Monotone Function Estimation for Computer Experiments

• Activity Number: 533
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Shirin Golchi*+ and Derek Bingham and Hugh A. Chipman and Dave Campbell
• Companies: Simon Fraser University and Simon Fraser University and Acadia University and Simon Fraser University
• Keywords: Computer Experiments ; Derivatives ; Gaussian Process ; MCMC ; Monotone

Abstract

In statistical modelling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all inputs. We develop a Bayesian approach to Gaussian process modelling capable of incorporating monotonicity information for computer model emulation. Markov chain Monte Carlo methods are used to sample from the posterior distribution of the process given the simulator output and monotonicity information. The performance of the proposed approach in terms of predictive accuracy and uncertainty quantification is demonstrated in a number of simulated examples as well as a real application.