Some Random Questions Simon Fraser University Department of

Some Random Questions Simon Fraser University Department of Statistics and Actuarial Sciences

Questions I have…many not smart • “Parameterization” – Came up several time – Can be choice for stochastic features in a computer model – Can be parameters in PDE’s…do these have error? How to account for? • Robert and Howard – How did you generate your ensembles – Wanted to understand sensitivity to certain parameters? How measure? Simon Fraser University Department of Statistics and Actuarial Sciences

Questions I have…many not smart • NCAR folks. . What was helpful or what did you learn? • Statisticians… new problems or new methodology? Simon Fraser University Department of Statistics and Actuarial Sciences

Questions I have…many not smart • Regarding PDE’s: • y~N(pde( ), ) • Elaine…interested in maximums (Bo? )…. failure models in Engineering ? Build physics right in? Simon Fraser University Department of Statistics and Actuarial Sciences

Questions I have…many not smart • • Guillaume – Added stochastic forcing…are models still closed Seem to have a lot of parameters…are they identifiable? • I do not think I understand the data assimilation (Josh? Jeff? ) Simon Fraser University Department of Statistics and Actuarial Sciences

GP’s have proven effective for emulating computer model output & data mining • Gaussian Spatial Process (GP) model frequently used in modeling response from complex computer codes • Emulating computer model output – output varies smoothly with input changes – output is essentially noise free – GP’s outperform other modeling approaches in this arena (mars, cart, …) • Data Mining – – compares favorably with other machine learning techniques noise is a more prominent feature Simon Fraser University Department of Statistics and Actuarial Sciences

Gaussian Process Models • Emulators to be used as a surrogate for the computer model 1. How to build likely model complexity into design/analysis – GP models are very complex and hard to interpret – Even more challenging in calibration/assimilation problems 2. Sample Size Issues – Do you have enough data to fit these models well? Simon Fraser University Department of Statistics and Actuarial Sciences

Complexity • Important elicitation problem • How complex is the response surface y(x) ? • How to build likely model complexity into design/analysis – GP models are very complex and hard to interpret – Even more challenging in calibration/assimilation problems Simon Fraser University Department of Statistics and Actuarial Sciences

Complexity Simon Fraser University Department of Statistics and Actuarial Sciences

Sample Size…Emulating a computer model Simon Fraser University Department of Statistics and Actuarial Sciences

Simulation • p= 27, n=50, 100, 200, 300, 500 Random design Symmetric LHS Predictions for 100 holdout x’s Simon Fraser University Department of Statistics and Actuarial Sciences