Rosenblatt Transformation

Examples demonstrating the Rosenblatt transformation for mapping between arbitrary distributions and uniform samples, and constructing PC representations from such mappings.

ex_ros.py

Basic Rosenblatt transformation in 2D.

Demonstrates forward and inverse Rosenblatt transformations. Constructs a Rosenblatt map from exponential-uniform samples, verifies that the forward map produces uniform samples, and that the inverse resamples from the original distribution.

ex_iros_1d.py

1D forward and inverse Rosenblatt transformation.

Constructs a Rosenblatt map from samples of an exponential-uniform distribution and plots both the forward and inverse maps against the true transformation.

ex_iros_2d.py

2D forward and inverse Rosenblatt transformation.

Constructs a Rosenblatt map from samples drawn from an exponential-uniform distribution and plots the conditional mapping slices for each dimension.

ex_ros_pc.py

PC from Rosenblatt transformation.

Maps samples to uniform via the Rosenblatt map, then fits PC coefficients to the inverse map using analytical regression.

ex_ros_pcj.py

Joint PC from Rosenblatt transformation.

Constructs a polynomial chaos representation from samples using a joint regression approach in the combined parametric and stochastic space.

ex_ros_pcs.py

Per-sample PC from Rosenblatt transformation.

Builds independent PC fits per parameter sample, contrasting with the joint approach in ex_ros_pcj.py.

ex_rospc_multiple.py

Repeated PC from Rosenblatt tests.

Repeatedly builds PC representations from random samples using the Rosenblatt transformation to assess consistency of the estimated mean and standard deviation across replicas.