Screening — Morris One-at-a-Time Method
The Screening, MOAT study uses the Morris one-step-at-a-time (MOAT) method, which means that in each run, only one input parameter is given a new value. This method is purely sample based and does not rely on a surrogate model. The Screening, MOAT study method first samples r trajectories with the Morris sampling method, where r is the repetition number. In the Morris sampling method, the input parameter space is partitioned into n levels for each parameter . Then, it picks r trajectories, where all the points on a trajectory are located from the nm positions, where the sampled data points are , j = 1, …, r, and m is the dimension of input parameters. More details about the Morris sampling method are described in Data Sampling — Morris Sampling. The input parameter values are mapped so as to lie in the range [0, 1]. Each value corresponds to an actual input parameter value . From the evaluated QoI data, the elementary effect for the ith input can be computed as
,
where
.
The sign in the above formula is chosen such that the perturbed point is inside the hypercube. From the elementary effect for all the r replication points, the MOAT mean for the ith input becomes
and the MOAT standard deviation for the ith input
,
where
.
The MOAT mean estimates the overall effect of an input parameter on the QoI, and the MOAT standard deviation measures the nonlinear effects of the input parameter and the interaction effect of this input parameter and others.
Note that the choice of n is strictly linked to the choice of r. If you consider a high value of n, the possible levels to be explored in the input parameter space are increased. If r is not also changed to a higher value, the effort of increasing the resolution in the input parameter space is wasted.
The MOAT method is economic in the sense that it requires a relatively small number of model evaluations. As a drawback, the method relies on the elementary effect, which uses finite differences. However, the final measures are obtained by averaging several elementary effects computed at different points of the input space, which lose the dependence on the specific points at which the elementary effects are computed. Therefore, this method is considered a global screening method. Note that MOAT provides the qualitative measure because the method provides the ranking in the order of importance of input parameters.