Design of computer experiments for optimization, estimation of function contours, and related objectives
A computer code or simulator is a mathematical representation of a physical system, for example a set of differential equations. Such a simulator takes a set of input values or conditions, x, and from them produces an output value, y (x), or several such outputs. For instance, one application we use for illustration simulates the average tidal power, y, generated as a function of a turbine location, x=(x1, x2), in the Bay of Fundy, Nova Scotia (Ranjan et al., 2011). Performing scientific or engineering experiments via such a computer code (ie, a computer experiment) is often more time and cost effective than running a physical experiment or collecting data directly. A computer experiment may have objectives similar to those of a physical experiment. For example, computer experiments are often used in manufacturing or process development. If y is a quality measure for a product or process, an experiment could aim to optimize y with respect to x. Similarly, an experiment might aim to find sets or contours of x values that make y equal a specified target value—a type of inverse problem. Such scientific and engineering objectives are naturally and efficiently achieved via so-called data-adaptive sequential design, which we describe below. Essentially, each new run (ie, new set of input values) is chosen based on the analysis of the data so far, to make the best expected improvement in the objective. In a computer experiment, choosing new experimental runs, restarting the….
|Journal||Statistics in Action: A Canadian Outlook|
|Publisher||Chapman and Hall/CRC|