Monte Carlo methods are simulation algorithms to estimate a numerical quantity in a statistical model of a real system. These algorithms are executed by computer programs. Variance reduction techniques (VRT) are needed, even though computer speed has been increasing dramatically, ever since the...

Optimization of simulated systems is the goal of many methods, but most methods assume known environments. We, however, develop a `robust' methodology that accounts for uncertain environments. Our methodology uses Taguchi's view of the uncertain world, but replaces his statistical techniques by...

Design Of Experiments (DOE) is needed for experiments with real-life systems, and with either deterministic or random simulation models. This contribution discusses the different types of DOE for these three domains, but focusses on random simulation. DOE may have two goals: sensitivity analysis...

Optimization of simulated systems is tackled by many methods, but most methods assume known environments. This article, however, develops a 'robust' methodology for uncertain environments. This methodology uses Taguchi's view of the uncertain world, but replaces his statistical techniques by...

This article presents an econometric analysis of the many data on the sealed-bid auction that sells mussels in Yerseke town, the Netherlands. The goals of this analysis are obtaining insight into the important factors that determine the price of these mussels, and quantifying the performance of...

This tutorial explains the basics of linear regression models. especially low-order polynomials. and the corresponding statistical designs. namely, designs of resolution III, IV, V, and Central Composite Designs (CCDs).This tutorial assumes 'white noise', which means that the residuals of the...

This chapter surveys two methods for the optimization of real-world systems that are modelled through simulation. These methods use either linear regression metamodels, or Kriging (Gaussian processes). The metamodel type guides the design of the experiment; this design fixes the input...

This tutorial reviews the design and analysis of simulation experiments. These experiments may have various goals: validation, prediction, sensitivity analysis, optimization (possibly robust), and risk or uncertainty analysis. These goals may be realized through metamodels. Two types of...

In this chapter we present Kriging also known as a Gaussian process (GP) model which is a mathematical interpolation method. To select the input combinations to be simulated, we use Latin hypercube sampling (LHS); we allow uniform and non-uniform distributions of the simulation inputs. Besides...

We derive new statistical tests for leave-one-out cross-validation of Kriging models. Graphically, we present these tests as scatterplots augmented with confidence intervals. We may wish to avoid extrapolation, which we define as prediction of the output for a point that is a vertex of the...