The Theories And Applications For Latin Hypercube Designs With Complex Construction

Latin hypercube designs are widely researched in computer experiments and numerical integration.We propose some Latin hypercube designs with complex constructions for some issues.The main work and innovations are shown as follows:1.We construct general nested Latin hypercube designs for the experiments with multi-accuracy.For the restrictions of ordinary nested Latin hypercube designs,We propose a new construction for nested designs,called general nested Latin hypercube designs.Such designs contain nested Latin hypercube designs as special cases.Apart from achieving optimal uniformity in one dimension,each layer of these designs is flexible in run sizes,and each run obeys uniform distribution which makes the sample mean based on this type of design is the unbiased estimator of the true mean.Moreover,theoretical results and numerical simulations show that GNLHs perform well on the sampling variance.Based on the two-layers general nested Latin hypercube designs,we propose multi-layers nested designs The run sizes of such designs are flexible and the properties of such designs are similar to the two-layers designs.2.We propose a general sliced designs based on randomly Latin hypercube designs.Such designs are useful for computer simulations which are carried out in batches,coming from multiply resources or having categorical variables.Most existing sliced Latin hypercube designs have equal batch sizes.We propose a new type of sliced Latin hypercube design that has unequal batch sizes.Such designs have optimal one-dimensional uniformity,each design point obeys uniform distribution which makes the estimators of the mean output of a given model based on such designs are unbiased.Their advantages are shown theoretically and numerically.3.We provide general sliced designs based on midpoint Latin hypercube designs In this work,we give,to the best of our knowledge,the first construction of sliced Latin hypercube designs that allow arbitrarily chosen run sizes for the slices.The whole designs are midpoint Latin hypercube designs and each slice can achieve optimal one-dimensional uniformity.We also provide an algorithm to reduce correlations of our proposed designs.4.We propose a construction for sequential Latin hypercube designs.Because the special one-dimensional uniformity of Latin hypercube designs,some Latin hypercube designs can be used as the initial design for sequential Latin hypercube designs,We provide an algorithm to construct the initial design of sequential Latin hypercube designs,this methods are easy to accomplish,and the whole designs are always Latin hypercube designs.Based on the initial design,we give algorithms to construct the designs for Stage2 and Stage 3.This construction guarantees that all the designs are Latin hypercube designs after each stage.Furthermore,we give some theoretical results about designs of each stage.