Sampling and Sensitivity Analysis

In progress…

Sensitivity Analysis Theory

LHS Sampling Theory

Halton Sampling Theory

The Halton sequence is a deterministic method for generating points in space. Because Halton sequences have low-discrepancy, meaning they approximate a uniform distribution well, points from the squence are categorized as quasi-random. The Halton sequence is constructed using a mathematical function called the radical inverse function to produce numbers on the unit hypercube $[0, 1]^{d}$ , where $d$ is the dimensionality of the parameter space. Parameter bounds defined in the ParameterCollection are used to scale the generated Halton sequence from the unit hypercube to the bounding region defining the parameter space.

Sensitivity Analysis Implementation

LHS Sampling Implementation

Halton Sampling Implementation

The SciPy [31] implementation of the Halton sequence (scipy.stats.qmc.Halton) is used in MatCal. Scrambling of the Halton sequence is supported with the “scramble” (bool) keyword (default False) in order to improve the statistical properties of the sequence, introducing a controlled randomness while preserving the low-discrepancy structure. The “rng” (int) keyword (default None) enables reproduciblity by allowing users to pass a random generator.