Second blog post of Google Summer of Code

It is the end of the 4th week of GSoC. Things have been going quite smoothly so far and it’s wonderful to see that I get to learn so many new things everyday as the project moves ahead.

I would like to describe the work I have been involved in for the last couple of weeks. My mentor and I decided to expand the scope my project to include Global Sensitivity Analysis and implementation of some of the most popular methods for it in DiffEqSensitivity.jl.

Sensitivity analysis (SA) allows the model output uncertainty to be ascribed to the source within the model thereby offering a means of evaluating the consistency between internal model structure and the system it tries to emulate (Campolongo and Saltelli, 1997; Campolongo et al., 1999; Saltelli et al., 2004) Global sensitivity analysis (GSA) aims to quantify the relative importance of input variables or factors in determining the value of a function. GSA analysis methods are mainly divided into.

1. Sampling based methods
2. Variance based methods
3. Screening methods

The first method we chose was Morris Method (Morris, 1991; Campolongo et al., 2007) which is a screening method.

The Morris method also known as Morris’s OAT method where OAT stands for One At a Time can be described in the following steps:

1. We calculate local sensitivity measures known as “elementary effects”, which are evaluated at various points in the input chosen such that a wide “spread” of the space is accounted for, to provide an approximate global importance measure.
2. The mean and variance of these elementary effects is computed.
3. A high value of the mean implies that a parameter is important, a high variance implies that its effects are non-linear or the result of interactions with other inputs.

The key to the Morris method is an efficient design for the selection of the input points which optimises coverage of the space and minimises the number of model evaluations required to calculate the elementary effects. The implementation can be found here. Next on the list are variance based methods, Sobol and eFAST which are the most popular in practoce.

Cheers!