The Morris Screening Method
The Morris method screens many inputs with few runs, flagging which are negligible, which are linear, and which are nonlinear or interacting.
A cheap global screen
When a model has dozens or hundreds of uncertain inputs, a full variance-based analysis is too expensive to start with. The Morris method - also called the elementary effects method - provides a global screening at a fraction of the cost, identifying which inputs are worth deeper study and which can be safely fixed.
Elementary effects
An elementary effect for input i is the change in output when i is perturbed by a fixed step, divided by the step, holding other inputs at a sampled point. The method computes several such effects for each input from different starting points scattered across the input space, so the effects are global rather than tied to one location.
One-at-a-time trajectories
Morris uses efficient trajectories through input space: from a random starting point, each input is stepped once in turn. A trajectory of d+1 runs yields one elementary effect per input. Repeating for r trajectories costs r times (d+1) runs - linear in the number of inputs, far cheaper than variance methods.
Two summary statistics
- mu-star: the mean of the absolute elementary effects, measuring overall influence
- sigma: the standard deviation of the effects, measuring nonlinearity and interaction
Reading the plot
Plotting sigma against mu-star classifies inputs. Low mu-star and low sigma means negligible. High mu-star and low sigma means an important, roughly linear effect. High sigma means the input is nonlinear or interacts with others - its effect depends on where you are in input space. This diagnosis guides the next, more detailed analysis.
In practice
Morris is the standard first pass before Sobol analysis. In Kronos model studies with many uncertain parameters, it inexpensively separates the handful of influential physics inputs from the many that barely move the machines' predicted performance, so that costly variance-based analysis is spent only where it matters.