.refinement.GradientEnhancedRefinement import GradientEnhancedRefinement
UQpy.sampling.stratified_sampling.refinement.GradientEnhancedRefinement