Title: Example Notebook Template

Copyright (C) 2014-2019 The BET Development Team

Description of example goes here. What are your motivations? Outline the process.

Characterize Parameter Space

Define the sampler that will be used to create the discretization object, which is the fundamental object used by BET to compute solutions to the stochastic inverse problem. The sampler and my_model is the interface of BET to the model, and it allows BET to create input/output samples of the model.

Suggested Changes

Try with and without random sampling.

If using random sampling, try num_samples = 1E3 and 1E4. What happens when num_samples = 1E2? Try using 'lhs' instead of 'random' in the random_sample_set.

If using regular sampling, try different numbers of samples per dimension.

Characterize Data Space

Compute the output distribution simple function approximation by propagating a different set of samples to implicitly define a Voronoi discretization of the data space, corresponding to an implicitly defined set of contour events defining a discretization of the input parameter space.

The probabilities of the Voronoi cells in the data space (and thus the probabilities of the corresponding contour events in the input parameter space) are determined by Monte Carlo sampling using a set of i.i.d. uniform samples to bin into these cells.

Suggested Changes

A standard Monte Carlo (MC) assumption is that every Voronoi cell has the same volume. If a regular grid of samples was used, then the standard MC assumption is true.

See what happens if the MC assumption is not assumed to be true, and if different numbers of points are used to estimate the volumes of the Voronoi cells.