Sampling plans based on balanced incomplete block designs for evaluating the importance of computer model inputs

The importance of individual inputs of a computer model is sometimes assessed using indices that reflect the amount of output variation that can be attributed to random variation in each input. We review two such indices, and consider input sampling plans that support estimation of one of them, the variance of conditional expectation or VCE (Mckay, 1995. Los Alamos National Laboratory Report NUREG/CR-6311, LA-12915-MS). Sampling plans suggested by Sobol’, Saltelli, and McKay, are examined and compared to a new sampling plan based on balanced incomplete block designs. The new design offers better sampling efficiency for the VCE than those of Sobol’ and Saltelli, and supports unbiased estimation of the index associated with each input.