# Morris Method

struct Morris <: GSAMethod
p_steps::Array{Int,1}
relative_scale::Bool
num_trajectory::Int
total_num_trajectory::Int
len_design_mat::Int
end

Morris has the following keyword arguments:

• p_steps - Vector of $\Delta$ for the step sizes in each direction. Required.
• relative_scale - The elementary effects are calculated with the assumption that the parameters lie in the range [0,1] but as this is not always the case scaling is used to get more informative, scaled effects. Defaults to false.
• total_num_trajectory, num_trajectory - The total number of design matrices that are generated out of which num_trajectory matrices with the highest spread are used in calculation.
• len_design_mat - The size of a design matrix.

## Morris Method Details

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:

We calculate local sensitivity measures known as “elementary effects”, which are calculated by measuring the perturbation in the output of the model on changing one parameter.

$EE_i = \frac{f(x_1,x_2,..x_i+ \Delta,..x_k) - y}{\Delta}$

These are evaluated at various points in the input chosen such that a wide “spread” of the parameter space is explored and considered in the analysis, to provide an approximate global importance measure. The mean and variance of these elementary effects is computed. 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. This method does not evaluate separately the contribution from the interaction and the contribution of the parameters individually and gives the effects for each parameter which takes into consideration all the interactions and its individual contribution.

### API

function gsa(f, method::Morris, p_range::AbstractVector; batch=false, kwargs...)

### Example

Morris method on Ishigami function

using GlobalSensitivity

function ishi(X)
A= 7
B= 0.1
sin(X[1]) + A*sin(X[2])^2+ B*X[3]^4 *sin(X[1])
end

lb = -ones(4)*π
ub = ones(4)*π

m = gsa(ishi, Morris(num_trajectory=500000), [[lb[i],ub[i]] for i in 1:4])