This demo shows the basic mechanics of the Multistage Bayesian Surrogate Methodology (MBSM). This methodology supports decision making for product and process design, analysis of computer experiments and other related engineering design applications. MBSM combines statistical modeling and optimal design of experiments, and offers the possibility of integrating information from sources with different levels of accuracy and cost. MBSM uses data collected in stages, using special design of experiment techniques. Information from previous stages is used to collect more data at optimal design sites and update adaptive approximating models, called surrogates.
This demo shows a two-stage surrogate building process, and illustrates the use of the methodology by simulating data collection from an analytical test function of three variables. The accuracy of the surrogate prediction is tested against the true generating analytical function at each stage. Information from the first stage prediction is used to (1) construct a better approximation for the second stage, and (2) collect data where is most needed at the second stage. This sequential and informative updating of information for inference and design is the main strength of this unique methodology.
The demo is divided in two sections. The first section begins with an analysis and geometrical interpretation of the first stage sampling technique, called maximin orthogonal array. Then, we present the analytical test function and the basic structure of the surrogate models. The second section presents the second stage optimal sample and the updated surrogate model. For each section, we test the accuracy of the surrogate prediction against the true analytical function. Details of the calculations can be seen by clicking on the Mathematica input links.
For questions and comments please contact Cristina H. Amon, Jorge E. Pacheco or David A. Romero
The following is a Mathematica file (.nb) that contains 3 examples of constructing surrogate models using MBSM with certain explanations included. For a more detailed explanation of the surrogate models see the first demo. If you do not have Mathematica you can download a reader version from the web page www.wolfram.com. The global optimization software used in these examples is not available to the general public. The objective of this demo is to illustrate the different frameworks and the applicability of each one. We are currently working on a manual version that will contain a more detailed description.
Link to the mathematica file (MBSM.nb)