Sliced Latin Hypercube Designs for Computer Experiments With Unequal Batch Sizes

Latin hypercube designs are frequently used in estimating the mean output value of computer simulations given random environmental factors. Sliced Latin hypercube designs are designs that can be partitioned into a number of batches so that both the whole design and the batches achieve optimal univariate uniformity. Such designs are useful for computer simulations that are carried out in batches, come from multiple resources, or have categorical variables. All existing sliced Latin hypercube designs have equal batch sizes. In this paper, we propose a new type of sliced Latin hypercube design that has unequal batch sizes and show their advantages theoretically and numerically.