Showing papers by "Pritam Ranjan published in 2012"

Sequential design for computer experiments with a flexible Bayesian additive model

Abstract: In computer experiments, a mathematical model implemented on a computer is used to represent complex physical phenomena. These models, known as computer simulators, enable experimental study of a virtual representation of the complex phenomena. Simulators can be thought of as complex functions that take many inputs and provide an output. Often these simulators are themselves expensive to compute, and may be approximated by "surrogate models" such as statistical regression models. In this paper we consider a new kind of surrogate model, a Bayesian ensemble of trees (Chipman, George, & McCulloch, 2010), with the specific goal of learning enough about the simulator that a particular feature of the simulator can be estimated. We focus on identifying the simulator's global minimum. Utilizing the Bayesian version of the expected improvement criterion (Jones, Schonlau, & Welch, 1998), we show that this ensemble is particularly effective when the simulator is ill-behaved, exhibiting nonstationarity or abrupt changes in the response. A number of illustrations of the approach are given, including a tidal power application. The

Sequential Design for Computer Experiments with a Flexible Bayesian Additive Model

Abstract: In computer experiments, a mathematical model implemented on a computer is used to represent complex physical phenomena. These models, known as computer simulators, enable experimental study of a virtual representation of the complex phenomena. Simulators can be thought of as complex functions that take many inputs and provide an output. Often these simulators are themselves expensive to compute, and may be approximated by "surrogate models" such as statistical regression models. In this paper we consider a new kind of surrogate model, a Bayesian ensemble of trees (Chipman et al. 2010), with the specific goal of learning enough about the simulator that a particular feature of the simulator can be estimated. We focus on identifying the simulator's global minimum. Utilizing the Bayesian version of the Expected Improvement criterion (Jones et al. 1998), we show that this ensemble is particularly effective when the simulator is ill-behaved, exhibiting nonstationarity or abrupt changes in the response. A number of illustrations of the approach are given, including a tidal power application.

Compliance Testing for Random Effects Models With Joint Acceptance Criteria

Abstract: For consumer protection, many governments perform random inspections on goods sold by weight or volume to ensure consistency between actual and labeled net contents. To pass inspection, random samples must jointly comply with restrictions placed on the individual sampled items and on the sample average. In this article, we consider the current United States National Institute of Standards and Technology joint acceptance criteria. Motivated by a problem from a real manufacturing process, we provide an approximation for the probability of sample acceptance that is applicable for processes with one or more known sources of variation via a random effects model. This approach also allows the assessment of the sampling scheme of the items. We use examples and simulations to assess the quality and accuracy of the approximation and illustrate how the methodology can be used to fine-tune process parameters for a prespecified probability of sample acceptance. Simulations are also used for estimating variance compon...