### Design and Analysis of Computer Experiments

Organizer and Session Chair: Brian Williams, Los Alamos National Laboratory**Accurate Emulators for Computer Experiments With Large-Volume Data**

Peter Z.G. Qian and Ben Haaland

University of Wisconsin-Madison

Performing physical experiments to explore a system of interest is sometimes not feasible. Experimentation could be unethical, costly, or inconvenient. In many situations, however, the system of interest can be modeled and input/output pairs from this model can be produced with the help of a computer. Since these input/output pairs are often time consuming to obtain, a typical goal is to build an inexpensive emulator which produces input/output pairs similar to the actual model. In this talk, we propose a new approach to building accurate emulators for computer experiments with large-volume data. By using nested space-filling designs and a multi-scale function approximation scheme, this method is numerically stable and can provide accurate emulators for computer experiments with large-volume data. The developed method is illustrated by several examples.

**Posterior Exploration for Computationally Intensive Forward Models**

Shane Reese, David Higdon, David Moulton, Jasper Vrugt, and Colin Fox

Los Alamos National Laboratory and Univ. of Otago

While standard single-site Metropolis updating proves e?ective in a variety of applications, it has the drawback of requiring many calls to the simulation model. Here we compare two MCMC schemes for simulation from the posterior: the multivariate random walk Metropolis algorithm and the distributed evolution MCMC sampler. Such schemes are alluring for computationally demanding inverse problems since they have the potential to update many components at once, while requiring only a single evaluation of the simulator. We consider new formulations based on faster, approximate simulators created by altering the multi-grid solver used in the simulator.

**Gaussian Surrogates for Models with Inputs and Outputs that are Functions of Time**

Max Morris

Iowa State University

Computer models of dynamic systems often produce outputs that are functions of time; models that solve systems of partial differential equations usually have this character. Time series output can often be usefully reduced via principal components to simplify analysis. Time series inputs are also common with such models, e.g. the functions that describe time-varying spatial boundary conditions, or so-called ``forcing functions'' used with p.d.e.'s. Besides being of high dimension, time series inputs may not have one or a few ``characteristic shapes'' that are more common with output functions, and that make p.c.a. an effective output preprocessor for analysis. In this talk, I describe how Gaussian process surrogates can be developed for models with inputs and outputs that are both smooth functions of time. Focus will be on construction of an appropriate covariance structure for such surrogates, some experimental design issues, and application to a model of marrow cell dynamics.