## Sample Generation

The importance of an input to an output is determined from their correlation. The samples used for correlation calculation are generated with the Latin Hypercube Sampling (LHS) method. The Latin Hypercube samples are generated in such a way that the correlations among the input parameters are less than or equal to 5%. Also, the Latin Hypercube samples are generated in such a way that each sample is randomly generated, but no two points share input parameters of the same value.

The Optimal Space-Filling Design (OSF) method of sample generation is an LHS design that is extended with postprocessing to achieve uniform space distribution of points, maximizing the distance between points. The image below illustrates how samples generated via the LHS method vary in placement from those generated by the OSF sampling method.

The image below illustrates the generation of 20 samples via the Monte Carlo, LHS, and OSF methods.

### Pearson’s Linear Correlation

• Uses actual data for correlation evaluation.

• Correlation coefficients are based on the sample values.

• Used to correlate linear relationships.

### Spearman’s Rank Correlation

• Uses ranks of data.

• Correlation coefficients are based on the rank of samples.

• Recognizes non-linear montonic relationships (which are less restrictive than linear ones). In a monotonic relationship, one of the following two things happens:

• As the value of one variable increases, the value of the other variable increases as well.

• As the value of one variable increases, the value of the other variable decreases.

• Deemed the more accurate method.