Exact optimal designs for computer experiments via Kriging metamodelling

Nowadays it is common to reproduce physical systems using mathematical simulation models and, despite the fact that computing resources continue to increase, computer simulations are growing in complexity. This leads to the adoption of surrogate models and one of the most popular methodologies is the well-known Ordinary Kriging, which is a statistical interpolator extensively used to approximate the output of deterministic simulation. This paper deals with the problem of finding suitable experimental plans for the Ordinary Kriging with exponential correlation structure. In particular, we derive exact optimal designs for prediction, estimation and information gain approaches in the one-dimensional case, giving further theoretical justifications for the adoption of the equidistant design. Moreover, we show that in some circumstances several results related to the uncorrelated setup still hold for correlated observations.     

Balance and randomness in sequential clinical trials: the dominant biased coin design

Efron's biased coin design (BCD) is a well‐known randomization technique that helps neutralize selection bias, while keeping the experiment fairly balanced for every sample size. Several extensions of this rule have been proposed, and their properties were analyzed from an asymptotic viewpoint and compared via simulations in a finite setup. The aim of this paper is to push forward these comparisons by taking also into account the adjustable BCD, which is never considered up to now. Firstly, we show that the adjustable BCD performs better than Efron's coin with respect to both loss of precision and randomness. Moreover, the adjustable BCD is always more balanced than the other coins and, only for some sample sizes, slightly more predictable. Therefore, we suggest the dominant BCD, namely a new and flexible class of procedures that can change the allocation rule step by step in order to ensure very good performance in terms of both balance and selection bias for any sample size. Our simulations demonstrate that the dominant BCD is more balanced and, at the same time, less or equally predictable than Atkinson's optimum BCD. Copyright © 2014 John Wiley & Sons, Ltd.